BibTeX
@MISC{Chandler12weightedsums,
author = {Gabriel Chandler and Wolfgang Polonik},
title = {Weighted sums and residual . . . },
year = {2012}
}
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Abstract
In the context of a time-varying AR-process we study both function indexed weighted sums, and sequential residual empirical processes. As for the latter it turns out that somewhat surprisingly, under appropriate assumptions, the non-parametric estimation of the parameter functions has a negligible asymptotic effect on the estimation of the error distribution. Function indexed weighted sum processes are generalized partial sums. An exponential inequality for such weighted sums of time-varying processes provides the basis for a weak convergence result of weighted sum processes. Properties of weighted sum processes are needed to treat the residual empirical processes. As an application of our results we discuss testing for the shape of the variance function.
Keyphrases
weighted sum process exponential inequality partial sum sum process residual empirical process parameter function time-varying process appropriate assumption weighted sum non-parametric estimation time-varying ar-process negligible asymptotic effect weak convergence result sequential residual empirical process error distribution variance function
