Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression.

*(English)*Zbl 0734.62070Summary: 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.

##### MSC:

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) |

##### Keywords:

serial correlation; dynamic conditional heteroskedasticity; regression disturbances; dependent alternatives; weak dependence; Limiting null distributions; fast Fourier transform
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##### References:

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