text:
Selecting the Correct Number of Factors in Approximate Factor Models: The Large Panel Case with Group Bridge Estimators
- Aubrey Waters
- 2 years ago
- Views:
1 Selecting the Correct umber of Factors in Approximate Factor Models: The Large Panel Case with Group Bridge Estimators Mehmet Caner Xu Han orth Carolina State University City University of Hong Kong ovember 5, 03 Abstract This paper proposes a group bridge estimator to select the correct number of factors in approximate factor models. It contributes to the literature on shrinkage estimation and factor models by extending the conventional bridge estimator from a single equation to a large panel context. The proposed estimator can consistently estimate the factor loadings of relevant factors and shrink the loadings of irrelevant factors to zero with a probability approaching one. Hence, it provides a consistent estimate for the number of factors. We also propose an algorithm for the new estimator; Monte Carlo experiments show that our algorithm converges reasonably fast and that our estimator has very good performance in small samples. An empirical example is also presented based on a commonly used US macroeconomic data set. Key words: bridge estimation, common factors, selection consistency We thank the co-editor Shakeeb Khan, an associate editor and two anonymous referees who made this paper better. We also thank Robin Sickles, James Stock, and the participants at the High Dimension Reduction Conference (December 00) in London, the Panel Data Conference (July 0) in Montreal, the CIREQ Econometrics Conference (May 03), and the orth American Summer Meeting of the Econometric Society (June 03) for their comments. Department of Economics, 468 elson Hall, Raleigh, C Department of Economics and Finance, City University of Hong Kong.
2 Introduction In recent years, factor models have become increasingly important in both finance and macroeconomics. These models use a small number of common factors to explain the co-movements of a large number of time series. In finance, factor models are the foundation for the extension of the arbitrage pricing theory (Chamberlain and Rothschild, 983). In macroeconomics, empirical evidence shows that a few factors can explain a substantial amount of the variation in major macroeconomic variables (Sargent and Sims, 977; Stock and Watson, 989; Giannone, Reichlin, and Sala, 004). Cross country differences have been explained using factor models by Gregory and Head (999) and Forni, Hallin, Lippi, and Reichlin (000). Other applications of factor models include forecasting (Stock and Watson, 00), dynamic stochastic general equilibrium macroeconomic models (Boivin and Giannoni, 006), structural VAR analysis (Bernanke, Boivin, and Eliasz, 005; Stock and Watson, 005; Forni and Gambetti, 00), and consumer demand and micro-behavior (Forni and Lippi, 997; Lewbel, 99). As the common factors are often unobserved, it is natural to ask how many factors should be included in practice. For example, in the factor-augmented VAR models of Bernanke, Boivin, and Eliasz (005), an incorrect number of common factors can lead to an inconsistent estimate of the space spanned by the structural shocks, and impulse responses based on such estimates may be misleading and result in bad policy suggestions. Recent papers by Stock and Watson (009) and Breitung and Eickmeier (0) also find that structural breaks in factor loadings can lead to a change in the number of factors in subsamples. This implies that correctly determining the number of factors in subsamples can help us detect structural changes in factor models. In this paper, we propose a group bridge estimator to determine the number of factors in approximate factor models. Compared to conventional information criteria, the bridge estimator has the advantage that it can conduct both estimation and model selection in one step. It avoids the instability caused by subset selection or stepwise deletion (Breiman, 996). The instability associated with model selection shows up in the following way: when new data is added, the estimated model changes dramatically. Hence, instability in a factor model context means that the estimated number of factors fluctuates widely around the true number as new data are introduced. Also, Horowitz, Huang, and Ma (008, HHM hereafter) show that the bridge estimator possesses the oracle property, i.e., it will provide efficient estimates as if the true model is given in advance. Moreover, as discussed in De Mol et al. (008), shrinkage based estimators such as bridge have certain optimal risk properties as seen in Donoho and Johnstone (994). Thus, we expect that the bridge estimator will preserve these good properties in the high dimensional factor models. This paper builds a connection between shrinkage estimation and factor models. Despite the large literature on both factor models and shrinkage estimation, the interaction between these two fields is rather small. Bai and g (008) apply the shrinkage estimation to select the relevant variables and refine forecasts based on factor models. However, their application of shrinkage estimation is still restricted to a single equation and does not apply to large panels. This paper
3 contributes to these two strands of the literature in the following ways. First, we extend the conventional bridge estimator from a single equation (such as Knight and Fu, 000; Caner and Knight, 03) to a large panel context. This extension is not trivial because shrinkage estimators in the literature (such as HHM) usually assume independent error terms. In contrast, our estimator allows the error terms to have correlations in both cross section and time dimensions. In addition, the regressors are not observed but estimated in factor models, so the estimation errors in factors bring another layer of difficulty to our extension. Moreover, the sparsity condition in factor models is different from the one that is common in the literature. Many papers allow the number of parameters to increase with the sample size (for example, Zou and Zhang, 009; Caner and Zhang, 03), but most of them rely on the sparsity condition that the number of nonzero coefficients has to diverge at a slower rate than the sample size. In factor models, however, the number of nonzero factor loadings is proportional to the cross-sectional dimension. Additionally, our estimator provides a new way to determine the number of factors. We prove that our estimator can consistently estimate the factor loadings (up to a rotation) of relevant factors and shrink the loadings of irrelevant factors to zero with a probability approaching one. Hence, given the estimated factors, this new estimator can select the correct model specification and conduct the estimation of factor loadings in one step. We penalize the Euclidean norm of the factor loading vectors. Specifically, all cells in the zero factor loading vectors are shrunk simultaneously. Thus, our estimation has a group structure. In recent years, much attention has been drawn to the estimation of the number of factors. Bai and g (00) and Onatski (00) propose statistics to determine the number of static factors in approximate factor models. Onatski (009) constructs tests for the number of factors based on the empirical distribution of eigenvalues of the data covariance matrix. Amengual and Watson (007), Bai and g (007), and Hallin and Liska (007) develop estimators for the number of dynamic factors. These methods are roughly equivalent to finding some threshold to distinguish large and small eigenvalues of the data covariance matrix. Some other related methods are developed by Kapetanios (00), Han (0), and Seung and Horenstein (03). We solve the problem from a different but related angle: the group bridge estimator directly focuses on the shrinkage estimation of the factor loading matrix. Simulations show that our estimator is robust to cross-sectional and serial correlations in the error terms and outperforms existing methods in certain cases. Section introduces the model, the assumptions, and presents the theoretical results of our estimator. Section 3 conducts simulations to explore the finite sample performance of our estimator. Section 4 provides an empirical example using a commonly used macroeconomic data set. Section 5 concludes. The appendix contains all proofs. The definitions of static factors, dynamic factors, and approximate factor models are discussed in the second paragraph of Section. 3
4 The Model We use the following representation for the factor model: X it = λ 0 i F 0 t + e it, (.) where X it is the observed data for the i th cross section at time t, for i =,,..., and t =,,..., T, F 0 t is an r vector of common factors, and λ 0 i is an r vector of factor loadings associated with Ft 0. The true number of factors is r. λ 0 i F t 0 is the common component of X it and e it is the idiosyncratic error. Ft 0, λ 0 i, e it and r are unobserved. Here we explain several terms used in our discussion of factor models. We call (.) an approximate factor model because our assumptions (see Section.) allow some cross-sectional correlations in the idiosyncratic errors. It is more general than a strict factor model, which assumes e it to be uncorrelated across i. Also, we refer to (.) as a static factor model because X it has a contemporaneous relationship with the factors. This is different from the dynamic factor model in Forni et al. (000). The dynamic factor model has the representation X it = q j= φ ij(l)f jt + e it, where the q dimensional dynamic factors are orthonormal white noises and the one-sided filters φ ij (L) are dynamic factor loadings. Hence, the factor model X it = a i f t + b i f t + e it has one dynamic factor but two static factors. Our focus is the static factor model with cross-sectionally correlated e it. For conciseness, we use the term factor model to refer to the static factor model and approximate factor model in the rest of the paper, unless otherwise specified. ow, we rewrite model (.) in the vector form: X i = F 0 λ 0 i + e i for i =,,...,, (.) where X i = (X i, X i,..., X it ) is a T -dimensional vector of observations on the i th cross section, F 0 = (F 0, F 0,..., F T 0) is a T r matrix of the unobserved factors, and e i = (e i, e i,..., e it ) is a T -dimensional vector of the idiosyncratic shock of the i th cross section. (.) and (.) can also be represented in the matrix form: X = F 0 Λ 0 + e, (.3) where X = (X, X,..., X ) is a T matrix of observed data, Λ 0 = (λ 0, λ0,..., λ0 ) is the r factor loading matrix, and e = (e, e,..., e ) is a T matrix of idiosyncratic shocks. We use Principal Components Analysis (PCA) to estimate unknown factors, and thereafter we use bridge estimation to get the correct number of factors. The conventional PCA minimizes the following objective function: T V (k) = min ) (X Λ k,f k( it λ k i Ft k ), (.4) t= 4
5 where the superscript k denotes the fact that the number of factors is to be determined, and both λ k i and F k t are k vectors. We consider 0 k p, where p is some predetermined upper bound such that p r. For a given k, the solution to the above objective function (.4) is that ˆF k (T k) is equal to T times the eigenvectors corresponding to the k largest eigenvalues of XX and ˆΛ k OLS = X ˆF k ( ˆF k ˆF k ) = X ˆF k /T (as eigenvectors are orthonormal, ˆF k ˆF k /T = I k ). Let C = min(, T ). We define our group bridge estimator as ˆΛ that minimizes the following objective function: ˆΛ = argmin Λ L(Λ) (.5) L(Λ) = T (X it λ i ˆF p t ) + γ ( ) α p λ ij, (.6) t= where ˆF p is the T p principal component estimate of the factors, ˆFt p is the transpose of the t th row of ˆF p, λ i = (λ i,..., λ ip ) is a p vector in a compact subset of R p, Λ (λ, λ,..., λ ) is C p, α is a constant with 0 < α < /, and γ is a tuning parameter. The penalty term in (.6) is different from that of a conventional bridge estimator such as the one in HHM (008). First, unlike the single equation shrinkage estimation, our penalty term is divided by C, which indicates that the tuning parameter will depend on both and T. Second, we use ( p ) α j= λ ij instead of the HHM (008) type of penalty p j= λ ij δ (0 < δ < ). A necessary condition for p j= λ ij δ to shrink the last p r columns of Λ to zero is that the corresponding non-penalized estimates for these loadings have to converge in probability to zero for all i s and j = r +,..., p. This necessary condition fails because the last p r columns of ˆF p are correlated with some X i s, due to the limited cross-sectional correlation among idiosyncratic errors. Hence, using p j= λ ij δ as the penalty will yield many zero and a few nonzero estimates in the last p r columns of Λ, and will cause overestimation if we use the number of nonzero columns in Λ as an estimator for r. To shrink the entire j th (j > r) column of Λ to zero, we apply the penalty term in (.6) to penalize the norm of the entire vector Λ j (λ j,..., λ j ) rather than each single element λ ij. The idea is related to the group LASSO (Yuan and Lin, 006), which is designed for single equation models. In a factor model setup, the analog of the group LASSO s penalty term will be proportional to p j= λ ij, which provides an intuition to explain why we have 0 < α < /. If =, then the model only involves a single equation, and the group LASSO s penalty reduces to p j= λ j. Accordingly, our penalty becomes p j= λ j α with 0 < α <, which is the familiar penalty term in a single equation bridge estimation. Huang et al. (009) also propose a group bridge estimator for single equation shrinkage estimation. In our large panel setup, the analog of Huang et al. s (009) penalty term will be proportional to p j= ( λ ij ) δ (0 < δ < ). Their penalty is designed to achieve selection consistency both within and among groups. Under this paper s framework, a group of coefficients correspond to a j= 5
