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16

First, Garch models stochastic volatility. Thus its use should be limited to estimating the volatility component. The difference in some of the volatility models is the assumption made of the random variance process components. I believe it has been popular because it is an extension of the ARCH family of models and it is relatively easy to setup and ...


11

You may want to first broadly categorize volatility models before comparing between them within each class, it does not make sense to compare standard deviation models with an implied vol model. I would broadly classify as follows: Historical realized volatility: Those include standard deviation (sum of squared deviations), realized range volatility ...


10

I think there are a lot of different ways to specify this problem. For simplicity, consider independent Garch processes $$ r_{1,t} \sim N\left(0,\sigma_{1,t}^{2}\right) $$ $$ \sigma_{1,t}^{2} = \beta_{1,1}+\beta_{1,2}\varepsilon_{1,t-1}^{2}+\beta_{1,3}\sigma_{1,t-1}^{2} $$ and $$ r_{2,t} \sim N\left(0,\sigma_{2,t}^{2}\right) $$ $$ \sigma_{2,t}^{2} = ...


7

Okay just to wind things down here, I think an important clarification is needed if readers might come and seek to a similar solution. The Geometric Brownian Motion (GBM) is a model of asset prices dynamics which is usually given as follows: $$ dS_t = \mu S_t dt + \sigma S_t dB_t$$ where $B_t$ is a standard brownian motion which has several important ...


6

The general procedure is to start out simple, real simple, and build your model up only as necessary. AR(q), q=0 to start with. Test the lagged autocorrelations of the error terms, and increase q until they are no longer significant. Test for ARCH, and if it's significant, you have an ARCH(q) model. Then move on with GARCH(1,q), GARCH(2,q), and when the ...


5

I'm guessing, and correct me if I'm wrong, you want to create a number of possible paths the stock price could follow with the local volatilty given by GARCH depending on the simulated history, or in pseudocode: N <- numberOfPaths T <- numberOfSteps for (i in 1:N) { newSeries <- pastPrices for (t in 1:T) { epsilon <- normrnd(0,1) ...


5

You can have a look at rgarch. It's quite versatile. From what I remember, you have to get it explicitly from R-Forge, as it's not available from CRAN. See the rgarch website for more details. Last time I checked, usage was something like this: spec.gjrGARCH = ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(1,1)), ...


5

ARCH and GARCH are, by essence heteroskedastic models, that is, with non-constant volatility. If you fit these models to your sample, it will provide you with a time series of the volatility for each point (you can construct it actually). If the values are not the same for all $t$, then the volatility is not constant, according to these models. What you ...


4

You want to set the parameter n.roll to the number of n.ahead, n.roll rolling forecasts you want. (The n.ahead parameter controls how many steps ahead you want to forecast for each roll date.) Thus by setting n.roll to a number almost equal to your sample size, and critically setting the out.sample parameter almost equal to your sample size, you're telling ...


4

I think there is some room for improvement here. 1. GARCH GARCH models are appropriate for modeling time series that exhibit a heavily-tailed distribution and display some degree of serial correlation. That's not the case. GARCH is used for modelling series where there is serial correlation in variance, not in actual observations. And heavy tails ...


4

There is no one right answer to this question, but a common starting place is to compare the bias and variance of the forecast vs. the realized variance. Take your forecasted variance $\hat y$ and regress them against the realized variance: $y = \beta_0 + \beta_1 \hat y + \epsilon$ A few things that you want to see: The forecast should be unbiased, ...


4

The return equation is just an econometric equation that models stock returns (or other asset returns) as a function of: (i) intercept (i.e. the average return), (ii) some independent variables/features, (iii) noise that has zero mean and time-varying variance. There are sometimes other things in the return equation too that form more advanced models. The ...


4

Ah, this is becoming a common question, just in R now. Please look at this [question] (GARCH model and prediction), it has R code to do the prediction. In brief, you keep predicting one day ahead. $\sigma_{t+k}^2 =w+\alpha u_{t+k-1}^2+\beta \sigma_{t+k-1}^2$. You already know $ w,\space \alpha \space and \space \beta $ the starting values are the last ...


3

To quickly answer and address your first question. ARMA - Fractionally integrated GARCH or FIGARCH is one of the more common methods used at higher frequencies, it handles some properties required for higher frequency that standard ARMA-GARCH does not There are also a few other so called long memory volatility models, and there are other models which i ...


