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Weather Derivatives and Stochastic Modelling of Temperature
We propose a continuous-time autoregressive model for the temperature dynamics with volatility being the product of a seasonal function and a stochastic process. We use the Barndorff-Nielsen and Shephard model for the stochastic volatility. The proposed temperature dynamics is flexible enough to model temperature data accurately, and at the same time being analytically tractable. Futures prices for commonly traded contracts at the Chicago Mercantile Exchange on indices like cooling- and heating-degree days and cumulative average temperatures are computed, as well as option prices on them.
1. Introduction
Protection against undesirable weather events, like, for instance, hurricanes and droughts, has been offered by insurance companies. In the recent decades, the securitization of such weather insurances has taken place, and nowadays one can trade weather derivative contracts at the Chicago Mercantile Exchange (CME), or more specialized weather contracts in the OTC market. At the CME, one finds derivatives written on temperature and snowfall indices, measured at different locations worldwide. The market for weather derivatives is emerging and gaining importance as a tool for hedging weather risk.
In this paper we propose a new model for the dynamics of temperature which forms the basis for pricing weather derivatives. The model generalizes the continuous-time autoregressive models suggested in Benth et al. [1] (see also Dornier and Querel [2] and Benth et al. [3]), to allow for stochastic volatility effects. Signs of stochastic volatility in the temperature variations have been detected in many data studies, for example, in an extensive study of daily US temperature series by Campbell and Diebold [4] and in Norwegian data by Benth and Šaltytė-Benth [5]. Campbell and Diebold suggested a seasonal generalized autoregressive conditional heteroskedasticity (GARCH) model to explain their observations, while here in this paper we suggest to model the variations by the stochastic volatility model of Barndorff-Nielsen and Shephard [6].
As it turns out, one may derive reasonably explicit expressions for futures prices of commonly traded contracts at the CME. Our proposed model is flexible in capturing the stylized features of temperature data, as well as being analytically tractable. To account for seasonality, we introduce a multiplicative structure, which is much simpler to analyse than the complex model suggested by Campbell and Diebold [4], where the seasonality comes in additively in the GARCH dynamics. One of the main advantages with our model is that it is set in a continuous-time framework, accommodating for a simple application of the theory of derivatives pricing. For example, we find that the volatility of futures prices on the cumulative average temperature is given by the temperature volatility, modified by a Samuelson effect inherited from the autoregressive structure of the temperature dynamics.
The risk premium in derivatives prices is parametrized by a time-dependent market price of risk. In addition, we include a market price of volatility risk. Thus, the risk loading in derivatives prices, interpreted as the risk premium in the financial setting, includes both temperature and volatility. In mathematical terms, the pricing measure is obtained by a combination of a Girsanov and Esscher transform.
We discuss the estimation of the proposed temperature model on data from Stockholm, Sweden. The purpose of the study is not to give a full-blown fitting of the model, but to outline the steps and to justify the model. Next, we discuss some issues related to the mean reversion of the model, where in particular we derive the so-called half-life of our temperature model. The importance of the various terms in the model is discussed.
We present our findings as follows. In the next section we review the basics of the CME market for weather derivatives. Next, in Section 3, our temperature model with seasonal stochastic volatility is defined and analysed. Section 4 contains results on the futures price dynamics for some commonly traded products at the CME. Some empirical considerations of our model and its applications to weather derivatives are presented in Section 5.
2. The Market for Temperature Derivatives
The organized market for temperature derivatives at the CME offers trade in futures contracts "delivering" various temperature indices measured at different locations in the world, including the US, Canada, Australia, Japan, and some countries in Europe. In addition, there are contracts written on snowfall in New York and frost conditions at Schiphol airport in Amsterdam. On the exchange one may also buy plain vanilla European call and put options on the futures.
The main temperature indices are so-called cooling-degree days (CDDs), heating-degree days (HDDs), and cumulative average temperature (CAT). The CAT index is for European cities mainly. For a measurement period , , the CDD index is measuring the demand for cooling and is defined as the cumulative amount of degrees above a threshold . Mathematically we express it as with being the daily average temperature on day , and the average is computed as the mean of the daily maximum and minimum observations. The threshold is in the market given as 18°C, or 65°F and is the trigger point for when air-conditioning is switched on. The measurement periods are set to weeks, months, or seasons consisting of two or more months, within the warmer parts of the year. A futures written on the CDD pays out an amount of money to the buyer proportional to the index, in US dollars for the American market, and in Euro for the European one (except London, where British Pounds is the currency). By entering such a contract, one essentially exchanges a fixed CDD against a floating, and thereby one may view these futures as swaps.
An HDD index is defined similarly to the CDD as the cumulative amount of temperatures below a threshold over a measurement period , that is, The index reflects the demand for heating at a certain location, and measurement periods are typically weeks, months, or seasons in the cold period (winter).
The CAT index is simply the accumulated average temperature over the measurement period defined as This index is used for European and Canadian cities at CME. CME also operates with a daily average index called the Pacific Rim measured in several Japanese cities. The Pacific Rim is simply the average of daily temperatures over a measurement period, with the daily temperature defined as the mean of the hourly observed temperatures.
Temperature futures may be used by energy producers to hedge their demand risk (see Perez-Gonzales and Yun [7] for a study of weather hedging of US energy utilities). Other typical users of such futures contracts for hedging purposes are electricity retailers, holiday resorts, producers of soft drinks and beer, or even organisers of outdoor sport events, and fairs. Also investors have seen the potential in weather derivatives as a tool for portfolio diversification, since the derivatives are not expected to correlate significantly with the financial markets (see Brockett et al. [8]).
For mathematical convenience, we will use integration rather than summation and define the three indices CDD, HDD, and CAT over a measurement period by respectively.
In this paper we are concerned with modelling the temperature dynamics accurately in continuous time. Moreover, we aim at deriving futures prices based on our proposed dynamics. In the literature, one finds several streams for pricing weather derivatives. The main approach is to model the stochastic temperature evolution and price by conditional risk-adjusted expectation (see Benth et al. [3]). This is motivated from fixed-income theory, where zero-coupon bonds are priced using a model for the short rate of interest and conditional risk-adjusted expectation (see, e.g., Duffie [9]). Another popular way to price derivatives is using the so-called burn analysis (see Jewson and Brix [10]). There, one computes the historical average of the index in question and prices by this figure. One may add a risk loading to this price. A more sophisticated pricing method is the so-called index modelling approach (see Jewson and Brix [10]), where one is modelling the historical index value by a probability distribution. Index modelling was applied by Dorfleitner and Wimmer [11] in an extensive empirical study of US futures prices at the CME. The drawback with these two ways of pricing is that you do not get any dynamics for the futures price. If one wants to derive option prices, one must have accessible the volatility of the futures price as well as the price itself. Although applying the burn analysis (index modelling) gives an accurate estimate on the historical index value (distribution), it is expected that a precise model of the temperature dynamics explains close to equally well the historical average (distribution). In addition, one obtains the stochasticity of the temperature evolution, which enables us to find the futures price dynamics and to price options on such futures.
Brockett et al. [8] applies the indifference pricing approach in a mean-variance setting to valuate weather derivatives. Davis [12] introduces the marginal utility approach to pricing of weather derivatives, which is based on hedging in correlated assets and modelling of the index as a geometric Brownian motion. Platen and West [13] suggest using a world index as a benchmark for weather derivatives pricing. Equilibrium theory has also been a popular approach for pricing weather derivatives. Cao and Wei [14] apply this to analyse US temperature futures (see also Hamisultane [15] for a more recent study).
3. A Model for the Temperature Dynamics with Seasonal Stochastic Volatility
Let be a complete filtered probability space with being a finite time horizon for which all the relevant financial assets in question exist.
We suppose that the temperature at time is defined as where is the deterministic seasonal mean function and is a stochastic process modelling the random fluctuations around the mean. In other words, is the deseasonalized temperatures.
The seasonal mean function is assumed to be real-valued continuous function. To capture the seasonal variations due to cold and warm periods of the year, and possible increase in temperatures due to global warming and urbanization, say, a possible structure of could be for constants , , , and , and with time measured in days. Such a specification of the seasonality function was suggested by Alaton et al. [16] in their analysis of temperatures observed in Bromma, Sweden. Benth and Šaltytė Benth [5] applied this seasonality function when modelling Norwegian temperature data and later used it for data measured in Lithuania and Sweden in the papers [1, 17, 18]. Mraoua and Bari [19] apply such a seasonal function on Moroccan data. Other, more sophisticated seasonal functions may of course be used (see Härdle and Lopez Cabrera [20] and Härdle et al. [21]).
