Simulation smoothing for state-space models: A computational efficiency analysis
Simulation smoothing involves drawing state variables (or innovations) in discrete time state-space models from their conditional distribution given parameters and observations. Gaussian simulation smoothing is of particular interest, not only for the direct analysis of Gaussian linear models, but also for the indirect analysis of more general models. Several methods for Gaussian simulation smoothing exist, most of which are based on the Kalman filter. Since states in Gaussian linear state-space models are Gaussian Markov random fields, it is also possible to apply the Cholesky Factor Algorithm (CFA) to draw states. This algorithm takes advantage of the band diagonal structure of the Hessian matrix of the log density to make efficient draws. We show how to exploit the special structure of state-space models to draw latent states even more efficiently. We analyse the computational efficiency of Kalman-filter-based methods, the CFA, and our new method using counts of operations and computational experiments. We show that for many important cases, our method is most efficient. Gains are particularly large for cases where the dimension of observed variables is large or where one makes repeated draws of states for the same parameter values. We apply our method to a multivariate Poisson model with time-varying intensities, which we use to analyse financial market transaction count data.
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- Chris Heaton & Victor Solo, 2004. "Identification of causal factor models of stationary time series," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 618-627, December.
- James H. Stock & Mark W. Watson, 1999.
NBER Working Papers
7023, National Bureau of Economic Research, Inc.
- Mario Forni & Marc Hallin & Lucrezia Reichlin & Marco Lippi, 2000.
"The generalised dynamic factor model: identification and estimation,"
ULB Institutional Repository
2013/10143, ULB -- Universite Libre de Bruxelles.
- Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
- Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 1999. "The Generalized Dynamic Factor Model: Identification and Estimation," CEPR Discussion Papers 2338, C.E.P.R. Discussion Papers.
- McCAUSLAND, William, 2008.
"The Hessian Method (Highly Efficient State Smoothing, In a Nutshell),"
Cahiers de recherche
2008-03, Universite de Montreal, Departement de sciences economiques.
- McCAUSLAND, William, 2008. "The Hessian Method (Highly Efficient State Smoothing, In a Nutshell)," Cahiers de recherche 03-2008, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Leonhard Knorr-Held, 2002. "On Block Updating in Markov Random Field Models for Disease Mapping," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(4), pages 597-614.
- Sangjoon Kim & Neil Shephard, 1994.
"Stochastic volatility: likelihood inference and comparison with ARCH models,"
3., Economics Group, Nuffield College, University of Oxford.
- Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 361-93, July.
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA.
- Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
- Jean Boivin & Marc Giannoni, 2006.
"DSGE Models in a Data-Rich Environment,"
NBER Working Papers
12772, National Bureau of Economic Research, Inc.
- Boivin, J. & Giannoni, M., 2007. "DSGE Models in a Data-Rich Environment," Working papers 162, Banque de France.
- Jean Boivin & Marc Giannoni, 2006. "DSGE Models in a Data-Rich Environment," NBER Technical Working Papers 0332, National Bureau of Economic Research, Inc.
- Marc P. Giannoni & Jean Boivin, 2005. "DSGE Models in a Data-Rich Environment," Computing in Economics and Finance 2005 431, Society for Computational Economics.
- Sylvia Fr�Hwirth-Schnatter & Helga Wagner, 2006. "Auxiliary mixture sampling for parameter-driven models of time series of counts with applications to state space modelling," Biometrika, Biometrika Trust, vol. 93(4), pages 827-841, December.
- J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
- Song, Juwon & Belin, Thomas R., 2008. "Choosing an appropriate number of factors in factor analysis with incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3560-3569, March.
- Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
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