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Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models

Author

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  • Siem Jan Koopman

    (VU University Amsterdam)

  • Andre Lucas

    (VU University Amsterdam)

  • Marcel Scharth

    (VU University Amsterdam)

Abstract

This paper led to a publication in the 'Journal of Business & Economic Statistics' , 2015, 33 (1), 114-127. We introduce a new efficient importance sampler for nonlinear non-Gaussian state space models. We propose a general and efficient likelihood evaluation method for this class of models via the combination of numerical and Monte Carlo integration methods. Our methodology explores the idea that only a small part of the likelihood evaluation problem requires simulation. We refer to our new method as numerically accelerated importance sampling. The method is computationally and numerically efficient, facilitates parameter estimation for models with high-dimensional state vectors, and overcomes a bias-variance trade-off encountered by other sampling methods. An elaborate simulation study and an empirical application for U.S. stock returns reveal large efficiency gains for a range of models used in financial econometrics.

Suggested Citation

  • Siem Jan Koopman & Andre Lucas & Marcel Scharth, 2011. "Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models," Tinbergen Institute Discussion Papers 11-057/4, Tinbergen Institute, revised 27 Jan 2012.
    • Handle: RePEc:tin:wpaper:20110057
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    References listed on IDEAS

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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Florian Heiss, 2008. "Sequential numerical integration in nonlinear state space models for microeconometric panel data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(3), pages 373-389.
    3. J. Durbin & S. J. Koopman, 2000. "Time series analysis of non‐Gaussian observations based on state space models from both classical and Bayesian perspectives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 3-56.
    4. Friedman, Moshe & Harris, Lawrence, 1998. "A Maximum Likelihood Approach for Non-Gaussian Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 284-291, July.
    5. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    6. Koopman, Siem Jan & Shephard, Neil & Creal, Drew, 2009. "Testing the assumptions behind importance sampling," Journal of Econometrics, Elsevier, vol. 149(1), pages 2-11, April.
    7. Luc Bauwens & Nikolaus Hautsch, 2006. "Stochastic Conditional Intensity Processes," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 450-493.
    8. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
    9. Engle, Robert F. & White (the late), Halbert (ed.), 1999. "Cointegration, Causality, and Forecasting: Festschrift in Honour of Clive W. J. Granger," OUP Catalogue, Oxford University Press, number 9780198296836.
    10. BAUWENS, Luc & VEREDAS, David, 1999. "The stochastic conditional duration model: a latent factor model for the analysis of financial durations," LIDAM Discussion Papers CORE 1999058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Bauwens, L. & Galli, F., 2009. "Efficient importance sampling for ML estimation of SCD models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1974-1992, April.
    12. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    13. Bauwens, Luc & Veredas, David, 2004. "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," Journal of Econometrics, Elsevier, vol. 119(2), pages 381-412, April.
    14. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
    15. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
    16. Borus Jungbacker & Siem Jan Koopman, 2007. "Monte Carlo Estimation for Nonlinear Non-Gaussian State Space Models," Biometrika, Biometrika Trust, vol. 94(4), pages 827-839.
    17. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Paper 321, Department of Economics, University of Pittsburgh, revised Jan 2007.
    18. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    19. 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.
    20. Danielsson, J & Richard, J-F, 1993. "Accelerated Gaussian Importance Sampler with Application to Dynamic Latent Variable Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 153-173, Suppl. De.
    21. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
    22. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
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    Citations

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    Cited by:

