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.
Best Answer
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.testfunction in R suggests that it takes residualsxand conditional variancesh.tas inputs. I presume the function treatsxas raw residuals that can be scaled by dividing by the square root conditional variancessqrt(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. Thesexare squares of standardized residuals that are further used in calculating the autocorrelations and using the latter to construct the test statistic(s).