3

Squaring normally distributed variables results chi-square distributions, which (as you imply) is why the chi-square distribution is used in hypothesis tests for the variance. If you estimate a Garch model and obtain the conditional variance at every point in time, you could use a chi-squared hypothesis test to ask a question like is the variance in a ...


3

I don't use Stata often, but the help() function is typically very good. Try help(garch). It looks like the command is garch _depvar_ _indepvars_ _options_ Here's the help page on the web.


3

You need to find the values of the GARCH parameters which fit best your data. To do so, you usually create a function simulating a GARCH simulation taking, as input the parameters, and you run it through an optimizer to that the sum of the squares of the differences of the simulations points and the sample points are minimal. Note that it will not give you ...


3

Fitting a time series on a given stock is really trade off between statistical risk and model error. If your time series is too short then your statistical error will be high. If your time series is too long, then the distribution of the market will probably have changed, and the your model error will be high. 5000 days is about 20 trading years. There is ...


3

Basically he's just saying that you don't have to estimate parameters assuming they're the same in every period. Arch and Garch parameters are typically estimated via maximum likelihood. In MLE, parameters are estimated by $$ \theta \equiv argmax\left\{ \sum_{t=1}^{T}ln\left(f\left(x_{t}|\theta\right)\right)\right\} $$ where $\theta$ are some parameters ...


3

$$ E\left[ {{y_t}|{{\cal F}_{t - 1}}} \right] = E\left[ {{\sigma _t}{z_t}|{{\cal F}_{t - 1}}} \right] = {\sigma _t}E\left[ {{z_t}} \right] = 0 $$ $$ {\mathop{\rm var}} \left[ {{y_t}|{{\cal F}_{t - 1}}} \right] = {\mathop{\rm var}} \left[ {{\sigma _t}{z_t}|{{\cal F}_{t - 1}}} \right] = \sigma _t^2{\mathop{\rm var}} \left[ {{z_t}} \right] = \sigma _t^2 $$ $$ ...


2

CRAN has a few: bayesGARCH gogarch ccgarch


2

I am going to supply an answer that is quite similar to SRKX's (which is very very good) because I want to discuss in more detail a few important things. First, you cannot use a stochastic volatility model for the SDE that you've provided as that's GBM with constant diffusion. However, based on what you've said it's obvious you wish to model a discretized ...


2

The Kupiec test is frequently used to back test VaR values. I would refer you to read this article from the federal reserve http://www.federalreserve.gov/pubs/feds/2005/200521/200521pap.pdf


2

The following thesis deals with VaR back testing procedures in the Basel framework link. In chapter 7 tests for violation clustering are presented. An R implementation of the runs test is e.g. given in the tseries package.


2

You would want to use garchfit if you have it. If you don't have access to that you could use http://www.kevinsheppard.com/wiki/MFE_MATLAB_Introduction. Anyway, as for the inputs, it could be a vector with a constant mean of zero. This would be like fitting an AR(p) model to the prices and then estimating the Garch parameters on the residuals.


2

I would recommend to use simple standard deviation (among the 2 options you offered). You are performing time series analysis of historical data points, you are not forecasting. Thus, why exposing yourself to a much more computationally intensive method? May I also point you to a related (not duplicate) thread: Why are GARCH models used to forecast ...


2

1.Is it correct, that the coefficients are now different to the coefficients of the arima output? It seems right that the ARMA coefficients are different. Indeed, in the second model, the GARCH component will capture fluctuations that the ARMA component will not have to capture, resulting in different ARMA parameter estimates. 2.This is the acf of ...


2

The interface from R to Ox is no longer supported by Rmetrics. You could look into the Rugarch package from CRAN instead. It supports a number of Garch specifications.


2

work you way from GARCH(4,4) to GARCH(0,0) removing the intercept too. 5*5*2-1 = 49 estimations Make sure your coefficients are all statistically significant at least to 95% confidence. Make sure you have no autocorrelation in your error terms. pacf and acf should be clean. Likelihood ratio tests assess whether you lose explaining power from ...


1

fopen,fscan are in stdio.h but it looks like Ox has their own include file. For some reason it's commented out in garchOxModelling.ox, uncomment that line only. #include <oxstd.h> //#include <packages/gnudraw/gnudraw.h> I remember I had to change this line as well since I used a newer G@rch distro. It was /Garch42/ , I changed it to ...



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