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Semiparametric estimation by model selection for locally stationary processes

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Summary. 

Over recent decades increasingly more attention has been paid to the problem of how to fit a parametric model of time series with time-varying parameters. A typical example is given by autoregressive models with time-varying parameters. We propose a procedure to fit such time-varying models to general non-stationary processes. The estimator is a maximum Whittle likelihood estimator on sieves. The results do not assume that the observed process belongs to a specific class of time-varying parametric models. We discuss in more detail the fitting of time-varying AR(p) processes for which we treat the problem of the selection of the order p, and we propose an iterative algorithm for the computation of the estimator. A comparison with model selection by Akaike's information criterion is provided through simulations.
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Keywords: Empirical spectral process; Locally stationary process; Model selection; Sieve estimator; Time-varying autoregressive process; Whittle likelihood

Document Type: Research Article

Affiliations: 1: Université catholique de Louvain, Louvain-la-Neuve, Belgium 2: Universität Heidelberg, Germany

Publication date: November 1, 2006

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