Estimation of stochastic volatility models: An approximation to the nonlinear state space representation

Junji Shimada, Yoshihiko Tsukuda

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The stochastic volatility (SV) model can be regarded as a nonlinear state space model. This article proposes the Laplace approximation method to the nonlinear state space representation and applies it for estimating the SV models. We examine how the approximation works by simulations as well as various empirical studies. The Monte Carlo experiments for the standard SV model indicate that our method is comparable to the Monte-Calro Likelihood (MCL; Durbin and Koopman, 1997), Maximum Likelihood (Fridman and Harris, 1998), and Markov chain Monte Carlo (MCMC) methods in the sense of mean square error in finite sample. The empirical studies for stock markets reveal that our method provides very similar estimates of coefficients to those of the MCL. We show a relationship of our Laplace approximation method to importance sampling.

Original languageEnglish
Pages (from-to)429-450
Number of pages22
JournalCommunications in Statistics: Simulation and Computation
Volume34
Issue number2
DOIs
Publication statusPublished - 2005 Jun 28

Keywords

  • Laplace approximation
  • Nonlinear state space representation
  • Stochastic volatility

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation

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