Locally stationary long memory estimation |
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Authors: | Franç ois Roueff,Rainer von Sachs |
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Affiliation: | a Institut Telecom, Telecom Paris, CNRS LTCI, 46 rue Barrault, 75634 Paris Cedex 13, Franceb Institut de statistique, biostatistique et sciences actuarielles (ISBA), IMMAQ, Université catholique de Louvain, Voie du Roman Pays, 20, B-1348 Louvain-la-Neuve, Belgium |
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Abstract: | There exists a wide literature on parametrically or semi-parametrically modelling strongly dependent time series using a long-memory parameter d, including more recent work on wavelet estimation. As a generalization of these latter approaches, in this work we allow the long-memory parameter d to be varying over time. We adopt a semi-parametric approach in order to avoid fitting a time-varying parametric model, such as tvARFIMA, to the observed data. We study the asymptotic behavior of a local log-regression wavelet estimator of the time-dependent d. Both simulations and a real data example complete our work on providing a fairly general approach. |
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Keywords: | primary, 62M10, 62M15, 62G05 secondary, 60G15 |
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