linear regression with GARCH/EGARCH errors

2014 9 23
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更新时间：2015 11 19
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I need to estimate a linear model with GARCH or EGARCH errors:
mean eqn: Y = c +b1X1 +b2X2 + e e_t ~ N(0,sigma_t^2)
vol eqn: sigma_t^2 follows GARCH or EGARCH
I have written the likelihood function and optimise it. I would prefer to use built-in matlab functions to estimate it (as a check).
any guidance appreciated!

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Philip
Philip 2014-10-14

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with a little guidance from Mathworks support, my PhD student solved this problem.
Use the "estimate" syntax to estimate a garch (1,1) or egarch(1,1) model.
Mdl = arima('Variance',egarch(1,1));
this seems to "turn off" the lagged AR terms in the conditional mean, but still allows e/garch in the conditional variance.
then, it's just a matter of:
[EstMdl,EstParamCov,logL,info] = estimate(Mdl,Y,'X',X);
The "X" tells matlab to expect a matrix of exogenous regressors. No need to include a vector of ones in X, since an intercept comes as standard in the "estimate" routine.

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aa ee
aa ee 2015-11-19
Thanks very much for the answer. Do you know how to extract the standard errors of estimated parameters?? Matlab "print" function explains very little on this matter.

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the cyclist
the cyclist 2014-9-23

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Do you have the Econometrics Toolbox? A garch() function is available in it. Here's a link to the documentation.

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Philip
Philip 2014-9-23
Yes, I have all the toolboxes. I have used garch() to fit a model, perhaps with a constant mu in the mean. My uncertainty surrounds how to get the conditioning variables (i.e,., regressors c + b1*X1 + b2*X2) in the mean equn.

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