Empirical analysis of temperature data in Norway, Sweden, and Lithuania (see Benth et al. [1, 5, 17, 18]), and US and Asian cities (see Cao and Wei [14] and Härdle and Lopez Cabrera [20]), suggest that the deseasonalized temperatures have an autoregressive structure on a daily scale. This motivates the use of a continuous-time autoregressive () model for (see Brockwell [22] for a general account on such processes).
For , a -dynamics is defined as follows. Define the -matrix by with being positive constants for , and the identity matrix. Observe that the determinant of is equal to , and hence is invertible. For a one-dimensional Brownian motion , we define the -dimensional Ornstein-Uhlenbeck process as where , is the canonical th unit vector in and constant. A process is defined as , with being the transpose of a vector . It seems that a is the most reasonable choice from an empirical point of view (see, e.g., Benth et al. [1] or Härdle and Lopez Cabrera [20], where the volatility is allowed to be time-dependent to allow for seasonality effects). In passing we note that a similar model has been used for wind speed modelling for New York and Lithuania, resulting in a process for deseasonalized data as the statistically optimal choice (see Šaltytė Benth and Benth [23] and Šaltytė Benth and Šaltytė [24]).
In this paper we are concerned with an extension of the model defined (3.4) to explain seasonality and stochastic volatility effects in the temperature variations. In Benth and Šaltytė Benth [5], it was observed that the residuals of temperature after explaining the autoregressive effects had a clear seasonality and signs of stochastic volatility (from a study of Norwegian temperatures). This seasonal structure can be partly explained by a seasonal variance. However, one is still left with signs of stochastic volatility observed as an exponentially decaying autocorrelation function for squared residuals. Similar observations were made by Campbell and Diebold [4] on US data. They suggest a GARCH volatility structure where a seasonal level component is added to model this. However, from a modelling and empirical point of view, it seems much more reasonable to consider a multiplicative structure between the seasonality and the stochasticity of the volatility. It is a rather standard approach in time series analysis to apply multiplicative models when dealing with phenomena having positive values. Using a multiplicative structure makes it easy to preserve the natural condition of positivity of the overall volatility. Also, empirically it becomes simple to estimate the seasonality and the stochastic volatility contributions in a stepwise procedure. We remark in passing that the seasonal GARCH model of Campbell and Diebold [4] may lead to negative values of the volatility. Our proposed stochastic volatility model will lend itself to analytical tractability when it comes to pricing of weather derivatives, which seems to become very complicated when using the seasonal GARCH model of Campbell and Diebold [4].
Hence, we propose the following model with seasonal stochastic volatility. Suppose that follows the dynamics where for a bounded positive continuous function , and being a stochastic process assumed to the positive. We assume that is strictly bounded away from zero, that is, there exists a constant such that for all .
In Benth et al. [1], the model (3.5) was considered with , that is, with no stochastic volatility effects. The function was estimated on data from Stockholm, Sweden, to be a truncated Fourier series of order four, having a yearly seasonality, that is, for , , with time being measured in days. This seasonal volatility has been observed and modelled for data in Sweden and Lithuania (see Benth et al. [1, 18]), and US and Asian cities (see Cao and Wei [14], Härdle and Lopez Cabrera [20] and Benth et al. [25]). Recently, Härdle et al. [21] proposed and applied a powerful local adaptive modelling approach to optimally estimate the volatility.
A class of stochastic volatility processes providing a great deal of flexibility in precise modelling of residual characteristics is given by the Barndorff-Nielsen and Shephard [6] (BNS) model. In mathematical terms, we have with Here, is a constant measuring the speed of mean reversion for the volatility process , which reverts to zero. The process is assumed to be a subordinator independent of , the Brownian motion, meaning a Lévy process with increasing paths. In this way one is ensured that is positive.
In the BNS model a dependency on in the subordinator is introduced. We choose a subordinator and define , which then again becomes a subordinator. This is convenient when estimating such a stochastic volatility model. In fact, one may get relatively explicit distributions for the "deseasonalized" residuals , which become conditionally normally distributed, with mean zero and variance . In stationarity of , this distribution becomes independent of , and therefore one may separate modelling of the distribution of these residuals from the dependency structure in the paths. For this stochastic volatility model, the squared residuals will have an exponentially decaying autocorrelation function, with decay rate . By superposition of such 's, the autocorrelation function may decay as a sum of exponentials. We refer to Barndorff-Nielsen and Shephard [6] for an extensive analysis of this class of stochastic volatility models. We remark that the stochastic BNS volatility does not become a GARCH dynamics in discrete time, but shares some similar properties.
In the rest of this paper we suppose that the deseasonalized temperature is given by where is defined in (3.5) and defined in (3.7) and (3.8).
4. Temperatures Futures Pricing
In this section we derive the futures price dynamics based on the CDD/HDD and CAT indices. This will be done with respect to some pricing measure specified in a moment.
We use the intrinsic notation for a temperature index over the measurement period , where TI = HDD/CDD or CAT. Let be the futures price for a contract returning the index . The futures contracts are settled at the end of measurement period, time , and the time value of a long position in the contract is where the constant is the risk-free interest rate. Thus, if is a probability equivalent to , we can define the futures price as by using that the contract is costless to enter and assuming that the futures price is adapted to the information at time , .
One may ask why we do not consider stochastic interest rates in this setup. In fact, it would not be any problem to do so, by, for example, assuming a risk-free spot rate . However, there is no reason why this should depend on the temperature, and a reasonable model would state independence between and . Thus, from the properties of conditional expectations, we would end up with the same pricing relations as in (4.2).
Note that the pricing measure is only equivalent to and not assumed to be a martingale measure. If temperature would be a tradeable asset, then the no-arbitrage theory of asset pricing (see, e.g., Duffie [9]) would demand that is an equivalent martingale measure, that is, a probability equivalent to under which the discounted temperature is a -martingale. Temperature is obviously not a tradeable asset, and the condition on being a martingale measure is not effective.
To restrict the class of pricing probabilities, we consider a deterministic combination of a Girsanov and Esscher transform. The Girsanov transform introduces a market price of risk with respect to the Brownian motion, while the Esscher transform will model a market price of volatility risk. In mathematical terms, we define the probability as with for , being two bounded continuous functions. Here, is the log-moment generating function of , that is, Note that the Novikov condition is satisfied for the Girsanov change of measure since , and being bounded. Furthermore, we assume exponential integrability of , that is, there exists a constant such that Then, the Esscher transform is well defined for all functions such that . We restrict our attention to this class of market prices of volatility risk. We find that is a -Brownian motion, independent of . Moreover, following the analysis in Benth et al. [3], it holds that is an independent increment process under , and, in the case where is a constant, a Lévy process.
There has been some work trying to reveal the existence and structure of the risk premium, or the market price of risk, for temperature derivatives. The theoretical benchmark approach by Platen and West [13] strongly argues against the existence of a risk premium in weather markets. The econometric study of US futures prices at CME performed by Dorfleitner and Wimmer [11] shows that the index modelling approach gives a very good prediction of prices, pointing towards a zero market price of risk. The results of Cao and Wei [14] is more inconclusive, as they are able to detect a significant (although small) market price of risk based on their equilibrium pricing approach. More recently, Hamisultane [15] showed using New York data that the estimates become very unstable within this pricing framework. Härdle and Lopez Cabrera [20] analyse various specifications of the market price of risk in an extensive empirical study of German futures prices. They find signs of a significant market price of risk for these contracts. Based on the abovementioned studies, one may choose the market price of risk as zero. As far as we know, there exists no empirical investigations on the volatility risk premium in weather markets. One may suspect that this is zero, but we include here for generality. Using would correspond to and be a choice following the indications of the study in Dorfleitner and Wimmer [11].
In the following proposition we compute the CAT futures price.
Proposition 4.1. The CAT futures price at time for a contract with measurement period , , is where
Proof. We know that the -dynamics of becomes for the -Brownian motion . Thus, from the multidimensional Itô formula, it holds for It follows that By conditioning on the -algebra generated by the paths of , and , and using the tower property of conditional expectation, we find that the last term above is equal to zero from the independent increment property of . Finally integrating with respect to yields the desired result.
Observe that the market price of volatility risk does not enter the CAT futures price explicitly, only the market price of risk . We derive the dynamics of the CAT futures price in the following proposition.
Proposition 4.2. The -dynamics of the CAT futures price is whereas the -dynamics becomes with defined in Proposition 4.1.
Proof. This follows by a straightforward application of the multidimensional Itô Formula, where the observation that is a -martingale simplify the derivations considerably.