6 column in the factor loading matrix. The context of this paper is different from that of Huang et al. (009), and we do not need to consider the within group selection for three reasons. First, within group selection means distinguishing zero from nonzero elements in the first r columns of Λ( p), but this is not necessary because our purpose is to distinguish the first r nonzero columns from the last p r zero columns of Λ, i.e., we only need to select groups in order to determine r. Second, it is well known that both factors and factor loadings estimated by principal components are consistent estimates of their original counterparts up to some rotations. The rotations can be so generic that the economic meanings of the principal component estimators are completely unclear. The within group selection is based on the post-rotation factor loadings. Hence, unless there is a specific reason to detect zero and nonzero elements in the post-rotation factor loading matrix, within group selection is not very meaningful under the current setup. Moreover, as our penalty term uses square rather than absolute values, the computation is much easier than that of the penalty used by Huang et al. (009). Hirose and Konishi (0) apply the group LASSO estimator in the context of strict factor models. However, their estimator is substantially different from (.5), primarily because they focus on selecting variables that are not affected by any of the factors, whereas this paper focuses on selecting factors that do not affect any of the variables. In other words, they are interested in which rows of Λ are zero, whereas we care about which columns of Λ are zero, so Hirose and Konishi s (0) penalty term cannot determine the number of factors by design. One could in principle construct a group LASSO estimator to select the zero columns of Λ. However, such an estimator is different from Hirose and Konishi (0), and its theoretical property is an open question and beyond the scope of this paper.. Assumptions Let A [trace(a A)] / denote the norm of matrix A and p denote convergence in probability. Our theoretical results are derived based on the following assumptions.. E Ft 0 4 <, T T t= Ft 0 Ft 0 p Σ F (r r) as T, and Σ F is finite, and positive definite.. λ 0 i λ <, Λ 0 Λ 0 / Σ Λ 0 as, and Σ Λ is finite, and positive definite. The j th column of Λ, denoted as Λ j, is inside a compact subset of R for all and j =,..., p. 3. There exists a positive and finite constant M that does not depend on or T, such that for all and T, (i). Ee it = 0, E e it 8 < M. (ii). E(e se t /) = E[ e is e it ] = ι (s, t), ι (s, s) M for all s, and T T T ι (s, t) M. s= t= 6
7 (iii). E(e it e jt ) = τ ij,t where τ ij,t τ ij for some τ ij and for all t. In addition τ ij M. j= (iv). E(e it e js ) = τ ij,ts and (v). For every (t, s), ( ) T T τ ij,ts M. j= s= t= E / [e is e it E(e is e it )] 4 M. 4. E[ T T t= F 0 t e it ] M. 5. The eigenvalues of the matrix (Σ Λ Σ F ) are distinct. 6. (i). As and T, γ C 0, where C = min(, T ). (ii). Also, as, where 0 < α < /. γ C α, Assumptions -4 are Assumptions A-D in Bai and g (00). Assumption is standard for factor models. With Assumption, we consider only nonrandom factor loadings. The results hold when the factor loadings are random but independent of factors and errors. The divergence rate of Λ Λ is assumed to be, which is the same as Bai and g (00). It is possible to allow a divergence rate slower than, which indicates a weaker factor structure. A slower divergence rate of Λ Λ will slow down the convergence rate of Ft k and change the divergence rate of γ specified in Assumption 6. We conjecture that our bridge estimator still works when Λ Λ diverges at a slower rate and we leave that as a future research topic. Assumption 3 allows cross-sectional as well as serial dependence in the idiosyncratic errors. Hence, the model follows an approximate factor structure. Assumption 4 allows for some dependency between factors and errors. Assumption 5 is Assumption G in Bai (003). This assumption ensures the existence of the limit of the rotation matrix H, which will be introduced in the next subsection. Assumption 6 is an assumption about the tuning parameter. Compared with the single equation bridge estimation where the tuning parameter only depends on or T, γ s divergence rate depends 7
8 on both and T. Hence, we extend the application of the bridge estimation from single equation models to large panels. Also, note that a conventional bridge penalty will involve the sum of λ ij δ with 0 < δ <. However, as we use λ ij instead of λ ij in the penalty term, the restriction on the power has to be adjusted accordingly, i.e., 0 < α <.. Theoretical Results Before discussing the main theoretical results, it is useful to describe some notations and transformations. We partition ˆF p in the following way: ˆF p = ( ˆF :r. ˆF (r+):p ), (.7) where ˆF :r corresponds to the first r columns of ˆF p, and ˆF (r+):p corresponds to the last p r columns of ˆF p. It is worth noting that there is an important difference between ˆF :r and ˆF (r+):p. It is well known that ˆF :r consistently estimates F 0 (for each t) up to some rotation (Bai, 003), but ˆF (r+):p is just some vectors containing noisy information from the idiosyncratic errors. In fact, the property of ˆF (r+):p is to the best of our knowledge still hardly discussed in either the factor model or random matrix theory literature. We will treat ˆF :r and ˆF (r+):p using different techniques. Let ˆF :r t denote the transpose of the t th row of ˆF :r. Bai (003) shows that ˆF :r t H Ft 0 p 0, where H is some r r matrix 3 converging to some nonsingular limit H 0. Since the factors are estimated up to the nonsingular rotation matrix H, we rewrite (.) as X i = F 0 H H λ 0 i + e i. (.8) Replacing the unobserved F 0 H with the principal component estimates ˆF p, we obtain the following transformation X i = ˆF :r H λ 0 i + e i + (F 0 H ˆF :r )H λ 0 i = ˆF p λ i + u i, (.9) where u i and λ i are defined as [ H λ 0 i ] u i e i ( ˆF :r F 0 H)H λ 0 i, λ i 0 (p r). (.0) We set the last p r entries of λ i equal to zero because the model has r factors. ote that ˆF p is This is why Bai and g (00) define their estimator for factors as ˆF k V k, where V k is a diagonal matrix consisting of the first k largest eigenvalues of XX / in a descending order. Since the k th (k > r) eigenvalue of XX / is O p (C ), the last p r columns of their factor matrix are asymptotically zeros and only the first r columns of the factor matrix matter. As their criteria focus on the sum of squared errors, this asymptotically not-of-full-column-rank design does not affect their result. Since we focus on estimating and penalizing the factor loadings, we use ˆF k to ensure full column rank instead of Bai and g s (00) ˆF k V k as the estimator for F 0. 3 The definition of H is given by Lemma in the Appendix. 8
9 an estimated regressor and the transformed error term u i involves two components: the true error term, which is heteroskedastic and serially correlated, and an additional term depending on ˆF :r, F 0 and λ 0 i. Compared with the i.i.d. errors in HHM (008) or the independent errors in Huang et al (009), our error term e i is much less restricted (see Assumption 3). Also, note that the second term in u i involves estimated factors via principal components and that (.6) uses estimated factors instead of the unobserved F 0. These are new in the shrinkage literature and bring an extra layer of difficulty. Hence, our estimator in large panels is a nontrivial extension of existing methods. Given the λ i defined above, we can obtain the transformed p loading matrix: Λ (λ,..., λ ) [Λ 0 H.0 (p r) ]. Thus, the goal is to prove that ˆΛ Λ converges to zero. The last p r columns ˆΛ should be zero and its first r columns should be nonzero, so that we can consistently determine the number of factors using the number of nonzero columns in ˆΛ. Let ˆλ i denote the transpose of the i th row of ˆΛ, the solution to (.6). The following theorem establishes the convergence rate of ˆλ i. Theorem : Under Assumptions - 6, ˆλ i λ i = O p (C ). It is noteworthy that this rate is not affected by γ, as long as the divergence rate of γ satisfies Assumption 6. This is an extension of Horowitz, Huang, and Ma s (008) result to a high dimensional factor model context. Under some appropriate assumptions, HHM (008) show that the bridge estimator (denoted by ˆβ) has the familiar OLS convergence rate, i.e., ˆβ β 0 = O p ( ), in a single equation model. In this paper, the rate depends on both and T and is similar to Bai s (003) result for the OLS estimator of factor loadings (given the principal components estimates of factors). Hence, Theorem shows that the group bridge estimator defined in (.5) is as good as conventional estimators in terms of convergence rate. The next theorem shows that our estimator can estimate the last p r columns of ˆΛ exactly as zeros with a probability converging to one. Theorem : Under Assumptions - 6, (i)ˆλ (r+):p = 0 (p r) with probability converging to one as, T, where ˆΛ (r+):p denotes the last p r columns of ˆΛ. (ii) P (ˆΛ j = 0) 0 as, T for any j =,, r, where ˆΛ j represents the j th column of the ˆΛ. This theorem shows that our estimator achieves the selection consistency for the zero elements in Λ : the first r columns in ˆΛ will be nonzero and last p r columns of ˆΛ will be zero as and T 9
10 diverge. Hence, it is natural to define the estimator for the number of factors as ˆr the number of nonzero columns of ˆΛ. (.) The following corollary establishes the consistency of ˆr, and the proof is straightforward given Theorem. Corollary : Under Assumptions - 6, the number of factors in (.3) can be consistently determined by ˆr..3 Computation In this subsection we show how to implement our method. The initial step is estimating the p factors via PCA in (.4). ext, we show how to solve the optimization in (.5) and (.6). As the bridge penalty is not differentiable at zero for 0 < α < /, standard gradient based methods are not applicable to our estimator. We develop an algorithm to compute the solution for (.6). Let ˆΛ (m) be the value of the m th iteration from the optimization algorithm, m = 0,,... Let T denote the convergence tolerance and ν denote some small positive number. In this paper, we set T = and ν = 0 4. Set the initial value equal to the OLS solution, ˆΛ (0) = X ˆF p /T. For m =,,..., () Let ˆΛ (m),j denote the j th column of ˆΛ (m). Compute g = (X ˆF p ˆΛ (m) ) ˆF p / and ˆΛ (m),j αγ g (j, ν) = [ ] (ˆΛ(m),j α /) ˆΛ(m),j + ν T C, where ν avoids the zero denominator when ˆΛ (m),j = 0. Since the value of the tuning parameter will be selected as well, the constant term T/C algorithm. Set g (ν) = [g (, ν), g (, ν),..., g (p, ν)]. (for a given sample) can be dropped in the () Define the p gradient matrix g = [g, g,..., g p ] ( p), and the i th element of the j th column g j (j =,..., p) is defined as g j i = g,ij + g (j, ν) i if λ (m),j i > T g j i = 0 if λ (m),j i T, where g,ij is the (i, j) th element of g, g (j, ν) i is the i th element of g (j, ν), and λ (m),j i element of ˆΛ (m),j. is the i th (3) Let max g denote the largest element in g in terms of absolute value. Re-scale g = g/ max g if max g > 0, otherwise set g = 0. (4) ˆΛ (m+) = ˆΛ (m) + g/( + m/750), where is the increment for this iteration algorithm. We set = 0 3, which follows the value used by HHM (008). 0
11 (5) Replace m by m + and repeat steps () - (5) until max,...,; j=,...,p λ(m),j i λ (m+),j i T. After convergence, we truncate λ (m),j i to zero if λ (m),j i T. (6) Set ˆr = the number of nonzero columns in ˆΛ (m). This algorithm is a modified version of the one proposed by HHM (008). We use the OLS estimate instead of zero as the initial value to accelerate the algorithm. Also, we modify HHM s computation of the gradient in step () so that the estimated loading will remain unchanged after being shrunk to zero. This is suggested by Fan and Li (00) and can substantially accelerate the convergence in our high dimensional setup. Additionally, note that in step (4) we gradually decrease the increment, as m increases by dividing + m/ This ensures the convergence of the algorithm. To see that the algorithm yields an estimator converging to the true value, first note that the algorithm approximates the bridge penalty function by αγ C p j= ˆ Λj (u u/) α + ν u du, (.) where the variable of integration u is an vector and Λ j is a line integral through the gradient of the approximated penalty term with the endpoint Λ j. (.) is continuously differentiable with respect to the vector Λ j, so the computed estimator will converge to the minimum of the approximated objective function. Also, the approximated penalty function and its gradient converge to the bridge penalty and its gradient as ν 0, respectively. Since all factor loadings are defined in a compact set by Assumption and the bridge estimator is a global minimizer by HHM (008), the minimum of the approximated objective function will converge to the minimum of (.6) as ν 0. Hence, our algorithm can generate a consistent estimator. To ensure that the algorithm is not trapped in a local minimum, we use the OLS estimate as the initial value, which is close to the global minimum of (.6) and reduces the computation load. One could also use multiple starting values to avoid obtaining a local minimum. To implement our estimator, we need to determine the values of α and γ. We set α = 0.5 as our benchmark value. We also vary α between 0. and 0.4; simulations (see Table 7) show that our estimator is very robust to the choice of α. The tuning parameter γ is set equal to ϕ [min(, T )] 0.45 because Assumption 6 requires that γ/c 0. The constant ϕ varies on the grid [.5:0.5:8]. Instead of searching on a grid such as γ =, 5, 0,..., 000 for all sample sizes, this setup allows the grid to change as the sample size changes, so that it avoids unnecessary computation and thus 4 Our Monte Carlo experiments show that the algorithm is reasonably fast and performs very well in terms of selecting the true value of r. We also tried 500 and 000 instead of 750 to adjust the increment, and the results are very similar and hence not reported.
