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Let’s consider linear regression model, estimated using OLS.

According to information from Hayashi (Econometrics, Chapter 2)

  • it must be the case of no serial correlation in errors to perform White’s test for conditional heteroskedasticity;
  • it must be the case of conditional homoskedasticity to perform both Ljung-Box Q test and Breusch-Godfrey test for absence of serial correlation.

Reasonable question arises: how someone should perform these kind of tests if H0 in one test is assumption in the other?

Maybe there exists some other tests, for example, for testing serial correlation that doesn’t rely on conditional homoskedasticity assumption or for testing conditional heteroskedasticity that doesn’t rely on no serial correlation assumption?

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  • $\begingroup$ Do you have a specific use case for these tests? What kind of data do you have? $\endgroup$ Commented Dec 11, 2023 at 7:35
  • $\begingroup$ @YashaswiMohanty No specific data for now, just theoretical research. $\endgroup$ Commented Dec 11, 2023 at 7:48

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Nobody answered this question, so I thought I would take a moment to. Hayashi is correct in his statements. Typically, serial correlation is the more pressing concern. You would test for serial correlation first, using, for example, a test that can be made robust to heteroskedasticity of unknown form.

The two better tests that come to mind are Durbin's M Test and the Breusch-Godfrey Test. Then if serial correlation is detected, you would correct for it and then test for heteroskedasticity.

Testing is done in this order because serial correlation typically invalidates a test for heteroskedasticity. Happy testing.

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  • $\begingroup$ The OP wrote it must be the case of conditional homoskedasticity to perform both Ljung-Box Q test and Breusch-Godfrey test for absence of serial correlation, but you are still suggesting the BG test even in presence of heteroskedasticity? $\endgroup$ Commented Feb 2 at 17:31
  • $\begingroup$ Yes, Richard. Both Durbin's M Test and the Breusch-Godfrey Test can be made robust to heteroskedasticity of unknown form. See Wooldridge's Introductory to Econometrics (Chapter 12). $\endgroup$ Commented Feb 2 at 20:18
  • $\begingroup$ Good. Perhaps it is a good idea to include that in your answer. $\endgroup$ Commented Feb 3 at 8:07
  • $\begingroup$ It is in the answer. $\endgroup$ Commented Feb 3 at 13:29
  • $\begingroup$ Sorry, it was not obvious to me because you mentioned a test that can be made robust to heteroskedasticity of unknown form and the two specific tests in separate paragraphs. Now I understand. $\endgroup$ Commented Feb 3 at 14:15

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