Modified efficient importance sampling for partially non-Gaussian state space models

Siem Jan Koopman*, Rutger Lit, Thuy Minh Nguyen

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

The construction of an importance density for partially non-Gaussian state space models is crucial when simulation methods are used for likelihood evaluation, signal extraction, and forecasting. The method of efficient importance sampling is successful in this respect, but we show that it can be implemented in a computationally more efficient manner using standard Kalman filter and smoothing methods. Efficient importance sampling is generally applicable for a wide range of models, but it is typically a custom-built procedure. For the class of partially non-Gaussian state space models, we present a general method for efficient importance sampling. Our novel method makes the efficient importance sampling methodology more accessible because it does not require the computation of a (possibly) complicated density kernel that needs to be tracked for each time period. The new method is illustrated for a stochastic volatility model with a Student's t distribution.

Original languageEnglish
Pages (from-to)44-62
Number of pages19
JournalStatistica Neerlandica
Volume73
Issue number1
DOIs
Publication statusPublished - 1 Feb 2019

Keywords

  • efficient importance sampling
  • Kalman filter
  • Monte Carlo maximum likelihood
  • non-Gaussian dynamic models
  • simulation smoothing

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