Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression. (English) Zbl 0734.62070

Summary: Broad classes of diagnostics for serial correlation and/or dynamic conditional heteroskedasticity of regression disturbances are considered. The classes include statistics with good power against strongly dependent alternatives, along with the usual ones that test against weak dependence, and many others. Limiting null distributions are obtained, under mild conditions on the dependence structure of the alternative against which the test is derived, on moments of the disturbances, and on the regressors. The various test statistics have a similar overall structure, and while tests against strongly dependent alternatives entail more computation than ones against weakly dependent alternatives, the difference can be slight if the fast Fourier transform is used.


62J05 Linear regression; mixed models
62F03 Parametric hypothesis testing
62J20 Diagnostics, and linear inference and regression
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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