Аннотация:
Locally stationary processes behave in an approximately stationary way over short periods of time.
For specific models such as the time varying autoregressive process
it is possible to describe the evolution of the entire process with a finite set of parameter curves.
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We assume that the locally stationary time series model is known, but the parameter curves are not.
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For estimation of the curves we use nonparametric kernel-type maximum likelihood estimates which depend on a smoothing parameter (bandwidth).
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To the best of our knowledge the theoretical behaviour of data adaptive bandwidth choice methods for such estimates
has not been considered in the literature. We propose an adaptive bandwidth choice via cross validation,
and show that it is asymptotically optimal in a specific sense with respect to a Kullback-Leibler-type distance measure.