WIAS Preprint No. 159, (1995)

Nonlinear wavelet estimation of time-varying autoregressive processes


  • Dahlhaus, Rainer
  • Neumann, Michael H.
  • von Sachs, Rainer

2010 Mathematics Subject Classification

  • 62M10 62F10


  • Nonstationary processes, time series, wavelet estimators, time-varying autoregression, nonlinear thresholding




We consider nonparametric estimation of the coefficients ai(·), i = 1,...,p , of a time-varying autoregressive process. Choosing an orthonormal wavelet basis representation of the functions ai(·), 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 ai(·) to be functions of inhomogeneous regularity, we apply nonlinear thresholding to the empirical coeffcients and obtain locally smoothed estimates of the ai(·). We show that the resulting estimators attain the usual minimax L2-rates up to a logarithmic factor, simultaneously in a large scale of Besov classes.

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