Nonlinear wavelet estimation of time-varying autoregressive processes

被引:49
作者
Dahlhaus, R
Neumann, MH
Von Sachs, R
机构
[1] Univ Heidelberg, Inst Angew Math, D-69120 Heidelberg, Germany
[2] Humboldt Univ, D-10178 Berlin, Germany
[3] Univ Catholique Louvain, Inst Stat, B-1348 Louvain, Belgium
关键词
nonlinear thresholding; non-stationary processes; time series; time-varying autoregression; wavelet estimators;
D O I
10.2307/3318448
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We consider nonparametric estimation of the parameter functions a(i)(.), 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.
引用
收藏
页码:873 / 906
页数:34
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