Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes
Rainer Dahlhaus, Michael H. Neumann, Rainer von Sachs · heiDOK (Heidelberg University) · 2016
. We consider nonparametric estimation of the parameter functions a i (\\Delta) , i = 1; : : : ; p , of 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. 1991 Mathematics Subject Classification. Primary 62M10; secondary 62F10 Key words and phrases. Nonstationary processes, time series, wavelet estimators, time-varying autoregression, nonlinear thresholdi...