The empirical process of autoregressive residuals
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.
|Date of creation:||17 Jan 2007|
|Date of revision:|
|Contact details of provider:|| Web page: https://www.nuffield.ox.ac.uk/economics/|
References listed on IDEAS
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- Nielsen, B., 1995.
"Bartlett Correction of the Unit Root test in Autoregressive Models,"
98, Economics Group, Nuffield College, University of Oxford.
- Bent Nielsen, 1995. "Bartlett correction of the unit root test in autoregressive models," Economics Papers 11 & 98., Economics Group, Nuffield College, University of Oxford.
- Johansen, S., 1999.
"A Bartlett Correction Factor for Tests on the Cointegrating Relations,"
Economics Working Papers
eco99/10, European University Institute.
- 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.
- 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.
- 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, 2001. "Order determination in general vector autoregressions," Economics Papers 2001-W10, Economics Group, Nuffield College, University of Oxford.
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