12 accelerates our algorithm. We follow the method developed by Wang et al. (009) to determine the optimal choice of γ. The optimal γ is the one that minimizes the following criterion: log[( ) T ( (X it ˆλ ˆF p + T i t ) ] + ˆr(γ) t= ) ( ) ln ln[ln()], + T where ˆr(γ) denotes the fact that the estimated number of factors is affected by the choice of γ. ote that the number of parameters in our model is proportional to, so we use ln[ln()] in the penalty, which has the same rate as suggested by Wang et al. (009). 3 Simulations In this section, we explore the finite sample properties of our estimator. We also compare our estimator with some of the estimators in the literature: IC p proposed by Bai and g (00), IC T ;n proposed by Hallin and Liska (007), ED proposed by Onatski (00), and ER and GR proposed by Seung and Horenstein (03). Given the principal component estimator ˆF k, Bai and g (00) use OLS to estimate the factor loadings by minimizing the sum of squared residuals: V (k, ˆF k ) = min Λ T (X it λ k i ˆF t k ). t= Then the IC p estimator is defined as the k that minimizes the following criterion: ( ) ( ) IC p (k) = log[v (k, ˆF + T k )] + k ln. + T The criterion can be considered the analog of the conventional BIC in the factor model context. It penalizes the integer k to prevent the model from overfitting. Hallin and Liska s (007) estimator is designed to determine the number of dynamic factors (usually denoted by q in the literature), but it is applicable in our Monte Carlo experiments where static and dynamic factors coincide by design, i.e. r = q. Hallin and Liska s (007) estimator follows the idea of Bai and g (00), but their penalty term involves an additional scale parameter c. In theory, the choice of c > 0 does not matter as and T. For a given and T, they propose an algorithm to select the scale parameter: c is varied on a predetermined grid ranging from zero to some positive number c, and their statistic is computed for each value of c using J nested subsamples (i =,..., j ; t =,..., T j ) for j =,..., J, where J is a fixed positive integer, 0 < <... < j <... < J = and 0 < T <... < T j <... < T J = T. Hallin and Liska (007) show that [0, c] will contain several intervals that generate estimates not varying across subsamples. They call these stability intervals and suggest that the c belonging to the second stability interval is the optimal one (the first stability intervals contains zero). Since the scale parameter in IC T ;n
Standardization and Estimation of the Number of Factors for Panel Data
Journal of Economic Theory and Econometrics, Vol. 23, No. 2, Jun. 2012, 79 88 Standardization and Estimation of the Number of Factors for Panel Data Ryan Greenaway-McGrevy Chirok Han Donggyu Sul AbstractMore information
SYSTEMS OF REGRESSION EQUATIONS 1. MULTIPLE EQUATIONS y nt = x nt n + u nt, n = 1,...,N, t = 1,...,T, x nt is 1 k, and n is k 1. This is a version of the standard regression model where the observationsMore information
Topics in Time Series Analysis
Topics in Time Series Analysis Massimiliano Marcellino EUI and Bocconi University This course reviews some recent developments in the analysis of time series data in economics, with a special emphasisMore information
Data analysis in supersaturated designs
Statistics & Probability Letters 59 (2002) 35 44 Data analysis in supersaturated designs Runze Li a;b;, Dennis K.J. Lin a;b a Department of Statistics, The Pennsylvania State University, University Park,More information
Factor analysis. Angela Montanari
Factor analysis Angela Montanari 1 Introduction Factor analysis is a statistical model that allows to explain the correlations between a large number of observed correlated variables through a small numberMore information
Detecting Big Structural Breaks in Large Factor Models
Detecting Big Structural Breaks in Large Factor Models Liang Chen Juan J. Dolado Jesús Gonzalo First Draft: May 2010 his draft: September 2013 Abstract ime invariance of factor loadings is a standard assumptionMore information
Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model
Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model 1 September 004 A. Introduction and assumptions The classical normal linear regression model can be writtenMore information
1 Short Introduction to Time Series
ECONOMICS 7344, Spring 202 Bent E. Sørensen January 24, 202 Short Introduction to Time Series A time series is a collection of stochastic variables x,.., x t,.., x T indexed by an integer value t. TheMore information
Big data in macroeconomics Lucrezia Reichlin London Business School and now-casting economics ltd. COEURE workshop Brussels 3-4 July 2015
Big data in macroeconomics Lucrezia Reichlin London Business School and now-casting economics ltd COEURE workshop Brussels 3-4 July 2015 WHAT IS BIG DATA IN ECONOMICS? Frank Diebold claimed to have introducedMore information
Least Squares Estimation
Least Squares Estimation SARA A VAN DE GEER Volume 2, pp 1041 1045 in Encyclopedia of Statistics in Behavioral Science ISBN-13: 978-0-470-86080-9 ISBN-10: 0-470-86080-4 Editors Brian S Everitt & DavidMore information
Mathematics Course 111: Algebra I Part IV: Vector Spaces
Mathematics Course 111: Algebra I Part IV: Vector Spaces D. R. Wilkins Academic Year 1996-7 9 Vector Spaces A vector space over some field K is an algebraic structure consisting of a set V on which areMore information
CHAPTER 8 FACTOR EXTRACTION BY MATRIX FACTORING TECHNIQUES. From Exploratory Factor Analysis Ledyard R Tucker and Robert C.
CHAPTER 8 FACTOR EXTRACTION BY MATRIX FACTORING TECHNIQUES From Exploratory Factor Analysis Ledyard R Tucker and Robert C MacCallum 1997 180 CHAPTER 8 FACTOR EXTRACTION BY MATRIX FACTORING TECHNIQUES InMore information
WORKING PAPER SERIES NO 700 / DECEMBER 2006 FORECASTING USING A LARGE NUMBER OF PREDICTORS IS BAYESIAN REGRESSION A VALID ALTERNATIVE TO PRINCIPAL COMPONENTS? by Christine De Mol, Domenico Giannone andMore information
Estimation and Inference in Cointegration Models Economics 582
Estimation and Inference in Cointegration Models Economics 582 Eric Zivot May 17, 2012 Tests for Cointegration Let the ( 1) vector Y be (1). Recall, Y is cointegrated with 0 cointegrating vectors if thereMore information
Department of Economics
Department of Economics On Testing for Diagonality of Large Dimensional Covariance Matrices George Kapetanios Working Paper No. 526 October 2004 ISSN 1473-0278 On Testing for Diagonality of Large DimensionalMore information
The VAR models discussed so fare are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series.
Cointegration The VAR models discussed so fare are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series. Economic theory, however, often implies equilibriumMore information
Factor Models and Dynamic Stochastic General Equilibrium models: a forecasting evaluation
Factor Models and Dynamic Stochastic General Equilibrium models: a forecasting evaluation Gabriele Palmegiani LUISS University of Rome Abstract This paper aims to put dynamic stochastic general equilibriumMore information
INDIRECT INFERENCE (prepared for: The New Palgrave Dictionary of Economics, Second Edition)
INDIRECT INFERENCE (prepared for: The New Palgrave Dictionary of Economics, Second Edition) Abstract Indirect inference is a simulation-based method for estimating the parameters of economic models. ItsMore information
Chapter 1. Vector autoregressions. 1.1 VARs and the identi cation problem
Chapter Vector autoregressions We begin by taking a look at the data of macroeconomics. A way to summarize the dynamics of macroeconomic data is to make use of vector autoregressions. VAR models have becomeMore information
Adaptive Online Gradient Descent
Adaptive Online Gradient Descent Peter L Bartlett Division of Computer Science Department of Statistics UC Berkeley Berkeley, CA 94709 bartlett@csberkeleyedu Elad Hazan IBM Almaden Research Center 650More information
Large Time-Varying Parameter VARs
Large Time-Varying Parameter VARs Gary Koop University of Strathclyde Dimitris Korobilis University of Glasgow Abstract In this paper we develop methods for estimation and forecasting in large timevaryingMore information
Chapter 4: Vector Autoregressive Models
Chapter 4: Vector Autoregressive Models 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie IV.1 Vector Autoregressive Models (VAR)...More information
Notes on Factoring. MA 206 Kurt Bryan
The General Approach Notes on Factoring MA 26 Kurt Bryan Suppose I hand you n, a 2 digit integer and tell you that n is composite, with smallest prime factor around 5 digits. Finding a nontrivial factorMore information
Centre for Central Banking Studies
Centre for Central Banking Studies Technical Handbook No. 4 Applied Bayesian econometrics for central bankers Andrew Blake and Haroon Mumtaz CCBS Technical Handbook No. 4 Applied Bayesian econometricsMore information
Multiple Linear Regression in Data Mining
Multiple Linear Regression in Data Mining Contents 2.1. A Review of Multiple Linear Regression 2.2. Illustration of the Regression Process 2.3. Subset Selection in Linear Regression 1 2 Chap. 2 MultipleMore information
MATH10212 Linear Algebra. Systems of Linear Equations. Definition. An n-dimensional vector is a row or a column of n numbers (or letters): a 1.
MATH10212 Linear Algebra Textbook: D. Poole, Linear Algebra: A Modern Introduction. Thompson, 2006. ISBN 0-534-40596-7. Systems of Linear Equations Definition. An n-dimensional vector is a row or a columnMore information
Marketing Mix Modelling and Big Data P. M Cain
1) Introduction Marketing Mix Modelling and Big Data P. M Cain Big data is generally defined in terms of the volume and variety of structured and unstructured information. Whereas structured data is storedMore information
Adaptive Search with Stochastic Acceptance Probabilities for Global Optimization
Adaptive Search with Stochastic Acceptance Probabilities for Global Optimization Archis Ghate a and Robert L. Smith b a Industrial Engineering, University of Washington, Box 352650, Seattle, Washington,More information
Forecasting Financial Time Series
Canberra, February, 2007 Contents Introduction 1 Introduction : Problems and Approaches 2 3 : Problems and Approaches : Problems and Approaches Time series: (Relative) returns r t = p t p t 1 p t 1, tMore information
The Characteristic Polynomial
Physics 116A Winter 2011 The Characteristic Polynomial 1 Coefficients of the characteristic polynomial Consider the eigenvalue problem for an n n matrix A, A v = λ v, v 0 (1) The solution to this problemMore information
1 Teaching notes on GMM 1.
Bent E. Sørensen January 23, 2007 1 Teaching notes on GMM 1. Generalized Method of Moment (GMM) estimation is one of two developments in econometrics in the 80ies that revolutionized empirical work inMore information
Degrees of Freedom and Model Search
Degrees of Freedom and Model Search Ryan J. Tibshirani Abstract Degrees of freedom is a fundamental concept in statistical modeling, as it provides a quantitative description of the amount of fitting performedMore information
How to assess the risk of a large portfolio? How to estimate a large covariance matrix?
Chapter 3 Sparse Portfolio Allocation This chapter touches some practical aspects of portfolio allocation and risk assessment from a large pool of financial assets (e.g. stocks) How to assess the riskMore information
Statistical Machine Learning
Statistical Machine Learning UoC Stats 37700, Winter quarter Lecture 4: classical linear and quadratic discriminants. 1 / 25 Linear separation For two classes in R d : simple idea: separate the classesMore information
One-shot learning and big data with n = 2
One-shot learning and big data with n = Lee H. Dicker Rutgers University Piscataway, NJ firstname.lastname@example.com Dean P. Foster University of Pennsylvania Philadelphia, PA email@example.com Abstract We modelMore information
By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
This material is posted here with permission of the IEEE Such permission of the IEEE does not in any way imply IEEE endorsement of any of Helsinki University of Technology's products or services InternalMore information
The primary goal of this thesis was to understand how the spatial dependence of
5 General discussion 5.1 Introduction The primary goal of this thesis was to understand how the spatial dependence of consumer attitudes can be modeled, what additional benefits the recovering of spatialMore information
Chapter 6: Multivariate Cointegration Analysis
Chapter 6: Multivariate Cointegration Analysis 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie VI. Multivariate CointegrationMore information
Machine Learning and Pattern Recognition Logistic Regression
Machine Learning and Pattern Recognition Logistic Regression Course Lecturer:Amos J Storkey Institute for Adaptive and Neural Computation School of Informatics University of Edinburgh Crichton Street,More information
BANACH AND HILBET SPACE EVIEW CHISTOPHE HEIL These notes will briefly review some basic concepts related to the theory of Banach and Hilbert spaces. We are not trying to give a complete development, butMore information
Predictability of Non-Linear Trading Rules in the US Stock Market Chong & Lam 2010
Department of Mathematics QF505 Topics in quantitative finance Group Project Report Predictability of on-linear Trading Rules in the US Stock Market Chong & Lam 010 ame: Liu Min Qi Yichen Zhang FengtianMore information
2. Linear regression with multiple regressors
2. Linear regression with multiple regressors Aim of this section: Introduction of the multiple regression model OLS estimation in multiple regression Measures-of-fit in multiple regression AssumptionsMore information
The Dirichlet Unit Theorem
Chapter 6 The Dirichlet Unit Theorem As usual, we will be working in the ring B of algebraic integers of a number field L. Two factorizations of an element of B are regarded as essentially the same ifMore information
Chapter 2. Dynamic panel data models
Chapter 2. Dynamic panel data models Master of Science in Economics - University of Geneva Christophe Hurlin, Université d Orléans Université d Orléans April 2010 Introduction De nition We now considerMore information
Econometric Analysis of Cross Section and Panel Data Second Edition. Jeffrey M. Wooldridge. The MIT Press Cambridge, Massachusetts London, England
Econometric Analysis of Cross Section and Panel Data Second Edition Jeffrey M. Wooldridge The MIT Press Cambridge, Massachusetts London, England Preface Acknowledgments xxi xxix I INTRODUCTION AND BACKGROUNDMore information
NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )
Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimatesMore information
D-optimal plans in observational studies
