Threshold autoregressive model blind identification based on array clustering

Jean-Marc Le Caillec ()
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Jean-Marc Le Caillec: IMT Atlantique - ITI - Département lmage et Traitement Information - IMT Atlantique - IMT Atlantique - IMT - Institut Mines-Télécom [Paris], Lab-STICC_M3 - Equipe Marine Mapping & Metrology - Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance - ENIB - École Nationale d'Ingénieurs de Brest - UBS - Université de Bretagne Sud - UBO - Université de Brest - ENSTA Bretagne - École Nationale Supérieure de Techniques Avancées Bretagne - IMT - Institut Mines-Télécom [Paris] - CNRS - Centre National de la Recherche Scientifique - UBL - Université Bretagne Loire - IMT Atlantique - IMT Atlantique - IMT - Institut Mines-Télécom [Paris]

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Abstract: In this paper, we propose a new algorithm to estimate all the parameters of a Self Exited Threshold AutoRegressive (SETAR) model from an observed time series. The aim of this algorithm is to relax all the hypotheses concerning the SETAR model for instance, the knowledge (or assumption) of the number of regimes, the switching variables, as well as of the switching function. For this, we reverse the usual framework of SETAR model identification of the previous papers, by first identifying the AR models using array clustering (instead of the switching variables and function) and second the switching conditions (instead of the AR models). The proposed algorithm is a pipeline of well-known algorithms in image/data processing allowing us to deal with the statistical non-stationarity of the observed time series. We pay a special attention on the results of each step over the possible discrepancies over the following step. Since we do not assume any SETAR model property, asymptotical properties of the identification results are difficult to derive. Thus, we validate our approach on several experiment sets. In order to assess the performance of our algorithm, we introduce global metrics and ancillary metrics to validate each step of the proposed algorithm.

Date: 2021-07
New Economics Papers: this item is included in nep-ecm
Note: View the original document on HAL open archive server: https://hal.science/hal-03210735v1
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Published in Signal Processing, 2021, 184, pp.108055. ⟨10.1016/j.sigpro.2021.108055⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03210735

DOI: 10.1016/j.sigpro.2021.108055

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