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Mon, 03 Apr 2000 00:00:00 +0200Mon, 03 Apr 2000 00:00:00 +0200Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/577
We consider nonparametric estimation of the coefficients a_i(.), i=1,...,p, on a time-varying autoregressive process. Choosing an orthonormal wavelet basis representation of the functions a_i(.), the empirical wavelet coefficients are derived from the time series data as the solution of a least squares minimization problem. In order to allow the a_i(.) to be functions of inhomogeneous regularity, we apply nonlinear thresholding to the empirical coefficients and obtain locally smoothed estimates of the a_i(.). We show that the resulting estimators attain the usual minimax L_2-rates up to a logarithmic factor, simultaneously in a large scale of Besov classes. The finite-sample behaviour of our procedure is demonstrated by application to two typical simulated examples.Michael H. Neumann; Rainer von Sachs; R. Dahlhauspreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/577Mon, 03 Apr 2000 00:00:00 +0200