IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v127y2018icp187-203.html
   My bibliography  Save this article

Sequential Bayesian inference for static parameters in dynamic state space models

Author

Listed:
  • Bhattacharya, Arnab
  • Wilson, Simon P.

Abstract

A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is able to use any valid approximation to the filtering and prediction densities of the state process. It computes the posterior distribution of the static parameters on a discrete grid that tracks the support dynamically. For inference of the state process, the Kalman filter and its extensions as well as cubature filtering have been used. It is illustrated with several examples including the stochastic volatility model and the challenging Kitagawa model and is compared to both online and offline methods. It is shown to provide a good trade off between speed and performance.

Suggested Citation

  • Bhattacharya, Arnab & Wilson, Simon P., 2018. "Sequential Bayesian inference for static parameters in dynamic state space models," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 187-203.
    • Handle: RePEc:eee:csdana:v:127:y:2018:i:c:p:187-203
    DOI: 10.1016/j.csda.2018.05.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318301336
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.05.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. George Poyiadjis & Arnaud Doucet & Sumeetpal S. Singh, 2011. "Particle approximations of the score and observed information matrix in state space models with application to parameter estimation," Biometrika, Biometrika Trust, vol. 98(1), pages 65-80.
    2. Zhijian He & Art B. Owen, 2016. "Extensible grids: uniform sampling on a space filling curve," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 917-931, September.
    3. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    4. Kastner, Gregor, 2016. "Dealing with Stochastic Volatility in Time Series Using the R Package stochvol," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i05).
    5. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    6. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    7. Nicolas Chopin & Alessandra Iacobucci & Jean-Michel Marin & Kerrie L. Mengersen & Christian P. Robert & Robin Ryder & Christian Schafer, 2010. "On Particle Learning," Working Papers 2010-22, Center for Research in Economics and Statistics.
    8. N. Chopin & P. E. Jacob & O. Papaspiliopoulos, 2013. "SMC-super-2: an efficient algorithm for sequential analysis of state space models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 397-426, June.
    9. Andrew Gelman, 2003. "A Bayesian Formulation of Exploratory Data Analysis and Goodness‐of‐fit Testing," International Statistical Review, International Statistical Institute, vol. 71(2), pages 369-382, August.
    10. repec:dau:papers:123456789/7305 is not listed on IDEAS
    11. Mathieu Gerber & Nicolas Chopin, 2015. "Sequential quasi Monte Carlo," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(3), pages 509-579, June.
    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. Guo, Kai & Ye, Zhisheng & Liu, Datong & Peng, Xiyuan, 2021. "UAV flight control sensing enhancement with a data-driven adaptive fusion model," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    2. Nathaniel Tomasetti & Catherine Forbes & Anastasios Panagiotelis, 2019. "Updating Variational Bayes: Fast Sequential Posterior Inference," Monash Econometrics and Business Statistics Working Papers 13/19, Monash University, Department of Econometrics and Business Statistics.

    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. Piotr Szczepocki, 2020. "Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 173-187, June.
    2. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2016. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Papers 1605.09484, arXiv.org.
    3. Arnaud Doucet & Neil Shephard, 2012. "Robust inference on parameters via particle filters and sandwich covariance matrices," Economics Papers 2012-W05, Economics Group, Nuffield College, University of Oxford.
    4. Salima El Kolei, 2013. "Parametric estimation of hidden stochastic model by contrast minimization and deconvolution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 1031-1081, November.
    5. Crucinio, Francesca R. & Johansen, Adam M., 2023. "Properties of marginal sequential Monte Carlo methods," Statistics & Probability Letters, Elsevier, vol. 203(C).
    6. Johan Dahlin & Mattias Villani & Thomas B. Schon, 2015. "Bayesian optimisation for fast approximate inference in state-space models with intractable likelihoods," Papers 1506.06975, arXiv.org, revised Jun 2017.
    7. Ruiz-Cárdenas, Ramiro & Krainski, Elias T. & Rue, Håvard, 2012. "Direct fitting of dynamic models using integrated nested Laplace approximations — INLA," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1808-1828.
    8. Axel Finke & Adam Johansen & Dario Spanò, 2014. "Static-parameter estimation in piecewise deterministic processes using particle Gibbs samplers," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 577-609, June.
    9. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    10. Matti Vihola & Jouni Helske & Jordan Franks, 2020. "Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1339-1376, December.
    11. Hubin, Aliaksandr & Storvik, Geir, 2018. "Mode jumping MCMC for Bayesian variable selection in GLMM," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 281-297.
    12. Szczepocki Piotr, 2020. "Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 173-187, June.
    13. Patrick Aschermayr & Konstantinos Kalogeropoulos, 2023. "Sequential Bayesian Learning for Hidden Semi-Markov Models," Papers 2301.10494, arXiv.org.
    14. Joshua Chan & Arnaud Doucet & Roberto León-González & Rodney W. Strachan, 2018. "Multivariate Stochastic Volatility with Co-Heteroscedasticity," Working Paper series 18-38, Rimini Centre for Economic Analysis.
    15. Arnaud Dufays, 2016. "Evolutionary Sequential Monte Carlo Samplers for Change-Point Models," Econometrics, MDPI, vol. 4(1), pages 1-33, March.
    16. Loaiza-Maya, Rubén & Smith, Michael Stanley & Nott, David J. & Danaher, Peter J., 2022. "Fast and accurate variational inference for models with many latent variables," Journal of Econometrics, Elsevier, vol. 230(2), pages 339-362.
    17. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    18. 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.
    19. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723.
    20. Brignone, Riccardo & Gonzato, Luca & Lütkebohmert, Eva, 2023. "Efficient Quasi-Bayesian Estimation of Affine Option Pricing Models Using Risk-Neutral Cumulants," Journal of Banking & Finance, Elsevier, vol. 148(C).

    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:eee:csdana:v:127:y:2018:i:c:p:187-203. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.