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Simulation smoothing for state-space models: A computational efficiency analysis

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Author Info

  • McCausland, William J.
  • Miller, Shirley
  • Pelletier, Denis

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 55 (2011)
Issue (Month): 1 (January)
Pages: 199-212

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Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:199-212

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Web page: http://www.elsevier.com/locate/csda

Related research

Keywords: State-space models Markov chain Monte Carlo Importance sampling Count data High frequency financial data;

References

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  1. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  2. 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.
  3. James H. Stock & Mark W. Watson, 1999. "Forecasting Inflation," NBER Working Papers 7023, National Bureau of Economic Research, Inc.
  4. 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.
  5. 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.
  6. Boivin, J. & Giannoni, M., 2007. "DSGE Models in a Data-Rich Environment," Working papers 162, Banque de France.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
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Cited by:
  1. Joshua C C Chan, 2012. "Moving Average Stochastic Volatility Models with Application to Inflation Forecast," ANU Working Papers in Economics and Econometrics 2012-591, Australian National University, College of Business and Economics, School of Economics.
  2. Joshua Chan & Rodney Strachan, 2012. "Estimation in Non-Linear Non-Gaussian State Space Models with Precision-Based Methods," CAMA Working Papers 2012-13, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.

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