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The empirical process of autoregressive residuals

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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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File URL: http://www.nuffield.ox.ac.uk/economics/papers/2007/w1/EnglerNielsen07.pdf
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Bibliographic Info

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
Date of revision:
Handle: RePEc:nuf:econwp:0701

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

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Keywords: Autogression; Empirical process; Kolmogorov-Smirnov test; Probability-Probability plots; Quantile-Quantile plots; Test for normality.;

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References

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  1. Bent Nielsen, 2001. "Order determination in general vector autoregressions," Economics Series Working Papers 2001-W10, University of Oxford, Department of Economics.
  2. 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.
  3. Bent Nielsen, 1995. "Bartlett correction of the unit root test in autoregressive models," Economics Papers 11 & 98., Economics Group, Nuffield College, University of Oxford.
  4. 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.
  5. Johansen, S., 1999. "A Bartlett Correction Factor for Tests on the Cointegrating Relations," Economics Working Papers eco99/10, European University Institute.
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Cited by:
  1. Giuseppe Cavaliere & Iliyan Georgiev, 2013. "Exploiting infinite variance through Dummy Variables in non-stationary autoregressions," Quaderni di Dipartimento 1, Department of Statistics, University of Bologna.
  2. Søren Johansen & Bent Nielsen, 2010. "Discussion of The Forward Search: Theory and Data Analysis by Anthony C. Atkinson, Marco Riani, and Andrea Ceroli," Economics Papers 2010-W02, Economics Group, Nuffield College, University of Oxford.
  3. 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), pages 1-29.
  4. Bent Nielsen & Søren Johansen, 2013. "Asymptotic analysis of the Forward Search," Economics Papers 2013-W02, Economics Group, Nuffield College, University of Oxford.
  5. Cizek, P., 2010. "Reweighted Least Trimmed Squares: An Alternative to One-Step Estimators," Discussion Paper 2010-91, Tilburg University, Center for Economic Research.
  6. Bent Nielsen & Zorica Mladenovic, 2009. "The role of income in money demand during hyper-inflation: the case of Yugoslavia," Economics Series Working Papers 2009-W02, University of Oxford, Department of Economics.
  7. B. Nielsen, 2009. "Test for cointegration rank in general vector autoregressions," Economics Papers 2009-W10, Economics Group, Nuffield College, University of Oxford.
  8. Cízek, Pavel, 2011. "Semiparametrically weighted robust estimation of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 774-788, January.
  9. Bent Nielsen & Andrew Whitby, 2012. "A Joint Chow Test for Structural Instability," Economics Papers 2012-W07, Economics Group, Nuffield College, University of Oxford.
  10. Mladenovic, Zorica & Petrovic, Pavle, 2010. "Cagan's paradox and money demand in hyperinflation: Revisited at daily frequency," Journal of International Money and Finance, Elsevier, vol. 29(7), pages 1369-1384, November.

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