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Analytical Derivatives for Markov Switching Models

Listed author(s):
  • Jeff Gable
  • Simon van Norden
  • Robert Vigfusson

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 Staff Working Papers with number 95-7.

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Handle: RePEc:bca:bocawp:95-7
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