Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State-Space Models

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  • Siem Jan Koopman
  • André Lucas, Tinbergen Institute and Duisenberg School of Finance, Vrije Universiteit Amsterdam, Netherlands
  • Marcel Scharth, University of New South Wales (UNSW) Australia

We propose a general likelihood evaluation method for nonlinear non-Gaussian state-space models using the simulation-based method of efficient importance sampling. We minimize the simulation effort by replacing some key steps of the likelihood estimation procedure by numerical integration. We refer to this method as numerically accelerated importance sampling. We show that the likelihood function for models with a high-dimensional state vector and a low-dimensional signal can be evaluated more efficiently using the new method. We report many efficiency gains in an extensive Monte Carlo study as well as in an empirical application using a stochastic volatility model for U.S. stock returns with multiple volatility factors. Supplementary materials for this article are available online.

Original languageEnglish
JournalJournal of Business and Economic Statistics
Pages (from-to)114-127
Number of pages14
Publication statusPublished - 2 Jan 2015

    Research areas

  • Control variables, Efficient importance sampling, Kalman filter, Numerical integration, Simulated maximum likelihood, Simulation smoothing, Stochastic volatility model

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