As is evident from this dynamics, the CAT futures price will have a seasonal stochastic volatility , dampened by the factor . This factor can be viewed as the integral of over the measurement period . Observe that for the case of a process, which is nothing but an ordinary Ornstein-Uhlenbeck process, this term collapses into , an exponential damping of the volatility of temperature as a function of "time-to-maturity" . This is known as the Samuelson effect in commodity markets. In the current context, we have a term which can be interpreted as the aggregation of the Samuelson effect over the measurement period (see Benth et al. [3] for a thorough analysis on the Samuelson effect for higher-order autoregressive models). The drift in the -dynamics of will depend explicitly on the parameter , defending the name market price of risk.
We next move our attention to CDD futures, which will become nonlinearly dependent on the temperature. Thus, we will not get as explicit results on their prices as for the CAT futures. It turns out to be useful to apply Fourier transform techniques (see Carr and Madan [26]).
Recall from Folland [27] that for a function , we have where is the Fourier transform of defined by Note the signs in the exponentials here, which are not following the standard definition.
Relevant to the analysis of CDD futures, consider the function , which is not in , but we can dampen it by an exponential function and get the following lemma.
Lemma 4.3. For any , the Fourier transform of the function is
Proof. We have The result follows by straightforward integration.
We apply this in our further analysis of the CDD futures price.
Proposition 4.4. The CDD futures price at time for a contract with measurement period , , is with given in Lemma 4.3 and given by where The constant can be arbitrarily chosen.
Proof. First, from the definition of the CDD index and the -dynamics of we find where we have introduced the short-hand notation . From Lemma 4.3 we find that (after commuting integration and expectation by appealing to the Fubini-Tonelli Theorem) The last equality follows from the -adaptedness of . To compute the conditional expectation in the last expression, we apply the tower property of conditional expectations with respect to the filtration generated by the paths of , and . This yields from the independence between and and the independent increment property of Brownian motion, We have Hence, by using the adaptedness of to and the independent increment property of under , Invoking the stochastic Fubini theorem (see Protter [28]) gives Finally, we compute the expectation by using the Radon-Nikodym derivative of with respect to and the log-moment generating function of . This proves the proposition.
Although seemingly very complex, the price dynamics of a CDD futures can be simulated by using the fast Fourier transform (FFT) technique (see Carr and Madan [26] for a discussion of this in the context of options). In fact, given and , one uses FFT to compute . This procedure will involve numerical integration over the measurement period and in the expression for . Since FFT is rather efficient, this seems to be preferable to a direct Monte Carlo simulation of .
The CDD futures price depends explicitly on the current states of the volatility and process . Since we define the deseasonalized temperature as the first coordinate of , this is observable from today's (time moment ) temperature after removing the value of the seasonal function . However, the remaining states of must be filtered from deseasonalized temperature observations. One may appeal to the Kalman filter for doing this, although the seasonality and stochastic volatility complicates this procedure. A tempting alternative is to use an Euler discretization of the dynamics as in Benth et al. [3] to relate the coordinates of to lagged observations of temperature. (In Benth et al. [3], the Euler discretization is performed for a time continuous, but deterministic, volatility. Note that there is no change in the steps for developing the same identification when having a stochastic volatility.) It is easily seen from the definition of that the quadratic variation process of the last coordinate, , is equal to and thus we may apply this to recover from observing the path of .
Since depends explicitly on , we get the interesting consequence that even though the temperature dynamics has continuous paths, the CDD futures dynamics will jump when jumps. Thus, the futures price dynamics will have discontinuous paths. See Benth [29] for a similar result in the context of commodity and power markets using the BNS stochastic volatility model. Note also that the market price of volatility risk appears explicitly in the price, contrary to CAT futures.
The HDD futures price dynamics can be computed analogously to the price. However, we may also resort to the so-called HDD-CDD parity which we collect from Benth et al. [1, Proposition 10.1]. It holds that We have formulas for both the CDD and CAT futures prices, and thus readily follows from (4.30).
4.1. A Discussion on Pricing of Options on Futures
The technique using Fourier transform is well adapted for option pricing as well, and we will briefly discuss this in connection with European call and put options written on CAT and CDD futures.
We start with a call option on a CAT futures, with exercise time and strike price , on a futures with measurement period , . The price of this call option at time is given by the no-arbitrage theory as As it turns out, the derivation of using Fourier techniques follows more or less exactly the same steps as computing the CDD futures price. In fact, we observe from Proposition 4.1, that Moreover, the payoff function of the call option is the same as the CDD index on a given day. By conditioning on the paths of , we can compute the option price step by step as in the proof of Proposition 4.4. This results in the following proposition.
Proposition 4.5. The price at time of a call option on a CAT futures with measurement period , exercise time , , and strike , is with given in Lemma 4.3 and and defined in Proposition 4.1.
Options on CDD futures are far more technically complicated to valuate. However, we may here as well resort to Fourier techniques and in principle obtain transparent price formulas. Considering a call option at time , with strike price and exercise time , we have the price as in (4.31), except that we substitute "CAT" with "CDD". Recalling from Proposition 4.4, we have Furthermore, from the dynamics of and , we can express both in terms of their current states and , in addition to integrals with respect to and from to . Similar considerations as for the CAT futures option can then be made, however, leading to a technically complex formula. We leave the details to the reader.
5. Some Empirical Considerations
We refer to an empirical estimation which can be found in Benth et al. [3] as a starting point for our discussion. There a data set of daily average temperatures measured in degrees Celsius in Stockholm, Sweden, is studied. The data are recorded from January 1, 1961 to May 25, 2006, altogether 16,570 data points after observations on February 29 in every leap year were removed. The parameters of the seasonal function as defined in (3.2) were estimated by least squares approach to be , , , and . This means that there is a small increase in average temperature over the considered measurement period. The overall average temperature is around 6.3°C. The amplitude is ±10.44, which means that on average in the winter temperatures go down to around −4°C, while summer temperatures reach above 16.7°C. After removing the seasonal function from the data, one finds based on the autocorrelation structure of the residuals that a process fits the deseasonalized data very well. The estimated parameters in the matrix are , and , leading to eigenvalues with negative real part and thus leads to a stationary dynamics.
Our main concern in this paper is the precise modelling of the residuals. We have proposed a model where the volatility is defined as the product of a deterministic seasonal function and a stochastic volatility process . The natural path to follow in estimating this is to first estimate the seasonal function. We use the approach suggested in Benth and Šaltytė Benth [5, 17], where a Fourier series of order four is chosen for , and estimated on daily empirical variances. Next, the residual data are divided by the estimated function, in order to deseasonalize them.
The residuals after removing the effect of the function and the autoregressive effects, are close to normally distributed (see Figure 10.11 in Benth et al. [3]). However, there are signs of heteroskedasticity, in particular, a normality plot shows signs of a heavy left tail in the distribution (see Figure 10.12 in Benth et al. [3]). Also, the value of 0.002 of the Kolmogorov-Smirnov test suggests to reject the normality hypothesis of the residuals. We remark in passing that recently Härdle et al. [21] have proposed a local adaptive approach to find an optimal smoothing parameter to locally estimate the seasonality and volatility. The approach aims at correcting the nonnormalities in the residuals. Their approach improves the normal distribution fit to residuals for many cities, but there are still signs of heavy tails (see in particular the QQ-plot of Berlin data in Figure 11 of Härdle et al. [21]). We also remark that in Benth and Šaltytė Benth [5], the empirical seasonal volatility was used as the estimate of , but still a clear sign of stochastic volatility were present when analysing the autocorrelation function of the squared residuals.
In Figure 1 we show the autocorrelation function of the squares of the deseasonalized residuals on a log-scale. Characteristically, the autocorrelation function decays with the lags, and eventually wiggle around zero. As mentioned earlier, the stationary autocorrelation function of is an exponential function with decay rate equal to the speed of mean reversion of , meaning a linearly decaying autocorrelation function on a log scale. We fit a linear function to the first 10 lags, with the estimate . In Figure 1 the estimated line is shown together with the empirical logarithmic autocorrelation function.
Admittedly, the linear fit to the log-autocorrelation function in Figure 1 is very rough. Since the line does not intersect at zero, it cannot be related directly to an exponential autocorrelation function. One may mend this deviancy by considering a sum of exponentials. From Figure 1 we may assume a very steeply decaying autocorrelation function for small lags (up to 2), and thereafter decaying according the fitted line shown in the plot. Even more, after approximately 10 lags the autocorrelation function seems to flatten out, and a new line with a different slope would fit better. This could easily be incorporated into our framework by considering a superpositioning of three processes of the type modelling the volatility. In that case, we would get a theoretical autocorrelation function being the sum of three exponentials, which would be approximately represented as a piecewise linear function on log scale if the mean reversion speeds , , and are sufficiently distinct. This could be attributed to a fast reversion of big volatility changes, whereas the medium to smaller variations in volatility are slowly reverting, say. The estimated would approximately correspond the the mean reversion of medium volatility changes. In order to estimate such a superposition, one must resort to filtering techniques, which are discussed in detail in Barndorff-Nielsen and Shephard [6].