D-optimal plans in observational studies Constanze Pumplün Stefan Rüping Katharina Morik Claus Weihs October 11, 2005 Abstract This paper investigates the use of Design of Experiments in observationalMore information
ECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE YUAN TIAN This synopsis is designed merely for keep a record of the materials covered in lectures. Please refer to your own lecture notes for all proofs.More information
Two Topics in Parametric Integration Applied to Stochastic Simulation in Industrial Engineering
Two Topics in Parametric Integration Applied to Stochastic Simulation in Industrial Engineering Department of Industrial Engineering and Management Sciences Northwestern University September 15th, 2014More information
Penalized regression: Introduction
Penalized regression: Introduction Patrick Breheny August 30 Patrick Breheny BST 764: Applied Statistical Modeling 1/19 Maximum likelihood Much of 20th-century statistics dealt with maximum likelihoodMore information
Financial TIme Series Analysis: Part II
Department of Mathematics and Statistics, University of Vaasa, Finland January 29 February 13, 2015 Feb 14, 2015 1 Univariate linear stochastic models: further topics Unobserved component model SignalMore information
THE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING 1. Introduction The Black-Scholes theory, which is the main subject of this course and its sequel, is based on the Efficient Market Hypothesis, that arbitragesMore information
4.5 Linear Dependence and Linear Independence
4.5 Linear Dependence and Linear Independence 267 32. {v 1, v 2 }, where v 1, v 2 are collinear vectors in R 3. 33. Prove that if S and S are subsets of a vector space V such that S is a subset of S, thenMore information
STATISTICA Formula Guide: Logistic Regression. Table of Contents
: Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 Sigma-Restricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 SummaryMore information
Factorization Theorems
Chapter 7 Factorization Theorems This chapter highlights a few of the many factorization theorems for matrices While some factorization results are relatively direct, others are iterative While some factorizationMore information
Clustering in the Linear Model
Short Guides to Microeconometrics Fall 2014 Kurt Schmidheiny Universität Basel Clustering in the Linear Model 2 1 Introduction Clustering in the Linear Model This handout extends the handout on The MultipleMore information
Subsets of Euclidean domains possessing a unique division algorithm
Subsets of Euclidean domains possessing a unique division algorithm Andrew D. Lewis 2009/03/16 Abstract Subsets of a Euclidean domain are characterised with the following objectives: (1) ensuring uniquenessMore information
Example 4.1 (nonlinear pendulum dynamics with friction) Figure 4.1: Pendulum. asin. k, a, and b. We study stability of the origin x
Lecture 4. LaSalle s Invariance Principle We begin with a motivating eample. Eample 4.1 (nonlinear pendulum dynamics with friction) Figure 4.1: Pendulum Dynamics of a pendulum with friction can be writtenMore information
MATLAB and Big Data: Illustrative Example
MATLAB and Big Data: Illustrative Example Rick Mansfield Cornell University August 19, 2014 Goals Use a concrete example from my research to: Demonstrate the value of vectorization Introduce key commands/functionsMore information
Powerful new tools for time series analysis
Christopher F Baum Boston College & DIW August 2007 hristopher F Baum ( Boston College & DIW) NASUG2007 1 / 26 Introduction This presentation discusses two recent developments in time series analysis byMore information
Notes V General Equilibrium: Positive Theory. 1 Walrasian Equilibrium and Excess Demand
Notes V General Equilibrium: Positive Theory In this lecture we go on considering a general equilibrium model of a private ownership economy. In contrast to the Notes IV, we focus on positive issues suchMore information
MATH 240 Fall, Chapter 1: Linear Equations and Matrices
MATH 240 Fall, 2007 Chapter Summaries for Kolman / Hill, Elementary Linear Algebra, 9th Ed. written by Prof. J. Beachy Sections 1.1 1.5, 2.1 2.3, 4.2 4.9, 3.1 3.5, 5.3 5.5, 6.1 6.3, 6.5, 7.1 7.3 DEFINITIONSMore information
OPTIMAl PREMIUM CONTROl IN A NON-liFE INSURANCE BUSINESS
ONDERZOEKSRAPPORT NR 8904 OPTIMAl PREMIUM CONTROl IN A NON-liFE INSURANCE BUSINESS BY M. VANDEBROEK & J. DHAENE D/1989/2376/5 1 IN A OPTIMAl PREMIUM CONTROl NON-liFE INSURANCE BUSINESS By Martina VandebroekMore information
Maximum Likelihood Estimation of an ARMA(p,q) Model
Maximum Likelihood Estimation of an ARMA(p,q) Model Constantino Hevia The World Bank. DECRG. October 8 This note describes the Matlab function arma_mle.m that computes the maximum likelihood estimatesMore information
Linear Threshold Units
Linear Threshold Units w x hx (... w n x n w We assume that each feature x j and each weight w j is a real number (we will relax this later) We will study three different algorithms for learning linearMore information
Chapter 5. Analysis of Multiple Time Series. 5.1 Vector Autoregressions
Chapter 5 Analysis of Multiple Time Series Note: The primary references for these notes are chapters 5 and 6 in Enders (2004). An alternative, but more technical treatment can be found in chapters 10-11More information
INDISTINGUISHABILITY OF ABSOLUTELY CONTINUOUS AND SINGULAR DISTRIBUTIONS STEVEN P. LALLEY AND ANDREW NOBEL Abstract. It is shown that there are no consistent decision rules for the hypothesis testing problemMore information
From the help desk: Bootstrapped standard errors
The Stata Journal (2003) 3, Number 1, pp. 71 80 From the help desk: Bootstrapped standard errors Weihua Guan Stata Corporation Abstract. Bootstrapping is a nonparametric approach for evaluating the distributionMore information
Inequality, Mobility and Income Distribution Comparisons
Fiscal Studies (1997) vol. 18, no. 3, pp. 93 30 Inequality, Mobility and Income Distribution Comparisons JOHN CREEDY * Abstract his paper examines the relationship between the cross-sectional and lifetimeMore information
Communication on the Grassmann Manifold: A Geometric Approach to the Noncoherent Multiple-Antenna Channel
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 48, NO. 2, FEBRUARY 2002 359 Communication on the Grassmann Manifold: A Geometric Approach to the Noncoherent Multiple-Antenna Channel Lizhong Zheng, StudentMore information
Statistical machine learning, high dimension and big data
Statistical machine learning, high dimension and big data S. Gaïffas 1 14 mars 2014 1 CMAP - Ecole Polytechnique Agenda for today Divide and Conquer principle for collaborative filtering Graphical modelling,More information
Lasso on Categorical Data
Lasso on Categorical Data Yunjin Choi, Rina Park, Michael Seo December 14, 2012 1 Introduction In social science studies, the variables of interest are often categorical, such as race, gender, and nationality.More information
FIXED EFFECTS AND RELATED ESTIMATORS FOR CORRELATED RANDOM COEFFICIENT AND TREATMENT EFFECT PANEL DATA MODELS Jeffrey M. Wooldridge Department of Economics Michigan State University East Lansing, MI 48824-1038More information
THE AUSTRALIAN BUSINESS CYCLE: A COINCIDENT INDICATOR APPROACH Christian Gillitzer, Jonathan Kearns and Anthony Richards Research Discussion Paper 2005-07 October 2005 Economic Group Reserve Bank of AustraliaMore information
Forecasting Retail Credit Market Conditions
Forecasting Retail Credit Market Conditions Eric McVittie Experian Experian and the marks used herein are service marks or registered trademarks of Experian Limited. Other products and company names mentionedMore information
MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS Systems of Equations and Matrices Representation of a linear system The general system of m equations in n unknowns can be written a x + a 2 x 2 + + a n x n b aMore information
Testing The Quantity Theory of Money in Greece: A Note
ERC Working Paper in Economic 03/10 November 2003 Testing The Quantity Theory of Money in Greece: A Note Erdal Özmen Department of Economics Middle East Technical University Ankara 06531, Turkey email@example.com information
On the Efficiency of Competitive Stock Markets Where Traders Have Diverse Information
Finance 400 A. Penati - G. Pennacchi Notes on On the Efficiency of Competitive Stock Markets Where Traders Have Diverse Information by Sanford Grossman This model shows how the heterogeneous informationMore information
Time Series Analysis
Time Series Analysis Forecasting with ARIMA models Andrés M. Alonso Carolina García-Martos Universidad Carlos III de Madrid Universidad Politécnica de Madrid June July, 2012 Alonso and García-Martos (UC3M-UPM)More information
NOTES ON LINEAR TRANSFORMATIONS Definition 1. Let V and W be vector spaces. A function T : V W is a linear transformation from V to W if the following two properties hold. i T v + v = T v + T v for allMore information
Random graphs with a given degree sequence
Sourav Chatterjee (NYU) Persi Diaconis (Stanford) Allan Sly (Microsoft) Let G be an undirected simple graph on n vertices. Let d 1,..., d n be the degrees of the vertices of G arranged in descending order.More information
Testing for serial correlation in linear panel-data models
The Stata Journal (2003) 3, Number 2, pp. 168 177 Testing for serial correlation in linear panel-data models David M. Drukker Stata Corporation Abstract. Because serial correlation in linear panel-dataMore information
Joint models for classification and comparison of mortality in different countries.
Joint models for classification and comparison of mortality in different countries. Viani D. Biatat 1 and Iain D. Currie 1 1 Department of Actuarial Mathematics and Statistics, and the Maxwell InstituteMore information
Online Appendices to the Corporate Propensity to Save
Online Appendices to the Corporate Propensity to Save Appendix A: Monte Carlo Experiments In order to allay skepticism of empirical results that have been produced by unusual estimators on fairly smallMore information
Macroeconomic Shocks and the Business Cycle: Evidence from a Structural Factor Model
Macroeconomic Shocks and the Business Cycle: Evidence from a Structural Factor Model Mario Forni Università di Modena e Reggio Emilia CEPR and RECent Luca Gambetti Universitat Autonoma de Barcelona andMore information
FORECASTING DEPOSIT GROWTH: Forecasting BIF and SAIF Assessable and Insured Deposits
Technical Paper Series Congressional Budget Office Washington, DC FORECASTING DEPOSIT GROWTH: Forecasting BIF and SAIF Assessable and Insured Deposits Albert D. Metz Microeconomic and Financial StudiesMore information
A Trading Strategy Based on the Lead-Lag Relationship of Spot and Futures Prices of the S&P 500
A Trading Strategy Based on the Lead-Lag Relationship of Spot and Futures Prices of the S&P 500 FE8827 Quantitative Trading Strategies 2010/11 Mini-Term 5 Nanyang Technological University Submitted By:More information
Corporate Defaults and Large Macroeconomic Shocks
Corporate Defaults and Large Macroeconomic Shocks Mathias Drehmann Bank of England Andrew Patton London School of Economics and Bank of England Steffen Sorensen Bank of England The presentation expressesMore information
Component Ordering in Independent Component Analysis Based on Data Power
Component Ordering in Independent Component Analysis Based on Data Power Anne Hendrikse Raymond Veldhuis University of Twente University of Twente Fac. EEMCS, Signals and Systems Group Fac. EEMCS, SignalsMore information
Stochastic Inventory Control
Chapter 3 Stochastic Inventory Control 1 In this chapter, we consider in much greater details certain dynamic inventory control problems of the type already encountered in section 1.3. In addition to theMore information
FULLY MODIFIED OLS FOR HEEROGENEOUS COINEGRAED PANELS Peter Pedroni ABSRAC his chapter uses fully modified OLS principles to develop new methods for estimating and testing hypotheses for cointegratingMore information
Similarity and Diagonalization. Similar Matrices
MATH022 Linear Algebra Brief lecture notes 48 Similarity and Diagonalization Similar Matrices Let A and B be n n matrices. We say that A is similar to B if there is an invertible n n matrix P such thatMore information
A Simple Model of Price Dispersion *
Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute Working Paper No. 112 http://www.dallasfed.org/assets/documents/institute/wpapers/2012/0112.pdf A Simple Model of Price DispersionMore information
The information content of lagged equity and bond yields
Economics Letters 68 (2000) 179 184 www.elsevier.com/ locate/ econbase The information content of lagged equity and bond yields Richard D.F. Harris *, Rene Sanchez-Valle School of Business and Economics,More information
Economics 24B Daniel McFadden 1999 1. INTRODUCTION CHAPTER 6. SIMULTANEOUS EQUATIONS Economic systems are usually described in terms of the behavior of various economic agents, and the equilibrium thatMore information
ELEC-E8104 Stochastics models and estimation, Lecture 3b: Linear Estimation in Static Systems
Stochastics models and estimation, Lecture 3b: Linear Estimation in Static Systems Minimum Mean Square Error (MMSE) MMSE estimation of Gaussian random vectors Linear MMSE estimator for arbitrarily distributedMore information
Comparing Features of Convenient Estimators for Binary Choice Models With Endogenous Regressors
Comparing Features of Convenient Estimators for Binary Choice Models With Endogenous Regressors Arthur Lewbel, Yingying Dong, and Thomas Tao Yang Boston College, University of California Irvine, and BostonMore information
The Variability of P-Values. Summary
The Variability of P-Values Dennis D. Boos Department of Statistics North Carolina State University Raleigh, NC 27695-8203 email@example.com August 15, 2009 NC State Statistics Departement Tech ReportMore information
Maximum likelihood estimation of mean reverting processes
Maximum likelihood estimation of mean reverting processes José Carlos García Franco Onward, Inc. email@example.com Abstract Mean reverting processes are frequently used models in real options. ForMore information
Impulse Response Functions
Impulse Response Functions Wouter J. Den Haan University of Amsterdam April 28, 2011 General definition IRFs The IRF gives the j th -period response when the system is shocked by a one-standard-deviationMore information


