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I have conducted a realized GARCH model and want to test for ARCH effects using the Li-Mak test as I have read that it is the best one for this purpose.

I am struggling on the question if residuals or standardized residuals have to be used. Even though this is not the right platform for R questions it would be kind if anybody could give me advice if Weighted.LM.test from the WeightedPortTest package in R uses the standardized residuals automatically if I enter residuals only.

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  • $\begingroup$ Thank you for your very useful answer. It helped me a lot. $\endgroup$
    – pnb.beg
    Jun 1, 2018 at 1:44

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Brief answer to the question: raw, nonstandardized residuals should be used.

If you have a fitted GARCH model, you want the stardardized innovations to be i.i.d. Therefore, you take their sample counterparts, standardized residuals, and conduct the Li-Mak test. The test inspects presence of autocorrelation in their squares. Presence of autocorrelation (high test statistic, low $p$-value, and rejection of the null hypothesis of no autocorrelation in squares) is a sign that your GARCH model has failed to capture all autoregressive conditional heteroskedastic patterns there are.

The description of the Weighted.LM.test function in R suggests that it takes residuals x and conditional variances h.t as inputs. I presume the function treats x as raw residuals that can be scaled by dividing by the square root conditional variances sqrt(h.t) so that standardized residuals are obtained. And indeed, there is a line of code that does that (or actually almost that) at the beginning of the function: x <- x^2/h.t. These x are squares of standardized residuals that are further used in calculating the autocorrelations and using the latter to construct the test statistic(s).

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