The empirical process of autoregressive residuals

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The empirical process of autoregressive residuals

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Bent Nielsen () (Nuffield College, Oxford University)
Eric Engler (Dept of Economics, Oxford University)

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Bent Nielsen

Abstract

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.

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Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2007-W01.

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Length: 28 pages
Date of creation: 17 Jan 2007
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Handle: RePEc:nuf:econwp:0701

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Web page: http://www.nuff.ox.ac.uk/economics/

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This paper has been announced in the following NEP Reports:

NEP-ALL-2007-02-17 (All new papers)
NEP-ECM-2007-02-17 (Econometrics)
NEP-ETS-2007-02-17 (Econometric Time Series)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Kilian, Lutz & Demiroglu, Ufuk, 2000. "Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 40-50, January.
Bent Nielsen, 1995. "Bartlett correction of the unit root test in autoregressive models," Economics Papers 11 & 98., Economics Group, Nuffield College, University of Oxford. [Downloadable!]
Other versions:
- Nielsen, B., 1995. "Bartlett Correction of the Unit Root test in Autoregressive Models," Economics Papers 98, Economics Group, Nuffield College, University of Oxford.
Johansen, S ren, 2000. "A Bartlett Correction Factor For Tests On The Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 16(05), pages 740-778, October. [Downloadable!]
Other versions:
- Johansen, S., 1999. "A Bartlett Correction Factor for Tests on the Cointegrating Relations," Economics Working Papers eco99/10, European University Institute.
Bent Nielsen, 2006. "Correlograms for non-stationary autoregressions," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 707-720. [Downloadable!] (restricted)
Other versions:
- Bent Nielsen, 2003. "Correlograms for non-stationary autoregressions," Economics Papers 2003-W11, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
Bent Nielsen, 2001. "Order determination in general vector autoregressions," Economics Papers 2001-W10, Economics Group, Nuffield College, University of Oxford. [Downloadable!]

Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Nielsen, Bent, 2008. "On the Explosive Nature of Hyper-Inflation Data," Economics Discussion Papers 2008-9, Kiel Institute for the World Economy. [Downloadable!]
Other versions:
- Nielsen, Bent, 2008. "On the Explosive Nature of Hyper-Inflation Data," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 2(21). [Downloadable!]

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