text:
- Description
The Rovledo traditional dining collection features a double pedestal dining table complemented with oversized upholstered chairs all accented by floral carving, and decorative base and feet. Matching hutch and buffet reflects all carefully selected design that will be the showpiece of your formal dining room.Includes
1 Dining Table, 4 Side Chairs and 2 Arm ChairsDimensions
Dining Table(60800), 46"W x 80" - 120"L (Includes 2 x 20"Leaves)
Side Chair(60802), 44"H
Arm Chair(60803), 44"H
Armrest: 25"H
Hutch and Buffet(60804), 72" x 20" x 91"H
More from this collection: Rovledo
- Additional Information
Additional Information
SKU 11392836 MPN 60800-SET GTIN N/A Brand Acme Collection Rovledo Assemble Length N/A Assemble Width N/A Assemble Height N/A Assembly Required Yes Material N/A Finish N/A Sizes N/A Styles N/A Shapes N/A Shipping Time 1-2 Weeks Free Shipping No
- Reviews
Disclaimer: Pictures displayed may include optional products not included in the price. Computer monitors often display color variations. Color swatches are shown if alternative colors are available. Please call us or email us if you have any questions!

subset: commoncrawl


text:
|Mr. John M. O'Connor - Grant is one of the career industry's thought lea...
About Grant Cooper
Grant Cooper, founder and President of CareerPro Resume Service and Strategic Résumés, is New Orleans' only Certified Résumé Writer (CARW awarded by the Career Directors International), and has recently been appointed as Louisiana State Representative for PRWRA. He has had articles published in professional journals, is used as a consultant by recruiters, media reporters, and corporations, and has been featured in numerous newspaper articles.
In addition, Mr. Cooper and his firm were selected by the Louisiana Department of Labor to conduct numerous career-related seminars, workshops, and résumé assessment services at job fairs and other events throughout the state of Louisiana. He is a graduate of Louisiana State University, Baton Rouge Campus, with over 20 years of business management, technical writing, and human resource experience in both the private and public sectors. Mr. Cooper worked in a management capacity for the U.S. Government, where he authored career development, employee training, and motivational seminars, and achieved numerous awards for outstanding achievements. He attended LSU School of Law and earned academic honors in undergraduate work at LSU (B.A.), with additional postgraduate work at both San Jose State University and Golden Gate University Master of Public Administration programs.
Headquartered in New Orleans, Louisiana, Strategic Résumés provides a nationwide custom-written résumé, career services, job search skills training, and business document writing service, with a 10,000+ résumé database representing clients in virtually all career fields, and has operated continuously since 1994. In addition to résumés, Mr. Cooper designs and writes business plans, proposals, presentations, marketing materials, and other business documents.
Recent examples of clients have included NFL football players, the CEO of a $2 billion company, several of Mayor Nagin's top department head appointees, the former captain of USA's World Cup men's soccer team, a renowned New Orleans chef who personally served Presidents Bush & Clinton, as well as physicians, police officers, scientists, professors, intelligence agents, politicians, engineers, executives, white and blue collar employees, nurses, attorneys, students, accountants, and priests.
If you notice offensive or incorrect information, please contact us.
Mr. John M. O'Connor
Career Pro of NC, Inc.


