130 articles – 87 references  [version française]
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 10th INTERNATIONAL CONFERENCE ON OPERATIONS RESEARCH, Habana : Cuba (2012)
 Estimating the Number of Regimes of Non-linear Autoregressive Models.
 (2012-03-06)
 Autoregressive regime-switching models are being widely used in modelling financial and economic time series such as business cycles (Hamilton, 1989; Lam, 1990), exchange rates (Engle and Hamilton, 1990), financial panics (Schwert, 1989) or stock prices (Wong and Li, 2000). When the number of regimes is fixed the statistical inference is relatively straightforward and the asymptotic properties of the estimates may be established (Francq and Roussignol, 1998; Krishnamurthy and Rydén, 1998; Douc R., Moulines E. and Rydén T., 2004). However, the problem of selecting the number of regimes is far less obvious and hasn't been completely answered yet. When the number of regimes is unknown, identifiability problems arise and the likelihood ratio test statistic (LRTS hereafter) is no longer convergent to a $\chi^{2}$-distribution. In this paper, we consider models which allow the series to switch between regimes and we propose to study such models without knowing the form of the density of the noise. The problem we address here is how to select the number of components or number of regimes. One possible method to answer this problem is to consider penalized criteria. The consistency of a modified BIC criterion was recently proven in the framework of likelihood criterion for linear switching models (see Oltéanu and Rynkiewicz). We extend these results to mixtures of nonlinear autoregressive models with mean square error criterion and prove the consistency of a penalized estimate for the number of components under some regularity conditions.
 1: Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM) Université Paris I - Panthéon-Sorbonne
 Subject : Mathematics/StatisticsStatistics/Statistics Theory
 Keyword(s): time series – switching regimes – mean square error – asymptotic statistic – models selection – multilayer perceptron
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 hal-00695539, version 1 http://hal.archives-ouvertes.fr/hal-00695539 oai:hal.archives-ouvertes.fr:hal-00695539 From: Joseph Rynkiewicz <> Submitted on: Wednesday, 9 May 2012 22:45:38 Updated on: Thursday, 10 May 2012 09:47:30