The final step in estimating our temperature model is to fit a subordinator process . This is done by appealing to the ingenious parametrization of by Barndorff-Nielsen and Shephard [6]. By using for a subordinator in the model for , they show that the stationary distribution of is independent of . Thus, the model for the residuals will become a variance mixture model, being a conditionally normally distributed with mean zero and variance equal to the stationary distribution of . For example, choosing the stationary distribution of to be generalized inverse Gaussian, the variance mixture model of the residuals becomes generalized hyperbolic distributed (see Barndorff-Nielsen and Shephard [6]) for discussion on this).
Based on this, we first select and fit a distribution to the deseasonalized residuals, and secondly construct the Lévy process which has the required stationary distribution . The process is called the background driving Lévy process, and Barndorff-Nielsen and Shephard [6] show that the distribution must be self-decomposable in order for to exist. In Benth and Šaltytė Benth [5], a generalized hyperbolic distribution was successfully fitted to the deseasonalized temperature residuals for data collected in several Norwegian cities. In this case, there exists a subordinator such that the stationary distribution of becomes generalized inverse Gaussian. The Lévy measure of can be explicitly characterised in terms of the selected distribution for the residuals.
One may ask whether some or all of the parameters in the specified temperature model may be time dependent. In our empirical analysis of Stockholm data, we have not detected any structural changes in the seasonality function . Furthermore, in an AR(1)-specification of the temperature model for Stockholm, we have investigated if there are any seasonality in the speed of mean reversion (study not reported). Looking at the estimates for particular months over the year, we did not find any pattern defending a seasonality in the speed of mean reversion (or, in the specification of the AR-matrix in our context). However, we refer to the paper by Zapranis and Alexandridis [30] for an analysis of temperature data in Paris, where the authors detect and model a seasonal mean reversion. We have not investigated if any of the other parameters in our model may vary with time.
To understand how fast the temperature dynamics is reverting back to its long-term average , we discuss the notion of half-life of the stochastic process . In Clewlow and Strickland [31] the half-life is defined to be the expected time it takes before the process is returned half way back to its mean from any position. We express this mathematically as the smallest time so that For an Ornstein-Uhlenbeck process (where , and ), Clewlow and Strickland [31] derives that . In the next Lemma we derive the half-life of .
Lemma 5.1. The half-life of defined in (3.9) is given by the solution of the equation when assuming that for .
Proof. First, we have after using the tower property of conditional expectations that Putting equal to yields Assuming for , we find that , and hence the result follows.
Note that the first coordinate of is equal to by definition. For convenience, we let the other coordinates be equal to zero in the above result. In reality, we should estimate the other states of by filtering the temperature data series in order to reveal their value at time zero. This means that the half-life becomes state dependent for higher-order autoregressive models.
For a temperature dynamics based on the Stockholm estimates referred to above, we find the solution to the half-life equation in Lemma 5.1 to be , that is, it takes on average slightly less than six days for today's temperature to revert half-way back to its long-term level.
Let us investigate the contribution from the various terms in the CAT futures price dynamics in order to get a feeling for their relative importance in the context of weather derivatives. For illustrative purposes, we choose a June contract, which starts measurement at time and ends at time (supposing time is measured from January 1). Recall the CAT futures price in Proposition 4.1. The first term with the seasonal function is equal to 191.5. Suppose now that current time is one week prior to June 1, that is, , and let for , but recalling . We set , meaning that the temperature is 5°C above the long-term mean level for that particular day. This leads to a value of 11.8 of the second term, which is around 5% of the value of the mean. By moving time to start of measurement, , we get the value 37.6 of the second term instead, which is close to 20% of the contribution of the long-term function to the CAT-futures price. This shows that the mean reversion of the temperature dynamics towards the seasonal mean function kills the effect of daily temperature variations quickly, and when being far from start of measurement the CAT futures price will be essentially constant (and equal to the seasonal mean for the measurement period). However, as we get closer to the start of measurement, the effect of the temperature variations become gradually more important and will impact the CAT futures price significantly. In Dorfleitner and Wimmer [11], an example of a seasonal futures contract (Chicago HDD winter contract) is presented, where the price is constant except from the last week prior to measurement. Then the observed futures price starts to wiggle. The seasonal function plays a dominating role of setting the level of the price. It is worthwhile to emphasize that the length of measurement period is of importance here. The shorter the measurement period will be, the smaller will the damping factor become, and the more sensitive the CAT futures price will become to variations in temperature. This effect is even more emphasized by the fact that the seasonal term becomes smaller with a smaller measurement period, increasing the relative importance of the second term. With the introduction of weekly futures contracts at the CME, this is an important observation. Obviously, the two last terms with the market price of risk can contribute arbitrarily high or little to the CAT futures price, by adjusting the level of . In a concrete application, one would estimate the from historical CAT futures prices. Referring to the studies in Benth et al. [25] and Härdle and Lopez Cabrera [20], we find that of the size 0.2 is reasonable. Thus, the terms involving will contribute very little compared to the seasonal function and the second term.
Let us investigate the stochastic volatility contribution to the CDD price. As we see from the pricing formula in Proposition 4.4, the influence of the stochastic volatility appears in the expression of , both explicity as , and implicitly via the characteristic function of the subordinator driving the dynamics of the volatility process. If we consider a model with no stochastic volatility, it is natural to suppose that . The function takes the form with defined in Proposition 4.4. Then, we find the difference between the stochastic volatility and constant cases as The first term is stochastically varying with the volatility around one, while the second term is determined by the market price of volatility risk through the characteristic function of . If is slowly varying around its mean, which naturally should be equal to one, then this first term will not contribute significantly. But due to potential jumps in the volatility, we may experience values of significantly larger than one, and thus impacting the futures price. The contribution of the second term depends on how big the market price of volatility risk is.
We are not aware of any empirical studies of the potential existence of a market price of volatility risk. One may estimate in the same way as , by for example, inferring it from minimizing the distance between theoretical and observed futures prices. Motivated by the studies of the market price of risk mentioned above (see Cao and Wei [14], Dorfleitner and Wimmer [11], Hamisultane [15], and Härdle and Lopez Cabrera [20]), one may suspect that the market price of volatility risk will be small and maybe not significant. It is to be noted, however, that even small values of may be big relative to the volatility, and thus modify significantly the effect of stochastic volatility viewed under the pricing measure .
In view of the existence of European-style call and put options written on the temperature futures, precise knowledge of the volatility is important. The volatility of the underlying temperature futures will determine the price of the option and play a crucial role in a hedging strategy of the option. In particular, the Samuelson effect of the volatility of the temperature futures makes the options particularly sensitive to the volatility close to measurement. Hence, a precise model for the stochastic volatility is important. The nonlinearity in the payoff of options also makes second-order effects in the underlying dynamics more pronounced, and thus even small stochastic volatility variations may become significant in the option dynamics.
The authors are grateful for the comments and critics from two anonymous referees, which led to a significant improvement of the original paper. Fred Espen Benth acknowledges financial support from the project Energy markets: modelling, optimization and simulation (emmos), funded by the Norwegian Research Council under Grant 205328/v30.
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This weekend I took a drive up to Monterey for a work conference. The nice thing about business trips in California is that I can drive with Julia, Isla, and Lilly. I booked a nice cottage in Pacific Grove that was right next to a golf course and the Point Pinos Lighthouse. The Point Pinos Lighthouse is the oldest operating lighthouse on the west coast, having been built in 1855. To stay on track for the 52 Hike Challenge this year, I knew I needed to find a hike I could try in the area. Luckily, there is a trail that follows the coast from Pacific Grove to Monterey.
This hike was 6.5 miles round-trip with virtually no change in elevation. The weather in Monterey was foggy for this hike, but that beat the rain we experienced during most of our stay.
Starting at the Point Pinos lighthouse, we walked down Asilomar Ave to Ocean View Blvd. The trail parallels Ocean View Blvd. all the way to Monterey. The first stretch of trail includes the John Denver memorial as part of the Pacific Grove Marine Gardens Park.
There was a huge storm moving into California over the weekend and we could see it's power. There were 15 foot swells powering in from the deep to crash hard on the rocky shores of the peninsula. We get a lot of year-round sun in Southern California, so I was really enjoying the foggy cool weather. Isla and Lilly were having the most fun though. It only took them a few minutes to coat their little legs in mud.