text:
Viewing 2 posts - 1 through 2 (of 2 total)
- July 18, 2013 at 10:35 amReply
i100anniFebruary 15, 2014 at 2:18 amReply
Hello, my friend, as to this website, there is a more advanced downloader needed. You can try Video Grabber pro. It could download videos from 100% websites.
Here are the steps:
1, Install Video Grabber pro according to the link I have given you.
2, Run this software and activate Video detector.
3, Enter your website and play the video you wanted to grab. Then the Video Grabber pro could detect your video URL and download it automatically.
Then you could find the downloaded video in your default folder.
It won't fail you.
Viewing 2 posts - 1 through 2 (of 2 total)


text:
Johnny Lewis (also credited as Johnny K. Lewis) was an American actor perhaps best known for his work on Sons of Anarchy.
Lewis was born to a Scientologist family, and his career in acting started when he starred in Scientology training movies. He then made appearances on television and landed guest-star roles in drama shows such as Boston Public and American Dreams. Leaving the Church of Scientology in his early 20s, he starred alongside Hilary Duff in Raise Your Voice, which was his debut feature film appearance. He continued appearing in TV shows such as the short-lived Quintuplets, four episodes of Drake & Josh, and the teen drama The O.C. But his most famous contribution to acting was his portrayal as Kip "Half-Sack" Epps, a character who appeared in the first two seasons of the drama series Sons of Anarchy.
Personal LifeEdit
Lewis established a small criminal record for himself, being arrested three times between the years of 2011 and 2012. In his first arrest, he attacked two men, injuring them in the head by bashing it with a bottle during a fistfight. Six weeks later, he was accused of attempting a break-in at a woman's house. A probation official voiced his concern that Lewis was suffering from some sort of mental-health issue as well as chemical dependency, and as a result, it would make him a threat to the community.
On September 26, 2012, Lewis and an 81-year-old woman named Catherine Davis were both found dead at a home in Los Angeles' Los Feliz area. Lewis was found dead at the home's driveway, while Davis was found dead inside the house, which was ransacked. Lewis was named a suspect in the case. According to witnesses, a man jumped the house's fence, assaulted two people next door, and then jumped back over the fence. The LAPD announced that Lewis was apparently killed by a fall from the roof, garage, or patio. The case is still being investigated.
- Undressed (1999) as Ray
- 7th Heaven (2000) as Norton
- Malcolm in the Middle (2000) as Cadet Martin
- Judging Amy (2001) as Desmond
- The Guardian (2002) as Ted Popper
- Yes, Dear (2002) as Ricky
- The Sausage Factory (2001-2002) as Gilby
- Boston Public (2001-2003) as Bodhi
- The Sausage Factory (the TV movie; 2003) as Gilby
- Drake and Josh (2004) as Scottie
- American Dreams (2003-2004) as Lenny
- Raise Your Voice (2004) as Engelbery "Kiwi" Wilson
- Quintuplets (2004-2005) as Pearce Chase
- Pretty Persuasion (2005) as Warren Prescott
- Underclassman (2005) as Jeffries
- Smallville (2005) as Gabriel Duncan
- O.C. (2005-2006) as Dennis "Chili" Childress
- CSI: Crime Scene Investigation (2006) as Tad Sidley
- Bones (2007) as Enzo Falcinella
- Palo Alto, CA (2007) as Nolan
- Shark (2007) as Michael Hackford
- Alien Vs. Predator: Requiem (2007) as Ricky
- One Missed Call (2008) as Brian Sousa
- Cold Case (2008) as Truitt "Spider" Leland - 1998
- Felon (2008) as Snowman
- Criminal Minds (2009) as Eric Olson
- Sons of Anarchy (2008-2009) as Kip "Half Sack" Epps
- The Runaways (2010) as Scottie
- Lovely Mollie (2011) as Tim
- Magic Valley (2011) as John
- City of Gardens (2012) as Jorge
On Criminal MindsEdit
Lewis appeared in the Season Four episode Zoe's Reprise, in which he portrayed copycat serial-turned-spree killer Eric Olson.


text:
Top 5 Fears Faced in Addiction Treatment
Seeking recovery from addiction will necessitate huge transformation over all areas of your life. Facing something so big, it is normal to feel fear, trepidation, and worry. Fear can be among one of the hardest emotions to overcome, but it can helped significantly by gaining the support of others, and becoming aware that you are not alone.
Many people have to face these same fears, and have survived coming out stronger. This means you can too. Here are some of the fears you are likely to face as you seek treatment and recovery.
1) Fear of facing life without a familiar coping mechanism
Drugs and alcohol sometimes provide a way to "dropping out" of life when things get stressful or traumatic, a way of forgetting your problems. In recovery, you gradually begin to realize that addiction brings with it more problems then it "solves," but when you stop using, that means that old tensions will arise back to the surface.
Having to deal with these problems more directly is one thing that can make the process of sobriety seem scary and uncomfortable.
2) Fear of failure or relapse
Recovery is often a lot of hard work, with life and death hanging in the balance. It is a new way of living that requires a total overhaul in everything you thought you knew about yourself. It may feel like old habits and temptations can rear their ugly head at any moment.
Whether you have been sober for one day or many years, there is going to be moments where remaining sober might feel like an enormous struggle.
3) Fear of lost relationships
You did not get caught up in the pain of addiction all by yourself. There were lots of people encouraging, enabling, teaching you how to be an addict, and celebrating mutual addictions in a way that often feels fun in the moment.
Making the radical change to no longer pursue substance abuse may force you to say goodbye to people who can't understand or support you in your decision. Letting go of those relationships can be painful.
4) Fear of losing your identity
Addiction overtakes your understanding of who you are, wiping out your true identity as every moment of your behavior is controlled by either being under the influence of a substance, or having a craving for it. But if you are not addict, then who are you?
Letting go of that identity gives you a unique opportunity to define yourself, but that can be frightening. Change, even when it's clearly for the better, can sometimes be a painful process of shedding what is comfortable, and venturing into the unknown.
5) Fear of judgment from others, or yourself
Addiction is fueled by denial. You lie to yourself, and to others, about actions you feel powerless to stop, and this hides the true cost of your behavior.
Admitting you need sobriety requires that you drop the mask of a healthy person, facing your fears and failures head on. You may be afraid that others will judge you for being an addict. Even worse, you may be afraid of facing yourself as a person helpless to stop using of your own power.
How to deal with fear
Having feelings of fear is a normal part of being human, especially in facing something new and unknown. Bravery does not come from suppressing or ignoring these feelings of fear, but rather, facing them and choosing to go on anyway. By taking one step towards recovery, in spite of your fear, you will gradually make the fear smaller.
Surround yourself with people who have made it before you, and who support your decision to pursue sobriety. Through experiences of conquering fear, you will learn that fear need not get in the way of healing.


text:
Bad boy Justin needs to be taught a lesson. So his...
- by Tuesday
- Rating:
- Published: 23 Sep 2016
- Updated: 6 Mar 2017
- Status: In Progress
Jaxson Cerver, a 16 year old boy has just made the big move from his hometown of Lethbridge, Alberta to the big state of America. Following after his Aunt Jeanette due to the tragic incident that caused the death of both his parents. Now taking up by his aunt in the large and bustling Central City. Taking an interest in his aunts work as a Journalist in CCPD, as well for the famous S.T.A.R. Labs which was settled just a few blocks across from the apartment he shared with his mother's sister. Though, the simple night of Chinese food and the Particle Accelerator coming online. Yet, when he all but expected this to be the greatest moment in all of humanity, the explosion caused that to slip his mind almost instantly. What will become of his life now? (taking as best I can from the TV show, The Flash.)
Join MovellasFind out what all the buzz is about. Join now to start sharing your creativity and passion
Loading ...


text:
Archive for February 22nd, 2012
A Little This, Little That: 6 Ways to Stay Looking Good
What are six ways to stay looking fresh and maximize your personal appearance? We've taken some tips from Askmen.com and put them all together in a grand stew, churned them out, and here we have some top tips for you to mull over:
And we're not talking Jersey Shore here men. Just something light and simple, so your blue veins aren't showing underneath your translucent skin. Try Jergen's Tinted Moisturizing Lotion that will give you a natural looking tan in about three days. Apply it all over the body after the shower, just lie you would any other lotion, but make sure to thoroughly wash your hands afterwards…if you don't, you'll have little orange stains in the crevices of knuckles, in between fingers, etc.
if you can't afford a trip to Bermuda right now, try a tanning bed and these Bermuda 10 Cent Lily Cufflinks
If you have a big nose, part your hair to one side. Of course this only works if you have long-ish hair or enough to at least part. But parting it to one side minimizes the ultra-symmetrical look that highlights your rather large nose and doesn't put it in the spot light so readily.
Grow a beard. It makes a small chin and facial structure look more masculine. (And use facial hair to define a round face)
Wear colors that complement your eyes (i.e. if you have blue eyes, go for light blue shirts. Green…green sweaters, accessories.)
Blue Textured Collared Shirt, Daniel Dolce
Chew Whitening Gum after meals. Yes, you heard right. Chewing whitening gum can release/get rid of some of that plaque or grim around teeth after meals. Just make sure it's sugar-free, because it kind of defeats the purpose if it's not. And it will add some whitening shine to your 60 watt smile.
Change your razor blades regularly. All that bacteria builds up between the blades and goes right back on your skin in the next use. Shaving also reduces a minimal top layer of skin, so by adding extra bacteria to that new skin, you're just asking for trouble. Buy extra packs of blades and switch out every week (or four to eight shaves).


text:
Lennon lands Lustig
Celtic have confirmed that they have reached a pre-contract agreement with Sweden international Mikael Lustig.
Last Updated: 25/11/11 10:52am
Celtic have confirmed that they have reached a pre-contract agreement with Sweden international Mikael Lustig.
The defender, who is currently on the books of Rosenborg, will officially join the Scottish Premier League giants on 1st January, 2012.
He will pen a three-year deal upon his arrival at Parkhead and claims he is looking forward to the challenge that awaits him in Glasgow.
"This is a really exciting time for me and I am delighted to be committing my future to Celtic," Lustig told the club's official website.
"I know a lot about Celtic, about the size of the club, the world-famous supporters and about the quality squad of players which is already there.
"I'm really looking forward to joining this squad, to the challenges ahead and hopefully playing my part in bringing some success to the club."
Bhoys boss Neil Lennon has been tracking Lustig for some time and is delighted to have finally put a deal in place for the 24-year-old full-back.
He said: "We are delighted to bring Mikael to Celtic. We believe he has the qualities to make a real impact at the club and we look forward to him joining us in January.
"He is a player with international pedigree and a defender with great versatility. He is someone who I feel will be a very positive addition to the squad.
"I like his attributes and he can play both positions (right-back and centre-half), but he's predominantly a right-back."


text:
|Home > Neiva
♀ Neiva
What does Neiva mean?
Neiva [nei-va] as a girls' name is pronounced NEE-vah. It is of Spanish origin, and the meaning of Neiva is "snow". Feminine variant of the Spanish word "nieve". Neva is the name of a river in Russia.
RELATED FORMS VIA NEVA Nevada, Nevara, NeveCREATIVE FORMS
(female) Neira, Neivi, ..
(male) Neian, Neita, .. MIDDLE NAME PAIRINGS
Neiva Hadlee (N.H.), ..
How popular is Neiva?
Neiva is an unusual first name for females. Neiva is also an unusual surname for all people. (2000 U.S. CENSUS)
Which version is better?with its variant forms and related girl names. Neve, Nevada and Neva are the prominent alternative forms of Neiva (OUTSIDE TOP 2000). These relations of Neiva were at the height of their popularity during the years 1890-1899, but now, the version Neva has become somewhat dated. (TOP 2000 NAMES, 2015)
Similar Names
Neiva is pronounced similarly to Naavah, Nava, Nevaeh, Nova▲ and Novia. Other recommended names are Adiva, Akiva, Aviva, Belva▼, Deva, Ediva, Eeva, Keeva, Keva, Kiva, Liva, Melva▼, Naia, Naida, Naila, Naima, Nea, Neala, Neda, Nedda, Nedra, Neema, Neena, Neera, Negida, Nehira, Neila, Neile, Neilla, Neima, Neina, Neka, Nela, Nelda▼, Nelia, Nelida, Nella, Nena, Nenica, Nenita, Nenna, Neola, Neoma, Nera, Nerida, Nerina, Neriya, Nesha, Nessa, Nesta, Neta, Netia, Netta, Nevsa, Neysa, Nia▲, Nika, Nila, Nina, Nira, Nita▼, Oliva, Reeva, Reva▼, Riva, Veeva, Viva▼, Yeva, Zeeva and Ziva. These names tend to be more commonly used than Neiva.See names in meaning and etymology.


