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

39 Pages Posted: 20 Mar 2011 Last revised: 28 Jan 2012

See all articles by Siem Jan Koopman

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics; Tinbergen Institute; Aarhus University - CREATES

Andre Lucas

Vrije Universiteit Amsterdam - School of Business and Economics; Tinbergen Institute

Marcel Scharth

The University of Sydney

Date Written: January 27, 2012

Abstract

We introduce a new efficient importance sampler for nonlinear non-Gaussian state space models. We propose a general and efficient likelihood evaluation method for this class of models via the combination of numerical and Monte Carlo integration methods. Our methodology explores the idea that only a small part of the likelihood evaluation problem requires simulation. We refer to our new method as numerically accelerated importance sampling. The method is computationally and numerically efficient, facilitates parameter estimation for models with high-dimensional state vectors, and overcomes a bias-variance trade-off encountered by other sampling methods. An elaborate simulation study and an empirical application for U.S. stock returns reveal large efficiency gains for a range of models used in financial econometrics.

Keywords: Kalman filter, Monte Carlo maximum likelihood, numerical integration, stochastic copula, stochastic conditional duration, stochastic volatility

JEL Classification: C15, C22

Suggested Citation

Koopman, Siem Jan and Lucas, Andre and Scharth, Marcel, Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models (January 27, 2012). Available at SSRN: https://ssrn.com/abstract=1790472 or http://dx.doi.org/10.2139/ssrn.1790472

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31205986019 (Phone)

HOME PAGE: http://sjkoopman.net

Tinbergen Institute ( email )

Gustav Mahlerplein 117
1082 MS Amsterdam
Netherlands

HOME PAGE: http://personal.vu.nl/s.j.koopman

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Andre Lucas

Vrije Universiteit Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31 20 598 6039 (Phone)
+31 20 598 6020 (Fax)

HOME PAGE: http://personal.vu.nl/a.lucas

Tinbergen Institute

Roetersstraat 31
Amsterdam, 1018 WB
Netherlands

HOME PAGE: http://www.tinbergen.nl

Marcel Scharth (Contact Author)

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

HOME PAGE: http://www.marcelscharth.com

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