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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.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2006.00564.x","type":"journal-article","created":{"date-parts":[[2006,10,24]],"date-time":"2006-10-24T15:34:04Z","timestamp":1161704044000},"page":"721-746","source":"Crossref","is-referenced-by-count":19,"title":["Semiparametric Estimation by Model Selection for Locally Stationary Processes"],"prefix":"10.1093","volume":"68","author":[{"given":"S\u00e9bastien","family":"Van Bellegem","sequence":"first","affiliation":[{"name":"Universit\u00e9 catholique de Louvain , Louvain-la-Neuve , Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rainer","family":"Dahlhaus","sequence":"additional","affiliation":[{"name":"Universit\u00e4t Heidelberg , Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2006,10,24]]},"reference":[{"key":"2023040708370390200_","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1214\/aos\/1009210692","article-title":"Adaptive estimation in autoregression or \u03b2-mixing regression via model selection","volume":"29","author":"Baraud","year":"2001","journal-title":"Ann. 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