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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.

Suggested Citation

  • McCausland, William J. & Miller, Shirley & Pelletier, Denis, 2011. "Simulation smoothing for state-space models: A computational efficiency analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 199-212, January.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:199-212
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    Cited by:

    1. Martin Iseringhausen, 2018. "The Time-Varying Asymmetry Of Exchange Rate Returns: A Stochastic Volatility – Stochastic Skewness Model," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 18/944, Ghent University, Faculty of Economics and Business Administration.
    2. Li, Junye, 2013. "An unscented Kalman smoother for volatility extraction: Evidence from stock prices and options," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 15-26.
    3. 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.
    4. Joshua C.C. Chan & Rodney Strachan, 2014. "The Zero Lower Bound: Implications for Modelling the Interest Rate," Working Paper series 42_14, Rimini Centre for Economic Analysis.
    5. repec:wly:jmoncb:v:49:y:2017:i:2-3:p:525-552 is not listed on IDEAS
    6. repec:taf:jnlbes:v:35:y:2017:i:1:p:17-28 is not listed on IDEAS
    7. Chan, Joshua C.C., 2013. "Moving average stochastic volatility models with application to inflation forecast," Journal of Econometrics, Elsevier, vol. 176(2), pages 162-172.
    8. Delle Monache, Davide & Petrella, Ivan, 2019. "Efficient Matrix Approach for Classical Inference in State Space Models," EMF Research Papers 19, Economic Modelling and Forecasting Group.
    9. Eric Eisenstat & Rodney W. Strachan, 2016. "Modelling Inflation Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(5), pages 805-820, August.
    10. Chan, Joshua & Strachan, Rodney, 2012. "Estimation in Non-Linear Non-Gaussian State Space Models with Precision-Based Methods," MPRA Paper 39360, University Library of Munich, Germany.
    11. Chan, Joshua C.C. & Grant, Angelia L., 2016. "Fast computation of the deviance information criterion for latent variable models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 847-859.
    12. 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.
    13. Joshua C. C. Chan, 2017. "The Stochastic Volatility in Mean Model With Time-Varying Parameters: An Application to Inflation Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 17-28, January.
    14. Liu, Wei-han, 2016. "A re-examination of maturity effect of energy futures price from the perspective of stochastic volatility," Energy Economics, Elsevier, vol. 56(C), pages 351-362.
    15. McCausland, William J., 2012. "The HESSIAN method: Highly efficient simulation smoothing, in a nutshell," Journal of Econometrics, Elsevier, vol. 168(2), pages 189-206.
    16. Darjus Hosszejni & Gregor Kastner, 2019. "Approaches Toward the Bayesian Estimation of the Stochastic Volatility Model with Leverage," Papers 1901.11491, arXiv.org.
    17. 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.
    18. 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.
    19. Angelia L. Grant & Joshua C.C. Chan, 2017. "A Bayesian Model Comparison for Trend‐Cycle Decompositions of Output," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(2-3), pages 525-552, March.
    20. Luis Uzeda, 2016. "State Correlation and Forecasting: A Bayesian Approach Using Unobserved Components Models," ANU Working Papers in Economics and Econometrics 2016-632, Australian National University, College of Business and Economics, School of Economics.
    21. Jamie L. Cross & Chenghan Hou & Aubrey Poon, 2018. "International Transmission of Macroeconomic Uncertainty in Small Open Economies: An Empirical Approach," Working Papers No 12/2018, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    22. repec:eee:ecmode:v:69:y:2018:i:c:p:291-300 is not listed on IDEAS

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