Estimation of stochastic volatility models via Monte Carlo maximum likelihood

Gleb Sandmann, Siem Jan Koopman*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


This paper discusses the Monte Carlo maximum likelihood method of estimating stochastic volatility (SV) models. The basic SV model can be expressed as a linear state space model with log chi-square disturbances. The likelihood function can be approximated arbitrarily accurately by decomposing it into a Gaussian part, constructed by the Kalman filter, and a remainder function, whose expectation is evaluated by simulation. No modifications of this estimation procedure are required when the basic SV model is extended in a number of directions likely to arise in applied empirical research. This compares favorably with alternative approaches. The finite sample performance of the new estimator is shown to be comparable to the Monte Carlo Markov chain (MCMC) method.

Original languageEnglish
Pages (from-to)271-301
Number of pages31
JournalJournal of Econometrics
Issue number2
Publication statusPublished - 8 Sept 1998
Externally publishedYes


  • GARCH model
  • Importance sampling
  • Kalman filter smoother
  • Monte Carlo simulation
  • Quasi-maximum likelihood
  • Stochastic Volatility
  • Unobserved components


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