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I also posted this question on the R-SIG-Finance mailing list (thanks to @aginensky's suggestion), and the author of rugarch replied it. The initial value of $\hat{\sigma}_1$$\hat{\sigma}^2_1$ by default is mean of squared residuals, and in this case it's sighat1[1] = sqrt(mean(X1^2)).

I also posted this question on the R-SIG-Finance mailing list (thanks to @aginensky's suggestion), and the author of rugarch replied it. The initial value of $\hat{\sigma}_1$ by default is mean of squared residuals, and in this case it's sighat1[1] = sqrt(mean(X1^2)).

I also posted this question on the R-SIG-Finance mailing list (thanks to @aginensky's suggestion), and the author of rugarch replied it. The initial value of $\hat{\sigma}^2_1$ by default is mean of squared residuals, and in this case it's sighat1[1] = sqrt(mean(X1^2)).

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I also posted this question on the R-SIG-Finance mailing list (thanks to @aginensky's suggestion), and the author of rugarch replied it. The initial value of $\hat{\sigma}_1$ by default is mean of squared residuals, and in this case it's sighat1[1] = sqrt(mean(X1^2)).