I have a time series model and obtain the following distribution of estimated errors:


I suspect that the errors are heteroscedastic in the sense that their variance depends on the level of one or more of the independent variables. I also can't rule out ARCH. That is why I want to conduct the White test and Engle's ARCH test, mentioned for example here. In both cases auxiliary models with squared estimated errors as dependent variable are estimated with OLS. The distribution of the squared estimated errors obtained from the estimated errors above looks as follows:


The heavy-tailedness of this distribution makes me worry about the OLS estimation. Are these worries justified? If so: is a way out to consider for example absolute errors or errors to the power of $3/2$ in the auxiliary regressions?


Let $\hat{u}_t$ denote the estimated errors which are shown in the first histogram. If I estimate, as an example for an auxiliary model in the White test framework (see Wooldridge p. 275), $$\hat{u}_t^2 = \delta_0 + \delta_1 \hat{y}_t + \delta_2\hat{y}_t^2 + v_t$$ with OLS, the distribution of the estimated errors $\hat{v}_t$ looks as follows:


So the heavy-tailedness carries through?!

  • $\begingroup$ When it comes to OLS, you should worry about the distribution of the model errors, not that of the dependent variable. You can assess the former by looking at the residuals of your model that has been estimated by OLS. $\endgroup$ Jun 2, 2020 at 13:25
  • 1
    $\begingroup$ @RichardHardy, I absolutely agree. I added an EDIT to my question that shows the estimated errors of an example auxiliary model. My perception is that heavy-tailedness carries through, do you agree? $\endgroup$
    – nluckn
    Jun 2, 2020 at 13:48
  • $\begingroup$ Yes, it looks like it. $\endgroup$ Jun 2, 2020 at 14:48


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