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Analytical Derivatives for Markov Switching Models

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  • Jeff Gable
  • Simon van Norden
  • Robert Vigfusson

Abstract

This paper derives analytical gradients for a broad class of regime-switching models with Markovian state-transition probabilities. Such models are usually estimated by maximum likelihood methods, which require the derivatives of the likelihood function with respect to the parameter vector. These gradients are usually calculated by means of numerical techniques. The paper shows that analytical gradients considerably speed up maximum-likelihood estimation with no loss in accuracy. A sample program listing is included. Dans cette etude, les auteurs derivent des gradients analytiques pour toute une categorie de modeles a changement de regime comportant des probabilits de transition a la Markov. Ces modeles sont generalement estimes a l'aide de methodes du maximum de vraisemblance, qui necessitent que la fonction de vraisemblance soit derivee par rapport au vecteur des parametres du modele. Les gradients sont habituellement calcules a l'aide de techniques numeriques. Les auteurs montrent que l'utilisation de gradients analytiques accelere considerablement les estimations effectuees a l'aide des methodes du maximum de vraisemblance, sans toutefois nuire a leur precision. Un imprime du programme informatique est fourni a la fin de l'etude.

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Paper provided by Bank of Canada in its series Working Papers with number 95-7.

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Handle: RePEc:bca:bocawp:95-7

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Cited by:
  1. Simon van Norden & Robert Vigfusson, 1996. "Regime-Switching Models: A Guide to the Bank of Canada Gauss Procedures," Econometrics 9603004, EconWPA.
  2. Murray, J. & Van Norden, S. & Vigfusson, R., 1996. "Excess Volatility and Speculative Bubbles in the Canadian Dollar: Real of Imagined?," Technical Reports 76, Bank of Canada.
  3. Ryan SULEIMANN, 2003. "New Technology Stock Market Indexes Contagion: A VAR-dccMVGARCH Approach," Econometrics 0307003, EconWPA, revised 18 Jul 2003.
  4. Ryan SULEIMANN, 2003. "The Contagion Effect Between the Volatilities of the NASDAQ-100 and the IT.CA :A Univariate and A Bivariate Switching Approach," Econometrics 0307002, EconWPA, revised 18 Jul 2003.
  5. Ryan SULEIMANN, 2003. "Should Stock Market Indexes Time Varying Correlations Be Taken Into Account? A Conditional Variance Multivariate Approach," Econometrics 0307004, EconWPA, revised 18 Jul 2003.
  6. Yang, Minxian, 2001. "Closed-form likelihood function of Markov-switching models," Economics Letters, Elsevier, vol. 70(3), pages 319-326, March.

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