The HESSIAN method: Highly efficient simulation smoothing, in a nutshell

William McCausland ()

Journal of Econometrics, 2012, vol. 168, issue 2, 189-206

Abstract: I introduce the HESSIAN (highly efficient simulation smoothing in a nutshell) method for numerically efficient simulation smoothing in state space models with univariate states. Given a vector θ of parameters, the vector of states α=(α1,…,αn) is Gaussian and the observed vector y=(y1⊤,…,yn⊤)⊤ need not be. I describe a procedure to construct a close approximation q(α|θ,y) to the target density p(α|θ,y). It requires code to compute five derivatives of logp(yt|θ,αt) with respect to αt, t=1,…,n, and is not otherwise model specific. Since q(α|θ,y) is proper, fully normalised and simulable, it can be used as an importance density for importance sampling (IS) or as a proposal density for Markov chain Monte Carlo (MCMC). HESSIAN is an acronym but it also refers to the (sparse) Hessian matrix of logp(α|θ,y) with respect to α—the HESSIAN method is based on sparse matrix operations rather than the Kalman filter. I construct q(α|θ,y) and a related approximation q(θ,α|y) of p(θ,α|y) for two stochastic volatility models, two stochastic count models and a stochastic duration model. I illustrate their use for numerical approximation of likelihood function values and marginal likelihoods, using IS, and for posterior inference, using IS and MCMC. Compared with other simulation smoothing methods, the HESSIAN method is highly numerically efficient. In an IS application featuring a Student’s t stochastic volatility model and n=8851 daily log returns, the efficiency of IS for numerical approximation of the elements of the posterior mean E[θ|y] is between 80% and 100%.

Keywords: State space models; Simulation smoothing; Importance sampling; MCMC; Stochastic volatility; Count models; Duration models (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (17)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304407611002752
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:168:y:2012:i:2:p:189-206

DOI: 10.1016/j.jeconom.2011.12.003

Access Statistics for this article

Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

More articles in Journal of Econometrics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().