Template-type: ReDIF-Paper 1.0
Author-Name: Bent Nielsen
Author-Email: bent.nielsen@nuffield.ox.ac.uk
Author-Workplace-Name: Nuffield College, Oxford University
Author-Workplace-Homepage: http://www.nuffield.ox.ac.uk/college/
Author-Name: Eric Engler
Author-Workplace-Name: Dept of Economics, Oxford University
Title: The empirical process of autoregressive residuals
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.
Keywords: Autogression, Empirical process, Kolmogorov-Smirnov test, Probability-Probability
plots, Quantile-Quantile plots, Test for normality.
Length: 28 pages
Creation-Date: 2007-01-17
Number: 2007-W01
File-URL: http://www.nuffield.ox.ac.uk/economics/papers/2007/w1/EnglerNielsen07.pdf
File-Format: application/pdf
Handle: RePEc:nuf:econwp:0701