Our first stop for the day came at Lover's Point. This is a very popular spot for visitor of Monterey, and there were a lot of people in the area to enjoy it. There is also a nice little beach shack restaurant with a standard fare menu.
The trail is paved with asphalt from Lover's Point to Monterey, which was nice, as it gave Isla and Lilly a chance to dry off. The beautiful views continued to unfold before us. There were beautiful Monterey Cyprus trees that reminded me of my time living in San Luis Obispo. If you've never seen Monterey Cyprus in person, make sure to take a trip to Montana de Oro, and then head up the coast through Carmel, Pacific Grove, and Monterey.
Just before reaching the city of Monterey we passed the Hopkins Marine Station of Stanford. Hopkins Station was founded in 1892, making it the oldest marine laboratory on the US Pacific Coast. It's beaches offer a protected area for harbor seals, and there were quite a few of them out enjoying the morning.
The Monterey Recreation trail continues on once you reach the city of Monterey, but we decided to stop at the aquarium, and enjoy a quick lunch. We didn't go into the aquarium, as they don't allow dogs, but I'll post some pictures below from a previous trip. If you've never been before, this is a "must see" aquarium.
The outside of the Monterey Bay Aquarium is just as beautiful as the inside. Isla and Lilly were getting a little anxious at this point though, as they didn't like the feeling of being out over the water. That was a good cue to turn back, so we hiked back on the same trail that delivered us to the city of Monterey.
Even though I had to work the rest of the weekend, this little hike put me in a great frame of mind. It also helped that it was foggy or raining while I was working, so I didn't feel like I was missing to much. On the way home, we stopped by old old stompin' ground of San Luis Obipso. Like always, we hit up Firestones for some tritip sandwiches and french fries, then finished the day with a stop by Pismo Beach.

subset: commoncrawl


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How to deal with Amazon Dash, customized content, cross-device user experience, and convergence of sales channels? In a retail business world that's clearly characterized and dominated by rising customer expectations, decreasing brand loyalty, reduced margins and an array of options for customers. Technological innovations provide an answer to these challenges and serve as a distinguishing feature to the competition.
Gartner has analyzed where retailers and marketers invest and what topics they should keep an eye on, disclosing at the same time the topics the industry will probably talk about the most:
Smart, networked devices of the Internet of Things (IoT) era are transforming digital commerce, shifting the buying decision of users to devices (things). An example is Amazon Dash, which was introduced in 2016 and re-orders preferred products at the touch of a button. So, looking at it from that perspective, these devices are a completely new kind of customer. The primitive form of this thing-commerce still needs a manual and explicit action, but once the devices become more sophisticated and users trust them, they will bear more responsibility. Then, it's about recurring purchases, such as consumer goods.
For retailers and marketers, obviously, a new situation arises. Devices will increasingly affect their businesses and will more often have to deal with "things". Consequently, they will have to deliver offers that convince IoT devices.
Personalization is more than ever a hot topic, especially since companies can less and less differentiate themselves by products and price. Instead, they try to stand out from the competition through customer experience. If companies analyze purchase intentions and interests, they can offer the user an added value, as individualized content can be shown, and the customer feels in good hands. A good personalization increases satisfaction and engagement, and increases the conversion rate.
Analysis of the customer journey
Users access different channels and devices on their 'path-to-purchase', as Criteo's State of Cross Device Commerce Report vividly points out: In 2016, one third of online retail transactions involved two or more devices, demonstrating that a good cross-device user experience is essential. Hence, retailers and marketers must optimize the respective channel for individual customer intention as well.
Accurately analyzing the customer journey improves customer satisfaction, translates into more continuity between channels, grants more attribution and user segmentation, and increases user personalization. The goal is clear: If the user is satisfied, he will buy faster.
Convergence of B2B and B2C
The increasing convergence of business models of B2B and B2C commerce is relevant in several ways.
For B2B companies trying to build physical sales channels (sales teams, partner sales teams, support teams, etc.) this convergence promises sinking costs as they are less dependent on existing sales channels. At the same time, an online store additionally increases overall sales and market presence, besides providing a better user experience which in turn strengthens conversions and sales.
On the other hand, B2C retailers can also benefit from the convergence, since they have the opportunity to improve their own purchasing experience with suppliers of raw materials or can strengthen the relationship with distributors and wholesalers based on their commerce platform.
By MediaBUZZ


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After dull 2009, UTV bullish with a dozen projects
Mumbai, Jan 9 (IANS) The year 2009 certainly didn't belong to UTV Motion Pictures. But the production house is bullish about 2010, with small budget films like 'Paan Singh Tomar' to biggies like 'Chance Pe Dance' set to woo audiences.
Mumbai, Jan 9 (IANS) The year 2009 certainly didn't belong to UTV Motion Pictures. But the production house is bullish about 2010, with small budget films like 'Paan Singh Tomar' to biggies like 'Chance Pe Dance' set to woo audiences.
A good chunk of the investment made in the Shahid Kapoor-Genelia D'Souza- starrer 'Chance Pe Dance' - UTV's first release of the year - has already been recovered and its box office revenue is expected to make it a profitable venture.
'The cost of production of 'Chance Pe Dance' is Rs.20 crore (Rs.200 million) while an additional Rs.5 crore has been spent on print and publicity. Given the kind of buzz the film has managed to create, it should be a matter of a few days before this investment is recovered,' said Siddharth Roy Kapoor, CEO, UTV Motion Pictures.
This year too the strategy of mixing up films across genres continues for UTV with a number of small budget films lined up in the next few months.
'We have 'Paan Singh Tomar' (Irrfan Khan), 'Peter Gaya Kaam Se' (Rajeev Khandelwal) and 'Phillum City' all set for release in February and March. We are supremely confident about these films.
'Then we also have bigger films like 'Chance Pe Dance' and Prakash Jha's 'Rajneeti' ready. We have our wheels moving and look forward to an eventful 2010 since we have close to half a dozen other films on the floors as well,' said Kapoor.
Commenting upon last year's poor performance, Kapoor said: 'Yes, we had a lower success rate in 2009. We did introspect the cause of those films which didn't work at the box office, just like we do for those which are successful. In any case, it was a mixed year for the industry in general.'
In fact, 2009 had begun on a good note for the UTV boss and producer, Ronnie Screwvala, with Anurag Kashyap's 'Dev D' finding critical acclaim as well as decent commercial success.
However, biggies like Rakeysh Omprakash Mehra's 'Delhi 6' and Ashutosh Gowariker's 'What's Your Raashee?' and Salman Khan's 'Main Aurr Mrs.Khanna' were setbacks that pegged the production house down to a large extent.
Kapoor refuses to blame the market situation for an unfortunate run.
'It's the audience which decides what they like and what they don't. If some films didn't work, it's a clear case of the audiences not liking them. We take it all as learning. Yes, we will continue to support each of our films and devise the kind of marketing and promotional plans they deserve,' he said.
Known as the messiah of small films, UTV has in the past few years enjoyed great success with 'Khosla Ka Ghosla', 'A Wednesday', 'Aamir', 'Mumbai Meri Jaan', 'Welcome To Sajjanpur' and 'Oye Lucky! Lucky Oye'.
However, luck didn't favour them in 2009 when smaller films like 'Dhoondte Reh Jaaoge', 'Agyaat' and 'Aagey Se Right' didn't earn much from the theatres.
(Joginder Tuteja can be contacted at [email protected])ALSO READ: Sandeep Reddy Vanga reveals why Ranveer Singh turned down doing Kabir Singh


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The Russian military has refuted the Turkish military's claims about the deaths of dozens of Syrian troops in Idlib, saying that Turkey's "irresponsible statements" can only lead to an escalation of the situation and to hastily-made decisions.
"The [Russian] Center for the Reconcilliation of the warring parties draws attention to the responsibility of officials from the Turkish ministry of defence for providing false information to the country's leadership in the Idlib de-escalation zone," the MoD-affiliated Center said in a statement Friday.
"Such irresponsible statements only contribute to the escalation of the situation and to the taking of hasty decisions which do not meet the mutual interests of Russia and Turkey," the Centre warned.
Earlier in the day, the Turkish military reported on the 'neutralization' of 63 Syrian troops. Before that, Ankara reported on the elimination of 101 personnel in attacks on 115 Syrian Army targets in response to Monday's attack on a Turkish observation post in Idlib which killed several Turkish troops.
"Such statements about the 'shelling' of Syrian government forces by units of the Turkish Armed Forces, and moreover, about the deaths of Syrian troops as a result, are untrue," the Centre stressed.
