when we estimate volatility by using GARCH model, is it possible to get residuals. if,so how to calculate the residuals.
As we know that residual is the difference between actual and predicted value, in this case, what is the actual volatility. (the estimated values of GARCH indicate estimated volatility).
Note that you estimate two equations simultaneously; namely the conditional mean equation and the conditional variance equation. Residuals are the difference between actual and predicted values in the conditional mean equation.
You can obtain standardized residuals by dividing residuals at each point in time t by the conditional standard deviation at that point in time.
For more details, you could refer to Brooks, C. (2002). Introductory Econometrics for Finance. Cambridge University Press.
thank you prof. Amira Akl Ahmed for your valid reply.
actually , my doubt is how to derive the residuals of the volatility, but not the returns. becuase, GARCH is ,basically, meant for estimating volatility,but not returns.
for calculation of standardized residuals is it true?
Volatility= Estimated from MSGARCH package in R
Residuals= abs(returns)-volatility;
standardized residuals=Residuals/volatility;
I have a similar question. given a fitted ARMA-GARCH model, I known all the estimated parameters, How can I calculate the model residuals manually? I tried by myself, the the calculated residuals are different from from those from R package such rugarch.
Brother, residuals that u use in the GARCH model are obtained as follows:
1. First, fit ARMA to the return series, say the best ARMA model is r(t) =ARMA(1,2)
2.secondly, find residuals(t)= logreturn(t)- r(t), and then finally this resulting series is called residuals. Then u use this series in the GARCH model fitting. That is it!
But if u are sure about the logreturn series has a constant mean, then u use logreturn minus that constant mean residuals for the GARCH model. This constant mean is called 'offset' in the GARCH toolbox. moreover, if that constant mean is zero, then u use return as residuals directly.
If you use R, then you can get residual from the code:
res = residuals( garchFit( your model) )
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