"The empirical process of autoregressive residuals"
ERIC ENGLER and BENT NIELSEN
Dept of Economics, 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.