The empirical process of autoregressive residuals
Bent Nielsen and
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Eric Engler: Dept of Economics, Oxford University
No 2007-W01, Economics Papers from Economics Group, Nuffield College, University of Oxford
The empirical process of the residuals from general autoregressions is investigated. If an intercept is included in the regression, the empirical process is asymptotically Gaussian and free of nuisance parameters. This contrasts the known result that in the unit root case without intercept the empirical process is asymptotically non-Gaussian. The result is used to establish asymptotic theory for the Kolmogorov-Smirnov test, Probability-Probability plots, and Quantile-Quantile plots. The link between sample moments and the empirical process of the residuals is established and used to establish the properties of the cumulant based tests for normality referred to as the Jarque-Bera test.
Keywords: Autogression; Empirical process; Kolmogorov-Smirnov test; Probability-Probability plots; Quantile-Quantile plots; Test for normality. (search for similar items in EconPapers)
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Journal Article: The empirical process of autoregressive residuals (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:nuf:econwp:0701
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