IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20050117.html
   My bibliography  Save this paper

On Importance Sampling for State Space Models

Author

Listed:
  • Borus Jungbacker

    (Vrije Universiteit Amsterdam)

  • Siem Jan Koopman

    (Vrije Universiteit Amsterdam)

Abstract

We consider likelihood inference and state estimation by means of importance sampling for state space models with a nonlinear non-Gaussian observation y ~ p(y|alpha) and a linear Gaussian state alpha ~ p(alpha). The importance density is chosen to be the Laplace approximation of the smoothing density p(alpha|y). We show that computationally efficient state space methods can be used to perform all necessary computations in all situations. It requires new derivations of the Kalman filter and smoother and the simulation smoother which do not rely on a linear Gaussian observation equation. Furthermore, results are presented that lead to a more effective implementation of importance sampling for state space models. An illustration is given for the stochastic volatility model with leverage.

Suggested Citation

  • Borus Jungbacker & Siem Jan Koopman, 2005. "On Importance Sampling for State Space Models," Tinbergen Institute Discussion Papers 05-117/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20050117
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/05117.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    4. 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.
    5. 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.
    6. 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.
    7. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Charles S. Bos & Phillip Gould, 2007. "Dynamic Correlations and Optimal Hedge Ratios," Tinbergen Institute Discussion Papers 07-025/4, Tinbergen Institute.
    2. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility (Revised in May 2007, Handbook of Financial Time Series (Published in "Handbook of Financial Time Series" (eds T.G. Andersen, R.A. Davis, Jens-Peter Kreiss," CARF F-Series CARF-F-094, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. M. Hakan Eratalay, 2016. "Estimation of Multivariate Stochastic Volatility Models: A Comparative Monte Carlo Study," International Econometric Review (IER), Econometric Research Association, vol. 8(2), pages 19-52, September.
    4. M. Hakan Eratalay, 2016. "Estimation of Multivariate Stochastic Volatility Models: A Comparative Monte Carlo Study," International Econometric Review (IER), Econometric Research Association, vol. 8(2), pages 19-52, September.
    5. Borus Jungbacker & Siem Jan Koopman, 2006. "Monte Carlo Likelihood Estimation for Three Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 385-408.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Siem Jan Koopman & André Lucas & Marcel Scharth, 2015. "Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State-Space Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 114-127, January.
    2. 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.
    3. Koopman, Siem Jan & Lucas, André, 2008. "A Non-Gaussian Panel Time Series Model for Estimating and Decomposing Default Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 510-525.
    4. Koopman, Siem Jan & Lucas, André, 2008. "A Non-Gaussian Panel Time Series Model for Estimating and Decomposing Default Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 510-525.
    5. Yasuhiro Omori & Siddhartha Chib & Neil Shephard & Jouchi Nakajima, 2004. "Stochastic Volatility with Leverage: Fast Likelihood Inference," CIRJE F-Series CIRJE-F-297, CIRJE, Faculty of Economics, University of Tokyo.
    6. Siem Jan Koopman & Marius Ooms & André Lucas & Kees van Montfort & Victor Van Der Geest, 2008. "Estimating systematic continuous‐time trends in recidivism using a non‐Gaussian panel data model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(1), pages 104-130, February.
    7. Borus Jungbacker & Siem Jan Koopman, 2006. "Model-Based Measurement of Actual Volatility in High-Frequency Data," Advances in Econometrics, in: Econometric Analysis of Financial and Economic Time Series, pages 183-210, Emerald Group Publishing Limited.
    8. Siem Jan Koopman & Charles S. Bos, 2002. "Time Series Models with a Common Stochastic Variance for Analysing Economic Time Series," Tinbergen Institute Discussion Papers 02-113/4, Tinbergen Institute.
    9. Alexander Tsyplakov, 2010. "Revealing the arcane: an introduction to the art of stochastic volatility models (in Russian)," Quantile, Quantile, issue 8, pages 69-122, July.
    10. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
    11. Siem Jan Koopman & John A. D. Aston, 2006. "A non-Gaussian generalization of the Airline model for robust seasonal adjustment," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(5), pages 325-349.
    12. Bernd Schwaab & Andre Lucas & Siem Jan Koopman, 2010. "Systemic Risk Diagnostics," Tinbergen Institute Discussion Papers 10-104/2/DSF 2, Tinbergen Institute, revised 29 Nov 2010.
    13. Tsyplakov, Alexander, 2010. "Revealing the arcane: an introduction to the art of stochastic volatility models," MPRA Paper 25511, University Library of Munich, Germany.
    14. 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.
    15. Siem Jan Koopman & Neil Shephard, 2002. "Testing the Assumptions Behind the Use of Importance Sampling," Economics Papers 2002-W17, Economics Group, Nuffield College, University of Oxford.
    16. Geweke, J. & Joel Horowitz & Pesaran, M.H., 2006. "Econometrics: A Bird’s Eye View," Cambridge Working Papers in Economics 0655, Faculty of Economics, University of Cambridge.
    17. Falk Bräuning & Siem Jan Koopman, 2016. "The dynamic factor network model with an application to global credit risk," Working Papers 16-13, Federal Reserve Bank of Boston.
    18. Mesters, G. & Koopman, S.J., 2014. "Generalized dynamic panel data models with random effects for cross-section and time," Journal of Econometrics, Elsevier, vol. 180(2), pages 127-140.
    19. Tommaso Proietti & Alessandra Luati, 2013. "Maximum likelihood estimation of time series models: the Kalman filter and beyond," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 15, pages 334-362, Edward Elgar Publishing.
    20. Yuta Kurose & Yasuhiro Omori, 2012. "Bayesian Analysis of Time-Varying Quantiles Using a Smoothing Spline," CIRJE F-Series CIRJE-F-845, CIRJE, Faculty of Economics, University of Tokyo.

    More about this item

    Keywords

    Kalman filter; Likelihood function; Monte Carlo integration; Newton-Raphson; Posterior mode estimation; Simulation smoothing; Stochastic volatility model;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tin:wpaper:20050117. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.