Weighted Sums and Residual Empirical Processes for Time-varying Processes
نویسنده
چکیده
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.
منابع مشابه
Weighted Sums and Residual Empirical Processes for Time-varying Processes
Function indexed weighted sums and sequential residual empirical processes based on time-varying AR-processes are studied. It is shown that under appropriate assumptions non-parametric estimation of the parameter functions does not influence the asymptotic distribution of the residual empirical process. An exponential inequality for weighted sums of time-varying processes provides the basis for...
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