Also on Friday, Turkey's military reported that it had carried out a series of airstrikes against Kurdish-governed areas in northern Iraq, killing six members of the Kurdistan Worker's Party, a Turkish-Kurdish militia group which has been waging a low-intensity guerilla war with Ankara for several decades. Those attacks were said to have taken place in the mountainous area of Qandil.
Repeated Ceasefire Violations
Tensions in northern Syria began escalating earlier this month, after eight Turkish nationals were killed by Syrian forces in an artillery strike on a Turkish observation post in militant-held Idlib province. The Syrian Army began a military operation in Idlib in late 2019 after militants in the region repeatedly violated a ceasefire brokered by Russia, Iran and Turkey in 2017 and claimed the lives of dozens of Syrian troops.
Damascus has vowed to continue fighting terrorist groups in Idlib and throughout the country notwithstanding recent Turkish threats of intervention, and has accused the Turkish government of supporting, arming and training terrorist groups operating in the region.
On Tuesday, a Syrian Army helicopter was shot down over Idlib by Turkish-backed militants believed to be allied to the Nusra Front.* On Friday, Nusra* militants reportedly shot down another helicopter in neighbouring Aleppo province.
Apart from the Syrian Kurdish-controlled area in northeastern Syria, Idlib remains the last major province outside of Damascus's control. In addition to the tens of thousands of militants believed to be concentrated in the region, Idlib is home to hundreds of thousands of civilians. Syrian forces have accused the terrorists of using civilians as human shields, while Ankara has voiced concerns over the prospect of hundreds of thousands of refugees flooding into southern Turkey amid ongoing military operations in the region.
On Thursday, amid deteriorating relations between Damascus and Ankara, Syria's parliament unanimously passed a motion recognizing the 1915-1923 ethnic cleansing and massacre of Armenians, Syrians and Assyrians by the Ottoman Empire. Turkey broadly condemned the gesture and accused Syria of "hypocrisy."
* An al-Qaeda-affiliated terrorist group outlawed in Russia and many other countries.


text:
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Berg Collection, New York Public Library. Not previously published.
These letters were edited with the assistance of Carol Bolton, Tim Fulford and Ian Packer
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I thank you for your enquiries for my brother. he arrived here this
morning soon after your letter, from which you will readily conclude that his wounds are slight & in a fair way. he has three
wounds, made with a pike in an attempt to board L'Hercule; his escape was almost miraculous, he fell at the second thrust between the
two ships, & caught a rope as he fell.
Mars and the French ship L'Hercule on 21 April 1798.
Poor Captain Hood is much regretted by all who knew him, my brother had experienced uncommon kindness from him, & he attended him to his grave.
I have been daily in expectation of your promised visit to Bristol, & this has kept me silent. you would however
have heard from me this week, as my book
We were under considerable anxiety when first we heard of the engagement, but it was fortunate that the first account we saw of his being wounded was by his own letter.
I shall be happy to congratulate you in June.
our remembrances to your mother – & believe me
I trust you will spare me a day when you visit Bath.


text:
White Claw Earrings
$14.00 Sale • Save
Spark joy in your day to day with this pair of Tiny Toy Earrings, handmade in Arlington, VA. Sterling Silver/ Sterling Gold Hooks featuring a miniature resin White Claw charm, designed for charm from every angle.
Product Details:
METAL: Sterling Silver Hook
MATERIAL: Charm made from resin
WEIGHT: 2 grams per earring.
Please note: Due to the one-of-a-kind nature of the medium, exact colors and patterns may vary slightly from the image shown.


text:
Written by Margie from get plus followers
Instagram is a solid social media network to help you increase your reach with your target audience.
From the pictures and videos, you have dynamic visuals to help you create more intriguing content.
Here are some ways Instagram's new features can help you widen your audience.
Utilizing Instagram's Stories Stickers
Whether the topic is finding coworking spaces or the best ingredients to use for soup, Instagram stories stickers can increase your engagement.
You can write a question, and people can respond in the box. You can post their answers and help get more out of your Instagram stories.
If you're trying to get feedback on your products, you can ask people their opinions about your offer.
Also, ask them about specific things they want to see from your brand. It'll increase your brand engagement and give you ideas on how to move forward with your business.
When you listen to your audience, it'll help you increase your leads and sales.
Also, you have a way of grabbing their attention and making them feel a part of your brand. Use the IG Stories sticker feature to help you bridge the gap between you and your following.
Save Your IG Live Posts
Some people don't have the time to spend an hour or so on your feed when you go live on Instagram.
They may miss topics that you discuss and want to refer back to them at a later date. The best thing you can do is post it in your IGTV section.
You can make a short story and even encourage people to send themselves a notification on their phones. It'll help them get ready for the next time you're on Instagram live.
When you save your posts, it increases engagement.
You'll have more comments and more chances to respond to like-minded people.
Also, you can begin to see what posts get the most traction and how people view your content.
Create a Schedule That Reach
You can get creative with how you post consistently on Instagram. If you're doing an interview-style series on Instagram, you can post the person you will talk to on Monday.
Maybe you can even get a few video clips of their music or a few words from them.
On Wednesday, you can reiterate with a biography and links to their profiles.
Thursday, you can go live and do some promotions and ask people what they want to know about the artist.
Friday, you can do the interview and make it an event where people have their favorite drink during happy hour and get some of their questions answered. Not to mention, you can have people write questions live on the chat.
Posting Instagram Reels
You can start creating Instagram reels, which can advertise your content. Maybe you have a contest and use a big brand to sponsor it.
You can summarize what you're doing and then have all of the information in the caption section.
Also, you can tag the brands, which gives them more traffic by default.
Reels get more attention on Instagram due to the algorithm favoring the content with the most interaction. You can cross-post these things on different social media networks.
You'll create a more well-known Instagram profile by having consistent video, photo, and written content.
Utilize Instagram's features to help you build a strong following on your social media networks.
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Do you want to share your content ideas on my blog? Contact today.


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The plot thickens, but doesn't it always?
New documents have emerged detailing former Trump national security adviser Michael Flynn's financial ties to Russian companies, including the U.S. subsidiary of Russian cybersecurity group Kaspersky Lab.
One invoice form dating back to 2015 shows payments to Flynn made by three Russian entities: $33,750 from state-sponsored news source RT TV, $11,250 from Volga-Dnepr Airlines and $11,250 from Kaspersky Government Security Solutions, Inc.
According to its website, the U.S. arm of Kaspersky Lab "designs, implements and delivers holistic cybersecurity services and solutions for the U.S. government, U.S. government contractors and the U.S. National Critical Infrastructure sector."
In response to the revelation, Kaspersky Lab stated that it paid Flynn the amount as a speaker fee for his appearance at the Government Cybersecurity Forum in 2015. As Business Insider reports, the event's other keynote speaker, U.S. Rep. Michael McCaul did not receive a payment to speak at the event.
Kaspersky is one of the most prominent names in cybersecurity, but the firm has faced scrutiny in the past over founder Eugene Kaspersky's speculated ties to Russian intelligence agencies. According to the company, Kaspersky Lab "has no ties to any government, but the company is proud to collaborate with the authorities of many countries, as well as international law enforcement agencies in the fight against cybercrime."
The documents were published today by the House Committee on Oversight and Government Reform, accompanied by a letter from ranking Democrat, Rep. Elijah E. Cummings.
"I cannot recall any time in our nation's history when the President selected as his National Security Advisor someone who violated the Constitution by accepting tens of thousands of dollars from an agent of a global adversary that attacked our democracy," he wrote.
As a result of his involvement with Russia, Flynn's remarkably brief 24 days in Trump's cabinet have already come to a close, but Flynn could still face consequences from rules designed to prevent retired officers from receiving payments from foreign governments.


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The record keeping needs of your business must be analyzed to determine the best bookkeeping system. All systems should provide the following information:
Each business has special needs that must be considered when establishing a bookkeeping system. Factors you should take into account include: legal structure of your business, your industry, the number of employees you have, the number of product lines or services and the number of locations your business operates.
The first step in setting up a bookkeeping system is the selection of the tax year or year end. The term "tax year" refers to the annual accounting period. The selection of a tax year is sometimes dictated by your legal structure. For instance, a C Corporation has no specific restrictions. However, S Corporations, sole proprietors and partnerships must usually follow a calendar year. Be sure to consult an expert before making a decision, since tax laws are subject to change.
The second step is to select the method of accounting. The most common are the cash method and the accrual method. The cash method recognizes income and expenses when the cash is received or disbursed. It provides the most flexible means for deferring taxable income into future tax years. The accrual method recognizes income and expenses based on when income is earned or an obligation to pay a debt is incurred. It generally provides better matching of revenue and expenditures.
