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B0535
Title: Adaptive bandwidth selection with cross validation for locally stationary processes Authors:  Stefan Richter - Heidelberg University (Germany) [presenting]
Rainer Dahlhaus - University of Heidelberg (Germany)
Abstract: Locally stationary processes behave in an approximately stationary way over short periods of time. There exists a subclass of such processes which allows a decomposition into a stationary time series model depending on a parameter, and a deterministic parameter curve which encodes the time dependence. A prominent example of such a process is the tvARMA process. We assume that the stationary time series model is known, but the parameter curves are not. For estimation of these curves, nonparametric kernel-type maximum likelihood estimates (depending on a smoothing parameter) have been proposed. To the best of our knowledge, the theoretical behavior of a data adaptive bandwidth choice method for such estimates has not been considered in the literature. We propose an adaptive bandwidth choice via cross validation. We prove that this procedure is asymptotically optimal with respect to a Kullback-Leibler-type distance measure under mild assumptions on the unknown parameter curve. The performance of the method is also studied in a simulation.