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Semiparametric estimation by model selection for locally stationary processes
Author(s) -
Van Bellegem Sébastien,
Dahlhaus Rainer
Publication year - 2006
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2006.00564.x
Subject(s) - akaike information criterion , estimator , autoregressive model , model selection , selection (genetic algorithm) , series (stratigraphy) , computation , parametric statistics , mathematical optimization , mathematics , star model , parametric model , semiparametric model , estimation theory , computer science , time series , autoregressive integrated moving average , algorithm , econometrics , statistics , artificial intelligence , paleontology , biology
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.