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State space Markov switching models using wavelets

Alencar Airlane P. (), Morettin Pedro A. and Toloi Clelia M.C.
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Alencar Airlane P.: Institute of Mathematics and Statistics, Statistics Department, University of São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, SP, Brazil
Morettin Pedro A.: Institute of Mathematics and Statistics, Statistics Department, University of São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, SP, Brazil
Toloi Clelia M.C.: Institute of Mathematics and Statistics, Statistics Department, University of São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, SP, Brazil

Studies in Nonlinear Dynamics & Econometrics, 2013, vol. 17, issue 2, 221-238

Abstract: We propose a state space model with Markov switching, whose regimes are associated with the model parameters and regime transition probabilities are modeled using wavelets. The estimation is based on the maximum likelihood method using the EM algorithm and a bootstrap method is proposed in order to assess the distribution of the maximum likelihood estimators. To evaluate the state variables and regime probabilities, the Kalman filter and a probability filter procedure conditional on each possible regime, at each instant, are used. These procedures are evaluated with simulated data and illustrated with the US monthly industrial production index from July 1968 to February 2011.

Date: 2013
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DOI: 10.1515/snde-2012-0020

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