The method of accounting that will be best for you will be determined by your business operations. While these are the two most common methods of accounting, there are specialized methods that may be used in certain industries. You may want to consult a tax advisor to determine the best method for your business. Once a method of accounting is adopted on the initial tax return, it can be changed only with the permission of the IRS. Permission is usually granted if switching from the cash method to the accrual method, and routinely denied for the reverse, although recent developments have facilitated the accrual and cash change.
The proper accounting method and maintenance of your records will help:
There are two basic mistakes that many business owners make when setting up their bookkeeping. The first occurs when the owner doesn't understand the importance of proper records and ignores the need to establish a record keeping system. Such business owners tend to use the "shoebox method" as they allow receipts, invoices and bills to accumulate in boxes or piles. The second mistake is overkill. The owner invests in an expensive array of hardware and software to maintain his/her records which ends up being too complicated to use. This should not imply that computers are ineffective tools in a bookkeeping system. Rather, it is important to invest in a system that can be easily operated and that meets the needs of your business.
Cash is absolutely critical to the growth and well-being of your business. You must plan and prepare for all future events and market changes. The most important aspect of planning and bookkeeping is effective cash flow management. Failure to properly plan cash flow is a leading cause of business failure. Understanding your cash flow is important for five reasons.
First, you will need cash to pay your fixed costs, such as rent, utilities, credit payments, etc.
Second, most businesses have seasonal cycles. For example, a retail business will probably have increased sales around Christmas; however, this will require a build-up in inventory in the fall when sales and cash flow may be slower. It is important to set aside funds for these changes in revenue and inventory.
Third, it is important to save for long-term investment and capital purchases, such as a new vehicle or a piece of equipment.
Fourth, you must have cash available, or a sufficient line of credit, for all emergency situations.
Fifth, pay attention to the impact of necessary tax payments.
Failure to properly plan for all five will damage both the short-term and long-term potential of your business. For example, you must frequently keep inventory on-hand in anticipation of potential clients, or you must purchase supplies for a contracted project weeks or even months before you receive payment for these goods. While it is important to have the necessary cash available to pay your bills, regardless of when your clients pay you, excess cash may be an indication of "idle money" with a potential for a greater return if invested in another part of your business.
Credit plays an important role in your cash flow — both the credit you receive from your suppliers and the credit you extend to your clients. If you do not pay your debts in a timely manner, it can reduce your access to credit in the future. Limiting your clients' ability to purchase on credit increases your short-term cash flow but may limit your customers' ability to make larger purchases in the long-term. A liberal credit policy can increase your sales. However, the increase in sales must be balanced against the cost of administering a credit program including collections and bad debts.
If you sell on credit, establish a credit policy and stick to it! It is important that your customers sign a contract or a credit application. State when interest will begin to accrue and disclose the specified interest rate and terms for balance due. Clearly disclose your right to sue or arbitrate in your home county. The contract should state that you are entitled to recover attorney fees and court costs.
Consider offering a discount for businesses that pay by cash or within X number of days of invoice. This may slightly reduce your revenue but will ultimately increase your cash flow as it encourages customers to pay in a more timely manner, and reduces the cost of administering your accounts receivable and the level of unpaid accounts.
You must register as a finance company if you extend credit to your non-business customers. Registration is completed through the Uniform Consumer Credit Code (UCCC), Colorado Office of the Attorney General, 1525 Sherman Street, 5th Floor, Denver, CO 80203. Credit sales between two businesses are considered private contractual agreements and are not subject to the UCCC.
It may be required to be in business for a period of time before you will be able to accept major credit cards. Credit cards are normally processed by banks. Contact your bank for more information on credit card policies or for a referral to a credit card processing service. Credit card processors collect a fee for processing credit card payments, usually a percentage of the sale which obviously reduces your cash flow. Take care to shop and compare the costs of these services.
Pricing and Sales Strategies
Your pricing strategy is an important part of your firm's cash flow and profitability. You must clearly understand your market, the competition and your customers to determine the proper price for your products or services. See the Marketing chapter of this guide for more information. A common mistake is to simply track and focus all efforts towards increased sales. While this might appear to increase cash flow – be careful. If your customers purchase on credit, you may simply reduce inventory without any cash to replenish stock for the next customer. Another problem occurs when sales increase beyond your capacity to satisfy your customers in a timely fashion. As a result, your sales increase in the short term, but your customers are less likely to provide repeat business or give you positive referrals. Remember, more sales don't always equal more profit!
There are several options:
This should be the choice if your business is extremely simple, has few employees, a single location, few products or services, and if it requires only a small part of your time or if you have a strong background in accounting principles.
If your basic bookkeeping system is simple and you require few or infrequent financial reports, a bookkeeper may be all that you need. The more complex the needs of your business, the more likely you will require an accountant. Both bookkeepers and accountants can be hired as employees or independent contractors depending upon the type and amount of assistance desired/or needed.
These services usually compile receipts, canceled checks and invoices, then process the data and prepare financial statements. This type of service is used when the business is more complex and requires a more sophisticated method for maintaining records, but can be cost effective when compared to an employee.
While a computer installed with a user friendly bookkeeping computer program can be a very important and useful tool, it does not replace self-education or the services of a bookkeeper or accountant.


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7 Key programmatic advertising trends for 2016
Programmatic advertising hit the mainstream in 2015, offering marketers a whole new way of reaching their audiences more effectively online. In 2016, programmatic advertising will continue to grow, develop and continue to be central to digital marketing. With this in mind, we've taken a look at some of the emerging trends and patterns to see what digital marketers and advertisers can expect from programmatic advertising in 2016.
1. Programmatic spending will be huge
Spend on digital advertising has increased year on year. In 2016, we will see the programmatic spending increase even further. Emarketer predicts that the UK programmatic ad spending alone will exceed £2 billion, a 37% increase in spending compared to 2015. Programmatic spend in the UK in 2016 will account for more than 50% of the total display advertising spend. The growth of programmatic mobile advertising has been particularly notable, with eMarkter predicting that around 75% of all mobile inventory to be bought programmatically in 2016. The UK is now considered to be the most advanced market when it comes to programmatic buying, and surely it will not be long before other markets follow this pattern too.
A rise in spending will also mean an increase in the competition. Programmatic providers will have to provide a better experience for both publishers and advertisers and overcome many of the challenges that were central to the programmatic advertising conversation in 2015. One of the fundamental arguments is that programmatic advertising is complicated and, therefore, making programmatic advertising less complicated for advertisers may be key in help marketers increase programmatic spend further. However, with a continually expanding ad tech space which includes advanced programmatic techniques, this won't be easy.
2. Increased creativity will lead to new inventory
In 2015, we saw somewhat of a display advertising renaissance, with programmatic advertising being one of the catalysts for this. Programmatic advertising has sparked creativity when it comes to advertising inventory, and today there is more variety than ever when it comes to online ad space. This year there will be more creative inventory available for publishers in a bid to create more viewable and engaging display ads. Increased creativity will not only be on the buying side of things but on the production side too. As more and more formats are made available to advertisers, advertisers will want it to be easier to create banner ad campaigns. Since Flash is no longer to go-to option for display advertisers and designers to build banner ads, in 2016 we will see those who create display ads need a platform to create campaigns in HTML5. However, this platform needs to be more that Flash translated to HTML5; advertisers need something that works well with programmatic buying; giving them the opportunity to scale-up campaigns quickly and build new formats with ease. With more creativity on the cards, we'll also see more talk about the programmatic creative.
Therefore, advertisers will be looking for innovative programs that look at display advertising in a whole new light, with a more interactive web in mind. Advertisers are moving away from static banner campaigns, and moving increasingly towards video and rich media banner ads - banner ads that perform better. While programmatic buying provides the opportunity to get creative with advertising inventory, display advertising production needs to catch up for programmatic buying to truly be a success.
3. Header bidding will become more accessible
Header bidding is one of the most advanced and technically sophisticated examples of programmatic advertising that started to get popular amongst publishers in 2015. Header bidding still faces a lot of challenges, mostly concerning usability. But, 2016 may be the year to overcome these as advertisers, as well as publishers realise the benefits of this technology.
4. 100% viewable ad impressions for sale
Ad viewability has been central to a lot of the programmatic discussion, as well as in the general debate surrounding the effectiveness of online display advertising. Last year there was a lot of debate about ad viewability, including the release of a critical report by IAB. One the key point was that advertisers when buying programmatically, had no idea if their ad impressions had been viewed by human eyes.
