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Operations Management and Econometrics

The HESSIAN Method: Highly Efficient Simulation Smoothing, In A Nutshell

Professor William McCausland, Economics Department, The University of Montreal

26th Mar 2010  11:00 am - Room 498 Merewether Building

State space models, which govern the interaction of observed data and unobserved states, are very useful in capturing dynamic relationships, especially where there are changing, but latent, economic conditions: the states may be state variables in macroeconomic models, volatility in asset markets or time-varying model parameters. In this paper, I describe the HESSIAN method for non-linear non-Gaussian state space models. It involves an approximation of the conditional density of states given data that can be evaluated and simulated exactly. The approximation can be used as a proposal density, for Bayesian inference using Markov chain Monte Carlo (MCMC) methods; or as an importance density, useful for approximating the likelihood function through simulations. Because the approximation is so close, fast MCMC and importance sampling are feasible and highly numerically efficient for problems where alternatives are inefficient or intractable. I compare the performance of the HESSIAN method with methods currently used in the literature.