# 11-057/4 (2011-03-22; 2012-01-27)

Siem Jan Koopman, VU University Amsterdam; Andre Lucas, VU University Amsterdam; Marcel Scharth, VU University Amsterdam
State space models, importance sampling, simulated maximum likelihood, stochastic volatility, stochastic copula, stochastic conditional duration
JEL codes:
C15, C22

This paper led to a publication in the 'Journal of Business & Economic Statistics', 2015, 33 (1), 114-127.

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.