Title: Efficient simulation and integrated likelihood estimation in state space models

Authors: Joshua C.C. Chan, Ivan Jeliazkov

Addresses: Department of Mathematics, University of Queensland, Brisbane, QLD 4072, Australia. ' Department of Economics, University of California, Irvine, 3151 Social Science Plaza, Irvine, CA 92697-5100, USA

Abstract: We consider the problem of implementing simple and efficient Markov chain Monte Carlo (MCMC) estimation algorithms for state space models. A conceptually transparent derivation of the posterior distribution of the states is discussed, which also leads to an efficient simulation algorithm that is modular, scalable and widely applicable. We also discuss a simple approach for evaluating the integrated likelihood, defined as the density of the data given the parameters but marginal of the state vector. We show that this high-dimensional integral can be easily evaluated with minimal computational and conceptual difficulty. Two empirical applications in macroeconomics demonstrate that the methods are versatile and computationally undemanding. In one application, involving a time-varying parameter model, we show that the methods allow for efficient handling of large state vectors. In our second application, involving a dynamic factor model, we introduce a new blocking strategy which results in improved MCMC mixing at little cost. The results demonstrate that the framework is simple, flexible and efficient.

Keywords: banded matrix; Bayesian estimation; collapsed sampler; Markov chain Monte Carlo; MCMC estimation; Kalman filter; state smoothing; dynamic factor model; time-varying parameter model; simulation; likelihood estimation; state space models; macroeconomics.

DOI: 10.1504/IJMMNO.2009.030090

International Journal of Mathematical Modelling and Numerical Optimisation, 2009 Vol.1 No.1/2, pp.101 - 120

Published online: 09 Dec 2009 *

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