# Forecasting volatility using GARCH

How do I forecast volatility using GARCH in STATA after estimating the conditional volatility?

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Don't yell STATA, just say Stata. This is not an acronym, unlike SPSS or SAS. –  StasK Jul 6 '12 at 0:31

ARCH postestimation help file explains it all. You will most likely need

     predict hat_volatility, variance


or

     predict hat_volatility_factor, het


depending on what exactly you mean by volatility''. The former is the full prediction, the latter is the multiplier that goes in front of the $\hat\sigma^2$.

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More generally, assume a Garch(1,1) model has been fit to $X$, a variable with a constant mean of zero. This model is of the form:$$\sigma_{t}^{2}=\beta_{0}+\beta_{1}\sigma_{t-1}^{2}+\beta_{2}\varepsilon_{t-1}^{2}$$ The next step is to scale the variable $X$ by the conditional standard deviation $\sigma_{t}$ to obtain $\varepsilon_{t}$, the scaled residuals. You would then simulate $\varepsilon_{t}$ under the relevant assumption (so for instance, if you estimate the Garch model with t errors, then you would simulate from that distribution). The future value of volatility would then be: $$\sigma_{t+1}^{2}=\beta_{0}+\beta_{1}\sigma_{t}^{2}+\beta_{2}\varepsilon_{t}^{2}$$ The values in $t+1$ are known, but thereafter you would use the simulated values. If you just want to get a single value for future volatility, rather than a large panel of simulated values, you can simply set $\varepsilon$ to be a vector of zeros.