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


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
Issue number1
Publication statusPublished - 1 Feb 2019


We would like to thank André Lucas, Marcel Scharth, and István Barra for giving comments on an earlier version of this paper. Koopman acknowledges support from CREATES, Center for Research in Econometric Analysis of Time Series (DNRF78) at Aarhus University, Denmark, and funded by the Danish National Research Foundation. The usual disclaimer applies.

FundersFunder number
Center for Research in Econometric Analysis of Time SeriesDNRF78
Aarhus Universitet
Danmarks Grundforskningsfond


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


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