DocumentCode :
2852607
Title :
Recursive estimation of a locally stationary process
Author :
Moulines, E. ; Roueff, François ; Priouret, P.
Author_Institution :
GET/Telecom Paris, CNRS LTCI, Paris, France
fYear :
2003
fDate :
28 Sept.-1 Oct. 2003
Firstpage :
110
Lastpage :
113
Abstract :
We consider the problem of estimating the parameters of a locally stationary autoregressive process. This approach models the time evolution of the spectral content of a time series by a [0,1] → Rd × R+ mapping of d linear prediction coefficients and the innovation variance. The identification problem for this model fits the classical non-parametric curve estimation theory. In this contribution we focus on recursive estimators and more particularly on the LMS (least mean square) algorithm. This estimator is based on a stochastic gradient approach. A precise study of its asymptotic behavior is proposed. It turns out that this estimator achieves the minimax rate only in a limited range of smoothness classes. We propose a bias reduction method which allows to achieve this rate in a wider range of smoothness classes.
Keywords :
autoregressive processes; gradient methods; least mean squares methods; recursive estimation; time series; asymptotic behavior; autoregressive process; bias reduction method; least mean square algorithm; linear prediction coefficient; locally stationary process; mapping; minimax rate; nonparametric curve estimation theory; recursive estimation; stochastic gradient approach; time series; Autoregressive processes; Density functional theory; Estimation theory; Least squares approximation; Minimax techniques; Parameter estimation; Recursive estimation; Signal processing algorithms; Stochastic processes; Technological innovation;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Statistical Signal Processing, 2003 IEEE Workshop on
Print_ISBN :
0-7803-7997-7
Type :
conf
DOI :
10.1109/SSP.2003.1289352
Filename :
1289352
Link To Document :
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