text:
No announcement yet.
EAT MOAR TATERS! Huh?
new posts
Originally posted by Quarry View Postlooked at those links, I still wonder if the starch causes spikes that would add to insulin resistance?
Just typing outloud... I have been debating doing tators or just fasting this week. DH is out of town so it would be a great time to not cook and have a clean kitchen all week65lbs gone and counting!!
Fat 2 Fit - One Woman's Journey
Originally posted by AlanC View PostI must admit I found that video mind-numbing.
That guy could package his presentations for insomnia treatmentzzzzzzzzzz..
Lost redirect <-CarbSane linkRetirement has afforded me the ultimate affluence, that of free time (Sahlins/Wells)
Originally posted by Meatgrrrl View PostHey well done LC. I lost about 4lb in my 4 days but had to stop because I was ill from a bug. Are you doing intermittent spuds or all the time?
All the time. Twice I have been on the brink of quitting so I had a greasy rosti with spices. The fat was enough variety to allow me to keep going, so minor deviations rather than ditching it. Works well!
Still reading through this thread, but just want tommention that I hope you guys are eating organic potatoes!! Root vegetables are among the worst to buy non-organic. Farmer's admit they'd never eat their own non-organic grown potatoes!
"Root vegetables absorb herbicides, pesticides, and fungicides that wind up in soil. In the case of potatoes--the nation's most popular vegetable--they're treated with fungicides during the growing season, then sprayed with herbicides to kill off the fibrous vines before harvesting. After they're dug up, the potatoes are treated yet again to prevent them from sprouting."
Read more: 7 Foods You Should Never Eat | Fox News
Originally posted by otzi View PostPeople around here get excited about novel ways to improve our health naturally. You should see what happened when I borrowed a lot of info from Ray's site on Cold Thermogenesis! http://www.marksdailyapple.com/forum/thread50560.html
Go to pages 11 and 17 and note the comments by Mr. ZzzzeroG. That's what I hoped would happen here.
When I started this thread, I figured people would say it was all BS and not give it a second thought. That's one of the reasons I didn't start right off with "....Ray Cronise says eat potatoes and lose weight." I figured if people took a liking to it, then we could give credit where credit's due. Done and done.
as they'd say down south, "Y'all give Otzi a break."
There is actually MUCH more to this than the "potato diet." That just happens to be a fun food that seems to fly in the face of the "bad carb" crowd. Anyone that's read much of my stuff knows I don't believe in "protein, carb and fat - speak."
It's great to see the success repeated. I just wanted everyone to know that "otzi" didn't intend on stealing anything and in fact sent a link soon after posting here.
oh, and I'm not a vegan, paleo, or any other such label. Just a scientist with a mid-life crisis calorimeter and an incredible drive to hack and understand.
I hope to have a little more time to hang out in the future, but just wanted everyone to ease up a little. If you are concerned about me "not getting credit" for something, you can always fill out some data sheets - I love crunching through data and the best part of these "N of 1" experiments is that everyone is at least eating the same thing...
Originally posted by Meatgrrrl View PostHey well done LC. I lost about 4lb in my 4 days but had to stop because I was ill from a bug. Are you doing intermittent spuds or all the time?
I wasn't really interested at first because weight loss has been mostly steady on a moderate macro diet, but as I get closer to my goal, the effects of my monthly cycle seem to be intensifying. I am ravenous and craving sweets and grains for several days after ovulation and was wondering if a heavy starch diet for those few days might be easier. I love potatoes, but have been kind of avoiding them because they are a lot of calories for the nutrients. However, if all potatoes, or mostly potatoes would make those days easier, it might be worth a try. Would I have to give up my 2 cups of coffee with milk in the morning in order not to balloon up eating plain potato the rest of the day?50yo, 5'3"
CW-125, part calorie counting, part transition to primal
GW- Goals are no longer weight-related


text:
Them Minners work reaaaaaal good...
|Bluegill Low Fat Minnow
The Low Fat Minnow isn't really much of a secret anymore, and it's been fished for everything from Tarpon to Trout. It has gone through many different versions over the past two years, and I've dialed it in to maximize effectiveness and simplicity in tying. Here is the original "write-up" about the Low Fat:
I love fishing for bass. Always have, always will. Largemouth bass are my favorite fish to chase by far, and up until about 5 years ago, I did it with a fly rod only. "Fly or die," was my mantra until I found my self living near, and having access to a private pond with an excellent population of healthy bucketmouth. This pond was covered by weeds most of the months out of the year, and I tried in vain to create the ultimate weedless fly, but I eventually came to the conclusion that I needed to get serious about gear fishing if I wanted to catch these fish. Long story short, I have about 14 baitcast rigs that get USED. I love everything about throwing big stuff for bass, and don't be fooled that it is any less technical than fly fishing.One fall, I was fishing a lake that has a huge bluegill population and we were throwing lipless crankbaits that yielded a fish on seemingly every cast. As I lipped a nice fish, It YACKED all over the deck of the boat. Up from the gullet came 4 or 5 bluegill minnows that really made me change the way I looked at fishing with bluegill patterns. I could literally see right through them, and their guts looked like little strands of krystal flash. Instead of going to try to find a crankbait with those characteristics, I immediately started creating a fly in my mind. Fishing with gear WILL improve your fly fishing and vise versa... Gear fishing that day led me to start working on a pattern that has both great profile, and translucency. Through much consultation with Uncle Ken, we decided that Senyo Laser dub is a very versatile material that really has some excellent properties in this fly, and the marabou acts the "guts" of the minnow that will not stay translucent. When stripped, this fly will flip around and do a 180, so its best to fish this one on a loop knot. I also didn't put any weight on this fly because the hook is a bit more beefy and will help the fly get down a bit. Happy fishing, and let us know how the "Low Fat" treats you.
|White on White Low Fat
~ Cheech
See the original video and our most popular recipes below this video.
***The Daiichi 3111 has been out of stock for quite a while, but these hooks work well in a pinch.
Gamakatsu SC15 Size 1
Gamakatsu B10s Size 4
Partridge Nordic Tube Hook Size 2
Hook: Daiichi 3111 1/0 (+)
Markers: Top: Brown and black. Bottom: Orange.
Hook: Daiichi 3111 1/0 (+)
Markers: Top: Black stripes and dot. Bottom: Neon blue and orange.
Markers: Top: Gray and black. Bottom: Red gill stripe.
Markers: Top: Gray and black. Bottom: Red gill stripe.
Hook: Daiichi 3111 1/0 (+)
Tail: Nature's Spirit Prime Marabou - White (BUY HERE)
Chenille: Palmer chenille - Pearl (BUY HERE)
Markers: Top: None. Bottom: Orange.
Markers: Top: Black stripes. Bottom: Orange gill plate and fins.
Here is the original Bluegill video.


text:
Delicious Gluten Free Sugar Free Healthy Carrot Cake
Recipe by stopusingupalltheids
There is an old recipe I was given for this ULTRA moist carrot cake that was to die for. Since I am a health nut I try to stay away from cake slices that are 900+ calories per serving (just a small exaggeration). But my boyfriend also has celiac disease, so I modified this recipe to be not only gluten free, but sugar-free as well (natural sugar, anyway) Here is the OLD recipe if you want it, of course you can make it healthy and keep all the calories, but really you can get almost the same taste out of this new one.
See Discussion:
Ingredients Nutrition
- 1 1⁄2 cups applesauce or 1 1⁄2 cups extra virgin olive oil
- 3 tablespoons Splenda sugar substitute
- 3 eggs (cage free)
- 1⁄2 cup brown rice flour
- 1⁄2 cup sorghum flour
- 1⁄2 cup quinoa flour
- 1⁄4 cup potato starch
- 1⁄4 cup tapioca starch
- 2 teaspoons xanthan gum
- 3 teaspoons cinnamon
- 2 teaspoons baking soda
- 2 teaspoons vanilla
- 3 cups carrots
- 20 ounces pineapple
- 1 cup coconut (sugar free)
- 1 cup walnuts
- 8 ounces light cream cheese
- 1 teaspoon vanilla
- 5 tablespoons Splenda sugar substitute
- cinnamon (optional)
- 1⁄4 cup walnuts (optional)
- 1⁄4 cup almonds (optional)
- 1⁄4 cup coconut (optional)
Directions See How It's Made
- (Make sure the carrots are grated before using them in the recipe, as well as chopping the almonds).
- Mix all ingredients together and bake in a 9x13-inch pan or in small cupcake holders (spray Pam butter-like spray) for 45 minutes on 350 degrees. If using oil instead of apple sauce, allow to cook one hour.
- Whip frosting ingredients together. Wait till cool to frost.
- To entice my daughter to eat them I put orange and yellow sprinkles on it, or you could also decorate it with little "frosting carrots". Have fun with this cake; it's very versatile and good for you. You can use all of the optional toppings as well if you'd like. You can reference the other cake here.
- On a side note, this frosting is also good with some sugar free fat free vanilla or cheesecake pudding, and also makes a great dipping sauce for apples.


text:
New Winter Graduate Course: Topics: Crisis Communication
In this new, online graduate-level course, students will learn the key elements of risk and crisis management, as well as their roles in any ongoing, proactive crisis communication process.
Students will be able to use the course professionally since it is taught from a learn it today, and apply it tomorrow approach. Though fully online, the class will feature a dynamic discussion environment where the instructor and students can interact and engage in multiple discussions.
The course will highlight best practices as well as foster learning from mistakes in poorly managed crisis situations.
Although this is not a core requirement, this course is an accepted elective for the SC&I, MCIS and MI programs and may be an elective in other Rutgers' masters programs.
The course's instructor, Dr. Richard Dool, has an extensive academic resume with a Doctorate in Management, MS in Management and a MA in Strategic Communication and Leadership. Additionally he has an active consulting practice that advises leaders and firms on strategic communication and organization renewals including the management of crisis situations. His background includes rescuing a company from near bankruptcy, leading the acquisition or divestiture of 11 companies and effectively managing companies in the US, UK, China, Brazil, Germany, France, India and Australia.


