Maximum Likelihood Estimation of the Markov-Switching GARCH Model Based on a General Collapsing Procedure

  • Maciej Augustyniak
  • Mathieu Boudreault
  • Manuel Morales


The Markov-switching GARCH model allows for a GARCH structure with time-varying parameters. This flexibility is unfortunately undermined by a path dependence problem which complicates the parameter estimation process. This problem led to the development of computationally intensive estimation methods and to simpler techniques based on an approximation of the model, known as collapsing procedures. This article develops an original algorithm to conduct maximum likelihood inference in the Markov-switching GARCH model, generalizing and improving previously proposed collapsing approaches. A new relationship between particle filtering and collapsing procedures is established which reveals that this algorithm corresponds to a deterministic particle filter. Simulation and empirical studies show that the proposed method allows for a fast and accurate estimation of the model.


Markov-switching Regime-switching GARCH Particle filtering Path dependence Collapsing 

Mathemathetics Subject Classification (2010)

60J05 62M05 62M20 65C35 65C60 91B84 91G70 


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Maciej Augustyniak
    • 1
    • 2
  • Mathieu Boudreault
    • 2
    • 3
  • Manuel Morales
    • 1
    • 2
  1. 1.Département de mathématiques et de statistiqueUniversité de MontréalMontrealCanada
  2. 2.Laboratoire de mathématiques actuarielles et financières QuantactCentre de recherches mathématiquesMontrealCanada
  3. 3.Département de mathématiquesUniversité du Québec à MontréalMontrealCanada

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