In 2015, 100% viewable ads became something of the holy grail of advertising inventory, with advertisers wanting more industry standards put in place. Google is already taking the lead in this area, by offering these types of impressions. This seems like a natural development for programmatic, not only will it mean that advertisers will be able to trust their programmatic platform more, but publishers will be able to treat this ad space as premium inventory. In an ideal world, we would see programmatic ad impressions with 100% viewability become the norm, but it may become a luxury product instead.
5. Programmatic everywhere, in every channel
Cross-channel advertising campaigns have always been difficult to execute due the sporadicity of advertising channels. In 2015, we saw the rise of programmatic not only on the desktop but also on mobile and TV. Advertisers found that cross-channel programmatic campaigns could be successful in 2015, and in 2016 they are planning to increase their budgets for this area.
6. Move towards ROI, away from awareness
Advertisers have used display advertising quite frequently for awareness campaigns, besides, from click-through rates have not been able to understand the impact of their display advertising campaigns. Due to advancements in marketing technology, marketers are focusing their efforts of the ROI generated. Marketers are moving the focus of their display advertising campaigns away from awareness and towards ROI. Advertisers say that one of the primary benefits of programmatic is an increased ROI. With ROI reporting in display advertising, programmatic advertising becomes incredibly important as it allows advertisers to increase their ROI through more effectively targeting their different audience segments. Which is not only good news for advertisers, but provides a better experience for the consumer.
7. Moment Marketing
Moment marketing will be one of the marketing trends that will shape 2016. Think of moment marketing is less planning and more marketing for the moment online, triggered by offline events. Understandably, moment marketing is popular in social media channels. For display advertisers, however, this has never been a reality for two reasons: firstly, creating banner ads has always been a long and arduous process and totally inflexible, before programmatic advertising it was impossible for marketers to market in the moment because they were forced to buy their advertising inventory in advanced and, therefore, couldn't change their banner ads or react to offline events once their campaign was published. However, programmatic advertising allows advertisers to buy ad inventory on an impression by impression basis, meaning that they can push their campaigns to the right people, at the right moment.
The area of programmatic advertising is continually expanding and becoming increasingly complicated technologically, and for users. In 2016, we'll more trends emerge, many of these focusing on making the programmatic experience better for marketers and their audiences. However, for marketers and advertisers it is important not to get overwhelmed, but instead, focus on your overall goals and then looking to see how technology can help you to reach them, rather than letting technology dictate the way you work.
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A butterfly can taste with its feet, ants tap each other with their antennae to talk to each other, and male stalk-eye flies attract a mate with their big round eyes. These are just a few fun facts shared by the WA Museum at various sites across Perth while the New Museum for WA is under construction in the Perth Cultural Centre. The Foundation's partnership with Quadrant Energy has helped to create a transportable, secure, multi-use 'Museum in a Container' that has appeared at the Perth Royal Show and the Awesome Festival over the October school holidays. Kids of all ages had the chance to create and build their own bugs of all shapes and sizes.
The 'Museum in a Container' engages with local communities at various sites including festivals, fairs and other community events. Upcoming events include:
- Saturday 27 October, 10am to 4pm, 2018 Maritime Day, B-Shed, Fremantle
- Saturday 10 & Sunday 11 November, 10am to 6pm, Act Belong Commit Bonjour Perth 2018, Market Square Park, Subiaco


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Bloomington, IL —
Michael Tipsord, CEO of insurance giant State Farm, has been making headlines this week for his controversial revelation that the entire company was founded solely to pay homage to the USSR's agricultural sector reforms.
"In the 1920s, when State Farm was founded, there were food shortages in Russia. The great Stalin launched a violent offensive against the rich land owners who were hoarding all the grain. This turned a nation of individual exploitative farms into one collective, prosperous…State Farm. We thought that was just so great, we decided to make an auto insurance company in honor of it. From car insurance to mutual funds, everything we do, we do for Papa Joe. May the kulaks rot in their graves." – Michael Tipsord, CEO of State Farm.
When Tipsord was asked how this agrarian policy related in any way to an insurance company, he doubled down on his beliefs. "I don't get why people are surprised to hear this. We have nothing to do with states or farms. Communists are the guys with state farms. This philosophy has guided us on every level, from the boardroom down to the janitors. We would absolutely resort to violence if it meant giving the people true liberation – liberation from our competitors' exorbitant fees and poor customer service, that is. We believe that Lenin, Stalin, and even Trotsky would have approved of our business model and corporate social responsibility initiatives. Like a good neighbor, State Farm is there to crush capitalism."
The interviewer asked, "Do your anti-capitalist beliefs interfere with your job at a large corporation?"
"Look," continued Tipsord, "it's like China. Sometimes, in order to build socialism, you have to play the game, embrace the markets, and accumulate wealth and power. But rest assured: Our goal is to guide the masses through their class struggle, provide them a revolutionary outlook drawn from Marxism, and ultimately, to completely smash the bourgeoisie. And if we're able to offer auto insurance discounts and competitive rates in the meantime – well, what a gift to the proletariat that is."


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ATV Unit
The All-Terrain Vehicle (ATV) Unit of the Harwich Police Department is tasked with detecting and deterring the operation of illegal off road vehicles on public and private properties in and around the Town of Harwich, as well as to provide assistance during search and rescue operations. It also is used for patrolling beaches and wooded areas where a patrol cruiser may have difficulty gaining access. The all-terrain vehicles' ability to travel in areas hard to reach by conventional vehicles will allow the officer to cut response time dramatically.
The ATV unit is made up of seven members of the Harwich Police Department. Each member had to attend a Massachusetts Criminal Justice Training Counsel approved course hosted by the MA Environmental Police. This course entailed not only the operation of the ATV's under different situations but also familiarized each officer with the machine and stressed safety at all times.
Sgt. Paul Boorack is the supervisor in charge of the ATV Unit.
The Harwich Police Department has two 4X4 ATV's which the department acquired through a Community Policing grant. Through the same grant process, the department was able to purchase a trailer, which is used to store the ATV's and make their deployment easy anywhere within town or to assist other agencies.
To learn more about the use of ATVs and other recreational vehicles in Massachusetts check out the following links:
Massachusetts Environmental Police
Massachusetts Energy and Environmental Affairs – list of authorized riding areas
Massachusetts State Law concerning the use of Off Road Vehicles


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I've been looking at the offensive line this week, but I jumped over to the defensive line after reading this tweet from Greg Bedard about Green Bay Packers DE Johnny Jolly and his low rating via Pro Football Focus. Obviously he's got some legal problems (and still hasn't signed his restricted free agent tender). If he doesn't sign by June 15th, then the Packers could lower the dollar amount. His only threat at that point would be to sit out the 2010 season, such as these guys threatened to do. While not a great player, he's remained solid during his career and well worth keeping as long as they control his rights. But whether it be over concerns about his play or ongoing legal problems, the Packers haven't stood pat. Who might play at left DE other than Jolly?
NT Ryan Pickett. While NT B.J. Raji played a lot at left DE in 2009, it was Pickett who was playing the position last month in practice. Though the most likely reason for the switch was to get Raji more time in at nose tackle, Packers.com now lists Raji as a NT exclusively while Pickett is a DE/NT. The player that isn't starting at NT will have the first shot at replacing Jolly at left DE (if he has to be replaced).
DE Mike Neal. The Packers 2nd round pick was a surprise selection in April. As a high draft choice he has to be considered an option to see playing time at left DE in 2010. However, it's not clear whether he'll be groomed at right DE in case DE Cullen Jenkins leaves in free agency after his four-year contract expires. I assume he'll receive reps on both sides.
DE C.J. Wilson. Same things that were said about Neal apply to Wilson (except the high draft choice part). On paper they're almost identical (6'3" and 290 lbs.). It's possible he's a hidden gem, but there usually is a good reason why players are undrafted until the 7th round. He'll need to have a solid training camp just to make the roster or practice squad, and he won't be given as much room to error as Neal will have.
DE Justin Harrell. He's at practice now which is more than you can say he did last year. It's hard to count on him, but I'm also mentioning him as only the 6th option. If he can stay healthy and on the field, maybe he can show us why the Packers selected him in the 1st round in 2007.
None of these names jump out as a star defender, but they're being asked to do the dirty work and occupy blockers so one of the linebackers can make a play. The likely starter isn't obvious, but that helps give any of these players a chance to win the starting job in training camp.


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EcoFlow AC Charging Cable
A 1.5m AC wall outlet charging cable to charge an EcoFlow DELTA or RIVER series power station
Use Case
To recharge an EcoFlow DELTA or RIVER series power station, use the charging cable to connect the unit to a wall outlet in your home or garage. Great for plugging in to outlets that are hard to reach.
Inside the Box
1x AC Charging Cable
- Type: AC Charging Cable
- Length: 1.5m