I am pretty confused about the ARCH model and forecasting of stock prices / stock returns. I have read some literature about forecasting with different models (AR,MA,ARMA) and i get the concept of them and I also implemented them on a time series (of a stock price in R). Now i want to do forecasting with a ARCH model but all I can find in the literature is the forecasting of volatility of a time series but not on forecasting of the time series itself. Is it even possible to do such a forecast with the ARCH model? And if so can you explain to me how i should approach?
I am confused. I don't understand the difference a ARMA and a GARCH process.. to me there are the same no ?  Here is the (G)ARCH(p, q) process  $$\sigma_t^2 =      \underbrace{     \underbrace{      \alpha_0       + \sum_{i=1}^q \alpha_ir_{t-i}^2}     _{ARCH}        + \sum_{i=1}^p\beta_i\sigma_{t-i}^2}     _{GARCH}$$  And here is the ARMA($p, q$):  $$ X_t = c + \varepsilon_t +  \sum_{i=1}^p \varphi_i X_{t-i} + \sum_{i=1}^q \theta_i \varepsilon_{t-i}.\,$$  Is the ARMA simply an extension of the GARCH, GARCH being used only for returns and with the assumption $r = \sigma\varepsilon$ where $\varepsilon$ follows a strong white process?
Calculating size of particular area below buffer in QGIS? I have a point shapefile of villages where data was collected in Northern Kenya. I created a buffer around those villages.   The second vector layer contains polygons defining areas according to vegetation type. So for example, a forest might be surrounded by a narrow ring of woodland in an area which is mainly grassland. I'm trying to obtain a percentage of each vegetation type within the buffer per village.   I'm using QGIS 1.7 Why marinade meat with acid or enzymes? Shutdown and User button missing in panel I faced with a problem after update,   I missed 2 buttons from above panel, System menu (including shutdown, suspend &amp; …) and User (including log out &amp; …)  how can I restore them !?... Individual Phase shift provided by Op-Amp in Closed loop configuration The plugin generated X characters of unexpected output during activation (WordPress) Are there any add-ons that will cause a browser to automatically refresh a page when a particular file changes on disk? For $x,y\in I:=[0,1]$ define the relation on $I$ as $x-y\in \Bbb Q$. How big (using cardinal number) is the cardinality of the equivalence class $[1/\sqrt2]$?  I have tried to solve it by finding the equivalence class but I'm not sure about the method that I can solve the question. Please, can you help me to solve it. Fibonacci divisibilty properties $ F_n\mid F_{kn},\,$ $\, \gcd(F_n,F_m) = F_{\gcd(n,m)}$ Can any one give a generalization of the following properties in a single proof? I have checked the results, which I have given below by trial and error method. I am looking for a general proof, which will cover the all my results below:   Every third Fibonacci number is even. 3 divides every 4th Fibonacci number. 5 divides every 5th Fibonacci number. 4 divides every 6th Fibonacci number. 13 divides every 7th Fibonacci number. 7 divides every 8th Fibonacci number. 17 divides every 9th Fibonacci number. 11 divides every 10th Fibonacci number. 6, 9, 12 and 16 divides every 12th Fibonacci number. 29 divides every 14th Fibonacci number. 10 and 61 divides every 15th Fibonacci number. 15 divides every 20th Fibonacci number. Label legend interval with number of elements in ArcMap? I have made a series of  in ArcMap 10. When I classify the interval the bottom of the dialogue tells how many elements are in the class.  Is it possible to have this number automatically places beside my class labels? A murder of crows? I love the subset of collective nouns known as the terms of venery. These are collective nouns specific to a particular group of animals. Some of the more inventive examples are: a murder of crows, a crash of rhinos, a mischief of mice, and a puddling of ducks (specifically swimming ducks).  Is there a standard for these group names and is there a central reference for them as with other zoological taxonomy?  I can see in the Wikipedia articles that the practice has its origins in Medieval Hunting tradition, but the Kangaroo (Mob), for instance would have been unknown at that time, so how do new collections come into being? By default, all browser instances use the same cookie for the same site. Is there a browser that doesn't follow this?  Or is there a Firefox plugin that can "wear" different cookies for a specific site? Proof that all abelian simple groups are cyclic groups of prime order Taylor expansion for $\arcsin^2{x}$ I stumbled upon this particular expansion that was included in  post.    $$ \displaystyle \arcsin^{2}(x) = \frac{1}{2} \sum_{n=1}^{\infty} \frac{1}{n^{2} \binom{2n}{n}} (2x)^{2n}$$    This caught my eye because I remember trying to derive a Taylor series for $\arcsin^{2}(x)$ a while ago without much success.  Can anyone prove this or point me to a material that would show a proof of this identity?  EDIT :  Feel free to use any mathematical apparatus at hand. I'm not interested in a proof fit for a certain level, nor am I looking for utmost elegance (though that would be lovely). On an Android phone the wallpaper spans across all of the home screens.  So what size should pictures be to fit properly as custom wallpapers? Unknown error: '' ("The cache has no package named wine-staging-i386") Boy Born on a Tuesday - is it just a language trick? Is it possible that using jQuery, I cancel/abort an Ajax request that I have not yet received the response from? How do you performance test JavaScript code? Algebra of LDA. Fisher discrimination power of a variable and Linear Discriminant Analysis Apparently,     the Fisher analysis aims at simultaneously maximising the   between-class separation, while minimising the within-class   dispersion. A useful measure of the discrimination power of a variable   is hence given by the diagonal quantity: $B_{ii}/W_{ii}$.     I understand that the size (p x p) of the Between (B) and Within-Class (W) matrices are given by the number of input variables, p. Given this, how can $B_{ii}/W_{ii}$ be a "useful measure of the discrimination power" of a single variable? At least two variables are required to construct the matrices B and W, so the respective traces would represent more than one variable.  Update: Am I right in thinking that $B_{ii}/W_{ii}$ is not a trace over a trace, where the sum is implied, but the matrix element $B_{ii}$ divided by $W_{ii}$? Currently that is the only way I can reconcile the expression with the concept. Can you use Wish to duplicate a spell at a higher level? Wish allows you to duplicate the effects of any spell L8 or lower. Does that include a lower-level spell, cast at L8? Say, as a Wizard, casting Heal at L8.  I'm leaning towards yes, but it wouldn't be the first time I assume the wrong answer...