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The empirical process of autoregressive residuals

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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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  • Bent Nielsen & Eric Engler, 2007. "The empirical process of autoregressive residuals," Economics Papers 2007-W01, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:0701
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    File URL: http://www.nuffield.ox.ac.uk/economics/papers/2007/w1/EnglerNielsen07.pdf
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    References listed on IDEAS

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    1. 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.
    2. Bent Nielsen, 1995. "Bartlett correction of the unit root test in autoregressive models," Economics Papers 11 & 98., Economics Group, Nuffield College, University of Oxford.
    3. Johansen, Søren, 2000. "A Bartlett Correction Factor For Tests On The Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 16(5), pages 740-778, October.
    4. 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, September.
    5. Bent Nielsen, 2001. "Order determination in general vector autoregressions," Economics Papers 2001-W10, Economics Group, Nuffield College, University of Oxford.
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    Cited by:

    1. B. Nielsen, 2009. "Test for cointegration rank in general vector autoregressions," Economics Papers 2009-W10, Economics Group, Nuffield College, University of Oxford.
    2. Pavel Čížek, 2013. "Reweighted least trimmed squares: an alternative to one-step estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 514-533, September.
    3. 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.
    4. Nielsen, Bent, 2008. "On the Explosive Nature of Hyper-Inflation Data," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 2, pages 1-29.
    5. Vanessa Berenguer-Rico & Søren Johansen & Bent Nielsen, 2019. "The analysis of marked and weighted empirical processes of estimated residuals," Economics Papers 2019-W03, Economics Group, Nuffield College, University of Oxford.
    6. Bent Nielsen & Andrew Whitby, 2015. "A Joint Chow Test for Structural Instability," Econometrics, MDPI, vol. 3(1), pages 1-31, March.
    7. repec:bot:quadip:118 is not listed on IDEAS
    8. Søren Johansen & Bent Nielsen, 2014. "Outlier detection algorithms for least squares time series regression," Economics Papers 2014-W04, Economics Group, Nuffield College, University of Oxford.
    9. Cavaliere, Giuseppe & Georgiev, Iliyan, 2013. "Exploiting Infinite Variance Through Dummy Variables In Nonstationary Autoregressions," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1162-1195, December.
    10. Søren Johansen & Bent Nielsen, 2014. "Optimal hedging with the cointegrated vector autoregressive model," Discussion Papers 14-23, University of Copenhagen. Department of Economics.
    11. Søren Johansen & Bent Nielsen, 2013. "Asymptotic analysis of the Forward Search," Discussion Papers 13-01, University of Copenhagen. Department of Economics.
    12. David H. Bernstein & Bent Nielsen, 2019. "Asymptotic Theory for Cointegration Analysis When the Cointegration Rank Is Deficient," Econometrics, MDPI, vol. 7(1), pages 1-24, January.
    13. Cízek, Pavel, 2011. "Semiparametrically weighted robust estimation of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 774-788, January.
    14. Zorica Mladenovic & Bent Nielsen, 2009. "The role of income in money demand during hyper-inflation: the case of Yugoslavia," Economics Papers 2009-W02, Economics Group, Nuffield College, University of Oxford.
    15. 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.
    16. Bent Nielsen & Soren Johansen, 2010. "Discussion of The Forward Search: Theory and Data Analysis," Economics Series Working Papers 2010-W02, University of Oxford, Department of Economics.
    17. Bent Nielsen & Andrew Whitby, 2015. "A Joint Chow Test for Structural Instability," Econometrics, MDPI, Open Access Journal, vol. 3(1), pages 156, March.

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    More about this item

    Keywords

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