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

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  • 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. 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.
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  3. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October.
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  5. 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.
  6. 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.
  7. 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.
  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.
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Cited by:
  1. 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.
  2. Joshua C.C. Chan & Angelia L. Grant, 2014. "Fast Computation of the Deviance Information Criterion for Latent Variable Models," CAMA Working Papers 2014-09, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  3. Joshua C.C. Chan, 2013. "Moving Average Stochastic Volatility Models with Application to Inflation Forecast," CAMA Working Papers 2013-31, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  4. Joshua C.C. Chan & Angelia L. Grant, 2014. "Issues in Comparing Stochastic Volatility Models Using the Deviance Information Criterion," CAMA Working Papers 2014-51, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  5. Joshua C C Chan & Cody Y L Hsiao, 2013. "Estimation of Stochastic Volatility Models with Heavy Tails and Serial Dependence," CAMA Working Papers 2013-74, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  6. McCausland, William J., 2012. "The HESSIAN method: Highly efficient simulation smoothing, in a nutshell," Journal of Econometrics, Elsevier, vol. 168(2), pages 189-206.
  7. Eric Eisenstat & Rodney W. Strachan, 2014. "Modelling Inflation Volatility," CAMA Working Papers 2014-21, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  8. Joshua C.C. Chan & Eric Eisenstat, 2013. "Gibbs Samplers for VARMA and Its Extensions," ANU Working Papers in Economics and Econometrics 2013-604, Australian National University, College of Business and Economics, School of Economics.
  9. Kastner, Gregor & Frühwirth-Schnatter, Sylvia, 2014. "Ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 408-423.

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