We consider nonparametric estimation of the parameter functions 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 functions of inhomogeneous regularity, we apply nonlinear thresholding to the empirical coefficients 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. The finite-sample behaviour of our procedure is demonstrated by application to two typical simulated examples.