text:
As the night got later, the blood red moon started to get darker and redder. Momizi Inubashiri, the White Wolf Tengu and subordinate of Aya Shameimaru, had once again got dragged in to Aya's trouble.
"W-wait. Yo-you can't do that!" Momizi said
"I can't? Why don't you give me four reasons why I can't" Sakuya replied coldly.
Momizi flinched, but was able to retort.
"We-Well for one thing, we didn't do anything wrong. Two, w-we were only speaking our opinions and telling everyone what we think.Th-three, we have the right to freedom of post and speech. And four, you don't hav-have any right to make us work for you. We could su-sue you, you kn-"
Sakuya kicked Momizi in the stomach with an inhuman force and impact caused her to fly back and crash into a rock.
"Momi!" Aya screamed and turn to Sakuya,"What are yo-"
Sakuya punched Aya in the stomach. Aya gasped for air and dropped to her knees.
"Trash like you are the reason why I'm always busy and never get a rest." She said cruelly.
Sakuya walked over to Momizi, her eyes glowing red, and picked the wolf Tengu by her neck.
Momizi struggle to get free.
"W-what are-" She struggled
A evil grin swept over Sakuya's face and she tighten her grip.
"Trash must be eliminated and destroyed."
"A-a-....Plea...sto...p..." Momizi gasped as Sakuya tighten her grip even more.
Then a gust of wind blew toward the maid, causing her to release Momizi. Aya caught flew to her and caught her subordinate.
"Momi! Are you alright?" Aya asked.
"M...miss Aya, tha-thank you." Momi said.
"Lets get out of here! That maid has gone mad."
As Aya and Momizi tried to run away, Sakuya started to laugh manically. Her laugh chilled the two to the back of their spine.
"Useless trash. You can not escape from me!" the maid said.
"What is wrong with her? It seem she finally lost it!" Aya implied.
Sakuya vanish.
"L...look! she's gone!"
"Who cares! We have to get out of here pronto!"
A knife stabbed Aya's right leg and caused her to fell along with Momizi.
Aya held her leg in pain.
"Ow! What the-" she said painfully
"Mi...Miss Aya!"
Sakuya appeared in front of the two tengu. Momizi drew out her sword.
"W...why are you doing this! W-we already apologized s...so why are you hurting us?!" She said in a mixed tone of both anger and fear.
Sakuya Smirked, her eyes glowing blood red.
A knife flew past Momizi's arm, grazing but left a deep cut, caused her to drop her blade.
"I have no reason to talk to trash" Sakuya said as she kicked Momizi causing her to fly back next to Aya.
"Now perish."
The tengu were then surrounded by knives which were aimed and ready to fly toward them. Sakuya laugh manically and gave the signal for the knives to move. Momizi shield Aya's body as a when the barrage of knives were just about to impale the two.
"Momi!" Aya cried.
The knives were let loose and flew toward the them but then when it was about to hit their target it froze. Sakuya's face turned pale and she dropped to her knees, holding her head.
"A....ahhh...My head..." She said painfully.
The two tengus opened their eyes and saw the maid in pain.
"W..What's ha...happening to her?" Momizi asked
"Who care's Momi, but nows our chance!" Aya replied
"Ar...are we going to counterattack?"
"No, you dummy! This would be perfect story for our newpaper!"
"I can see it now!Breaking news!Aya Shameimaru (and her helper), wiped the floor with the out of control Scarlet Devil maid. Gensokyo was saved thanks to her (and helper)!"
"Mi..miss Aya..."
"It'll be our next best story! I'm a genius Momi! Hahahahaha!!!"
"I th...think we should focus on getting ou...out of here right now."
"You never were much of a helper you know that Momi. We have a chance now to get a great story and you're thinking about running away? Shame on you!"
"We...Well at least I'm thinking ab...about our lives!"
"What are you talking about?! You know getting stories are more important than our liv-"
Sakuya unleashed a bloodthirsty and painful cry, causing the two tengu to jump.
"On second thought..." Aya said.
Sakuya howled in pain and ran away from sight.
The girls watched silently as the maid disappear from their sight.
Aya broke the silence.
"Well, looks like I solved that problem."
Momizi glared at her.
"Okay,okay."We" solved that problem. Now, what say we go to Mystia's and drink until we forget what happen. What do you say? Eh?"
Momizi,could not contain her rage any longer,exploded.
"Wh...WHAT?! WE ALMOST GOT KI..KILLED AND YOU'RE STILL THI...THINKING ABOUT DRINKING?! IT WAS ALL YO..YOUR FAULT! IF YOU JUST LI...LISTEN TO ME FOR ONCE, THESE THI...THINGS WOULDN'T HAVE HAPPEN!" Momizi screamed at Aya enraged.
"Okay! Calm down! It's not like we actually died or anything so why you getting so angry for? Besides, it's not like you're paying for the drinks."
"Ye...yes I am. You're going to run aw...away after you had enough make me pa...pay for all the drinks,li...like you always do." "Whatever. Let's go"
Aya stand up, only to fall down and started screaming in pain while holding her right leg.
"Ooow! I forgot that I got stabbed. I can't even walk now." She complained, and turned to Momizi with a grin.
"Wa...wait what? I'm not ca...carrying you! Can't you fl...fly?"
"Well I could but I'm still injured. Besides I saved your doggy behind so move it!"
Momizi sighed.
"I...if it wasn't for that pro...promise I made, I would have been free and happy." She said as she hosted Aya onto her back.She grunted and struggle to hold her friend up."Mi...miss Aya, you got to stop ea...eating so much..."
"How rude. Either do it without complaining or don't do it at all."
"You say that but you're still making me carry you" Momizi said under her breath.
"Now! To Mystia's stand! March!" Aya commended and slapped Momizi butt. The wolf tengu jumped.
"I...I'm not your horse! Do...don't do that!!"
"Whatever! Now move already."
Momizi grunted and started to move. After a few steps, Momizi stopped and dropped Aya on the drop with a thump.
"Ow, Momi why did you do that? Geez, what is wrong with you?" Aya said while rubbing her sore behind.
Momizi fell to her knees and grabbed her head. Aya noticed and went over to her.
"Momi, what's wrong?"
"My head...it...it..." she said painfully.
"What are you doing? Get a hold of yourself!"
"St...stay away...I...I can't..."
She swung her arm and knocked Aya back away from her.
"Momi! What is wrong with you!?"
"A....hel...help...me!" Momizi cried.
From a distance came sound of a bell from a clock tower. It rang marking that it was midnight. It inaudible at first but it soon grew louder and louder until even the two tengus can hear it.
Upon hearing the bell Momizi screamed in pain while holding her head. Her eyes began to turn blood red and her fangs grew.
"What's going on?" Aya asked in fear.
She watched as her friend fell to the ground with all four in pain. Momizi's nails grew until they became claws and she grew larger by the minute until her clothes were shredded. After her transformation she got up on two feet and howled at the moon, a bone chilling howl of anger, despair and pain. Aya struggle to get up but because of the wound from the knife she winced in pain and could not fully stand. She tried to get closer to her friend who was whimpering, like a dog who had been thrown out of its home.
"Momi…." Aya said nervously, reaching out to touch her friend.
Momizi jolted and slash at her like a wild animal. Aya's jumped back and fell.
A dark red liquid gusted out of her chest.
"Wha…"She said dumbstruck as held her chest painfully. She looked down at her hand, covered in blood and coughed.
More blood gusted out. Aya entire body fell on to the ground while clasping her chest. The last thing she was able to see was Momizi standing in front of her, blood dripping from her claws and eyes glowing deep red, and the blood red moon which seemed to be hovering over her friend, like it was controlling her. It may have been because of her wound but she swore she could see a grin on the tainted moon. A evil grin, one of like a death god, taunting her,laughing at her pain and despair.
"Mo...mi...." Aya blacked out.


text:
HCG Pregnyl is a prescription medication that was approved over 25 years ago for female fertility issues and pediatric hormone therapy. HCG Pregnyl is distributed by the Schering-Plough Corporation and is referred to as Pregnyl.
What Is Pregnyl?
Pregnyl is the liquid, purified prescription form of human chorionic gonadotropin (HCG). Pregnyl contains the luteinizing hormone (LH) and the follicle stimulating hormone (FSH) which, when produced naturally in the female human body during the course of a normal menstrual cycle, trigger ovulation.
Why Is Pregnyl Used?
Pregnyl has been used to treat fertility issues. Pregnyl may be administered to women after first finishing a round of another medication, called menotropins, to cause ovulation. Pregnyl may also be used in prepubescent boys to initiate the dropping of the testicles.
How Is Pregnyl Used?
Pregnyl is administered by a medical professional with a syringe in the form of an intramuscular injection.
A woman receiving Pregnyl for fertility-related issues will typically receive only one dose. Young boys receiving treatment often get three doses of Pregnyl per week for approximately three weeks.
Side Effects
Common side effects of Pregnyl include headaches, drowsiness and soreness at the injection site. Women should be especially aware of abdominal pain or swelling, chest pain, slurred speech or weakness on one side of the body; any signs of severe allergic reactions should be discussed with medical professionals immediately.
Related Searches
You May Also Like
Fertility Drugs That Cause Multiple Births
Getting pregnant does not come naturally for some couples, who may turn to fertility treatments to aid in conception. Many couples use...
The Average Cost of HCG Injections
Human chorionic gonadatropin (hCG) is produced by the placenta during pregnancy. The hormone stimulates changes in a pregnant woman's body, including increases...
How to Inject HCG
As a part of the hCG weight loss protocol originated by Dr. ATW Simeons, you will need to be given injections of...
How to Use Novarel Injections for Weight Loss
Novarel is a brand of human chorionic gonadotropin (HCG) drugs. HCG is a hormone found only in pregnant women; however, in the...
How to Build Muscle Mass Using HCG
HCG, or human chorionic gonadotropin, is a naturally occurring hormone that plays a role in the development of an ovum (egg) and...


text:
Throat Bangers 23Favorites [+]
Pay-Per-Minute Viewing
You can now enjoy this movie on your iPhone®, iPad®, or compatible Smart TV & Android devices.
Purchase Options
Pay-Per-MinutePurchase Minutes
Streaming Rentals
Available MP4 sizes:SD 480p (1.6 GB)
DRM-free downloads offer content that is not limited by standard Digital Rights Management (DRM) access technologies. These technologies allow hardware manufacturers, publishers, copyright holders and individuals to limit the usage of digital content.
When you purchase DRM-free downloadable content, that content is available for you to download on any computer and save to a disk whenever you like. You can also download to multiple computers. There is no timeframe associated with your purchase and the content will not expire.
Running Time: 105 minutes
Released: 06/2008
Studio Name: Devil's Film Devils Film
Series: Throat Bangers
Stars: Yana Nevskaya Monika Dino Miranda Timo Hardy Marijo (f) Macroc ...More
Description: Deep, Messy Blowjobs!! This is all about oral sex! Otherwise known as fellatio, head, blow job, deep throat, or the best 5 minutes of silence a married man can ask for!!
9 Scenes from Throat Bangers 23
Throat Bangers 23: Scene 1 Free Preview
Sex Acts: Oral Sex, Throat Fucking, Vaginal Sex
Throat Bangers 23: Scene 2 Free Preview
Sex Acts: Deep Throating, Oral Sex, Throat Fucking, Blowjob
Throat Bangers 23: Scene 3 Free Preview
Sex Acts: Oral Sex, Throat Fucking
Throat Bangers 23: Scene 4 Free Preview
Throat Bangers 23: Scene 5 Free Preview
Throat Bangers 23: Scene 6 Free Preview
Sex Acts: Toy Play - Vaginal, Deep Throating, Oral Sex, Throat Fucking, Masturbation
Positions: Kneeling, Sitting, Laying, Crouching/Squatting, Standing
Throat Bangers 23: Scene 7 Free Preview
Throat Bangers 23: Scene 8 Free Preview
Throat Bangers 23: Scene 9 Free Preview
Recommended Movies
AEBN Cams