    1. Jean-François Richard, 2015. "Likelihood Evaluation of High-Dimensional Spatial Latent Gaussian Models with Non-Gaussian Response Variables," Working Paper 5778, Department of Economics, University of Pittsburgh.
    2. Baştürk, N. & Borowska, A. & Grassi, S. & Hoogerheide, L. & van Dijk, H.K., 2019. "Forecast density combinations of dynamic models and data driven portfolio strategies," Journal of Econometrics, Elsevier, vol. 210(1), pages 170-186.
    3. Hong Li & Yang Lu, 2018. "A Bayesian non-parametric model for small population mortality," Post-Print hal-02419000, HAL.
    4. Leopoldo Catania & Roberto Di Mari & Paolo Santucci de Magistris, 2019. "Dynamic discrete mixtures for high frequency prices," Discussion Papers 19/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    5. Siem Jan Koopman & Rutger Lit & Thuy Minh Nguyen, 2012. "Fast Efficient Importance Sampling by State Space Methods," Tinbergen Institute Discussion Papers 12-008/4, Tinbergen Institute, revised 16 Oct 2014.
    6. Blasques, Francisco & Koopman, Siem Jan & Lucas, Andre & Schaumburg, Julia, 2016. "Spillover dynamics for systemic risk measurement using spatial financial time series models," Journal of Econometrics, Elsevier, vol. 195(2), pages 211-223.
    7. Rutger Jan Lange, 2020. "Bellman filtering for state-space models," Tinbergen Institute Discussion Papers 20-052/III, Tinbergen Institute, revised 19 May 2021.
    8. Siem Jan Koopman & Rutger Lit & André Lucas, 2017. "Intraday Stochastic Volatility in Discrete Price Changes: The Dynamic Skellam Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1490-1503, October.
    9. Mengheng Li & Siem Jan (S.J.) Koopman, 2018. "Unobserved Components with Stochastic Volatility in U.S. Inflation: Estimation and Signal Extraction," Tinbergen Institute Discussion Papers 18-027/III, Tinbergen Institute.
    10. Lange, Rutger-Jan, 2024. "Bellman filtering and smoothing for state–space models," Journal of Econometrics, Elsevier, vol. 238(2).
    11. Siem Jan Koopman & Marcel Scharth, 2012. "The Analysis of Stochastic Volatility in the Presence of Daily Realized Measures," Journal of Financial Econometrics, Oxford University Press, vol. 11(1), pages 76-115, December.
    12. István Barra & Lennart Hoogerheide & Siem Jan Koopman & André Lucas, 2017. "Joint Bayesian Analysis of Parameters and States in Nonlinear non‐Gaussian State Space Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(5), pages 1003-1026, August.
    13. Siem Jan Koopman & André Lucas & Marcel Scharth, 2016. "Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models," The Review of Economics and Statistics, MIT Press, vol. 98(1), pages 97-110, March.
    14. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2022. "Realized matrix-exponential stochastic volatility with asymmetry, long memory and higher-moment spillovers," Journal of Econometrics, Elsevier, vol. 227(1), pages 285-304.
    15. Mao, Xiuping & Ruiz, Esther & Veiga, Helena, 2017. "Threshold stochastic volatility: Properties and forecasting," International Journal of Forecasting, Elsevier, vol. 33(4), pages 1105-1123.
    16. S. J. Koopman & G. Mesters, 2017. "Empirical Bayes Methods for Dynamic Factor Models," The Review of Economics and Statistics, MIT Press, vol. 99(3), pages 486-498, July.
    17. Scharth, Marcel & Kohn, Robert, 2016. "Particle efficient importance sampling," Journal of Econometrics, Elsevier, vol. 190(1), pages 133-147.
    18. Rub'en Loaiza-Maya & Didier Nibbering, 2022. "Efficient variational approximations for state space models," Papers 2210.11010, arXiv.org, revised Jun 2023.
    19. repec:cte:wsrepe:ws142618 is not listed on IDEAS
    20. Caterina Schiavoni & Siem Jan Koopman & Franz Palm & Stephan Smeekes & Jan van den Brakel, 2021. "Time-varying state correlations in state space models and their estimation via indirect inference," Tinbergen Institute Discussion Papers 21-020/III, Tinbergen Institute.
    21. Casarin, Roberto & Grassi, Stefano & Ravazzolo, Francesco & van Dijk, Herman K., 2023. "A flexible predictive density combination for large financial data sets in regular and crisis periods," Journal of Econometrics, Elsevier, vol. 237(2).
    22. Siem Jan Koopman & Rutger Lit & André Lucas, 2014. "The Dynamic Skellam Model with Applications," Tinbergen Institute Discussion Papers 14-032/IV/DSF73, Tinbergen Institute, revised 06 Jul 2015.

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    More about this item

    Keywords

    State space models; importance sampling; simulated maximum likelihood; stochastic volatility; stochastic copula; stochastic conditional duration;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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