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Parameterisation and Efficient MCMC Estimation of Non-Gaussian State Space Models

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  • Chris M Strickland
  • Gael Martin
  • Catherine S Forbes

Abstract

The impact of parameterisation on the simulation efficiency of Bayesian Markov chain Monte Carlo (MCMC) algorithms for two non-Gaussian state space models is examined. Specifically, focus is given to particular forms of the stochastic conditional duration (SCD) model and the stochastic volatility (SV) model, with four alternative parameterisations of each model considered. A controlled experiment using simulated data reveals that relationships exist between the simulation efficiency of the MCMC sampler, the magnitudes of the population parameters and the particular parameterisation of the state space model. Results of an empirical analysis of two separate transaction data sets for the SCD model, as well as equity and exchange rate data sets for the SV model, are also reported. Both the simulation and empirical results reveal that substantial gains in simulation efficiency can be obtained from simple reparameterisations of both types of non-Gaussian state space models.

Suggested Citation

  • Chris M Strickland & Gael Martin & Catherine S Forbes, 2006. "Parameterisation and Efficient MCMC Estimation of Non-Gaussian State Space Models," Monash Econometrics and Business Statistics Working Papers 22/06, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2006-22
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2006/wp22-06.pdf
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    Cited by:

    1. Hautsch, Nikolaus & Yang, Fuyu, 2012. "Bayesian inference in a Stochastic Volatility Nelson–Siegel model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3774-3792.
    2. Brendan P.M. McCabe & Gael Martin & Keith Freeland, 2010. "A Quasi-locally Most powerful Test for Correlation in the conditional Variance of Positive Data," Monash Econometrics and Business Statistics Working Papers 2/10, Monash University, Department of Econometrics and Business Statistics.
    3. 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.
    4. Grassi, S. & Proietti, T., 2014. "Characterising economic trends by Bayesian stochastic model specification search," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 359-374.
    5. Jouchi Nakajima & Yasuhiro Omori, 2010. "Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student's t-Distribution Models," CIRJE F-Series CIRJE-F-738, CIRJE, Faculty of Economics, University of Tokyo.
    6. Nakajima, Jouchi & Omori, Yasuhiro, 2012. "Stochastic volatility model with leverage and asymmetrically heavy-tailed error using GH skew Student’s t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3690-3704.
    7. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    8. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    9. Kreuzer, Alexander & Czado, Claudia, 2021. "Bayesian inference for a single factor copula stochastic volatility model using Hamiltonian Monte Carlo," Econometrics and Statistics, Elsevier, vol. 19(C), pages 130-150.
    10. Gregor Kastner & Sylvia Fruhwirth-Schnatter & Hedibert Freitas Lopes, 2016. "Efficient Bayesian Inference for Multivariate Factor Stochastic Volatility Models," Papers 1602.08154, arXiv.org, revised Jul 2017.
    11. McCausland, William J., 2012. "The HESSIAN method: Highly efficient simulation smoothing, in a nutshell," Journal of Econometrics, Elsevier, vol. 168(2), pages 189-206.
    12. Tommaso, Proietti & Stefano, Grassi, 2010. "Bayesian stochastic model specification search for seasonal and calendar effects," MPRA Paper 27305, University Library of Munich, Germany.
    13. Strickland, Christopher & Burdett, Robert & Mengersen, Kerrie & Denham, Robert, 2014. "PySSM: A Python Module for Bayesian Inference of Linear Gaussian State Space Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i06).
    14. Strickland, Chris M. & Turner, Ian. W. & Denham, Robert & Mengersen, Kerrie L., 2009. "Efficient Bayesian estimation of multivariate state space models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4116-4125, October.

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    More about this item

    Keywords

    Bayesian methodology; stochastic volatility; durations; non-centred in location; non-centred in scale; inefficiency factors.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G1 - Financial Economics - - General Financial Markets

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