%0 Journal Article
%@ 1350-7265
%A Dahlhaus, Rainer
%A Neumann, Michael H.
%A von Sachs, Rainer
%C Aarhus
%D 1999
%F heidok:21429
%J Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability
%K Nonlinear thresholding; non-stationary processes; time series; time-varying autoregression;  wavelet estimators
%N 5
%P 873-906
%R 10.11588/heidok.00021429
%T Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes
%U https://archiv.ub.uni-heidelberg.de/volltextserver/21429/
%V 5
%X We consider nonparametric estimation of the coefficients, of atime-varying autoregressive process. Choosing an orthonormal wavelet basisrepresentation of the coefficient functions, the empirical wavelet coefficientsare derived from the time series data as the solution of a least squares minimizationproblem. In order to allow the coefficient functions to be of inhomogeneous regularity,we apply nonlinear thresholding to the empirical coefficients and obtain locally smoothedestimates of the coefficient functions. We show that the resulting estimators attain theusual minimax L_2-rates up to a logarithm factor, simultaneously in a large scale of Besovclasses.