IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v45y1999i4p325-333.html
   My bibliography  Save this article

The use of approximating models in Monte Carlo maximum likelihood estimation

Author

Listed:
  • Kuk, Anthony Y. C.

Abstract

To obtain the likelihood of a non-Gaussian state-space model, Durbin and Koopman (1997, Biometrika, 84, 669-684) first calculate the likelihood under an approximating linear Gaussian model and then use Monte Carlo methods to estimate the necessary adjustment factor. We show that Durbin and Koopman's method is closely related to a method proposed by Geyer (1994, J. Roy. Statist. Soc. B 56, 261-274) for simulating the likelihood of a random-effects model and to a method proposed by Schall (1991, Biometrika, 78, 719-727) for approximating the maximum likelihood estimate of a generalised linear mixed model. A hybrid method is proposed for approximating the entire likelihood function as opposed to Durbin and Koopman's pointwise approximation. We also suggest an alternative class of approximating models based on conjugate latent process and apply it to approximate the likelihood of a time series model for count data.

Suggested Citation

  • Kuk, Anthony Y. C., 1999. "The use of approximating models in Monte Carlo maximum likelihood estimation," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 325-333, December.
    • Handle: RePEc:eee:stapro:v:45:y:1999:i:4:p:325-333
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(99)00074-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 407-417, October.
    2. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 422-422, October.
    3. P. Vidoni, 1999. "Exponential family state space models based on a conjugate latent process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 213-221.
    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. Richard A. Davis & Thomas C. M. Lee & Gabriel A. Rodriguez‐Yam, 2008. "Break Detection for a Class of Nonlinear Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 834-867, September.
    2. Christian N. Brinch, 2008. "Simulated Maximum Likelihood using Tilted Importance Sampling," Discussion Papers 540, Statistics Norway, Research Department.

    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. Yang Lu, 2020. "A simple parameter‐driven binary time series model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(2), pages 187-199, March.
    2. Kostas Triantafyllopoulos, 2009. "Inference of Dynamic Generalized Linear Models: On‐Line Computation and Appraisal," International Statistical Review, International Statistical Institute, vol. 77(3), pages 430-450, December.
    3. de Pinho, Frank M. & Franco, Glaura C. & Silva, Ralph S., 2016. "Modeling volatility using state space models with heavy tailed distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 108-127.
    4. Harvey, A., 2008. "Dynamic distributions and changing copulas," Cambridge Working Papers in Economics 0839, Faculty of Economics, University of Cambridge.
    5. Wagner Barreto-Souza, 2019. "Mixed Poisson INAR(1) processes," Statistical Papers, Springer, vol. 60(6), pages 2119-2139, December.
    6. Brannas, Kurt, 1995. "Prediction and control for a time-series count data model," International Journal of Forecasting, Elsevier, vol. 11(2), pages 263-270, June.
    7. Snyder, Ralph D. & Ord, J. Keith & Beaumont, Adrian, 2012. "Forecasting the intermittent demand for slow-moving inventories: A modelling approach," International Journal of Forecasting, Elsevier, vol. 28(2), pages 485-496.
    8. Youn Ahn, Jae & Jeong, Himchan & Lu, Yang, 2021. "On the ordering of credibility factors," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 626-638.
    9. HEINEN, Andréas, 2003. "Modelling time series count data: an autoregressive conditional Poisson model," LIDAM Discussion Papers CORE 2003062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Nobuhiko Terui & Masataka Ban, 2013. "Multivariate Time Series Model with Hierarchical Structure for Over-dispersed Discrete Outcomes," TMARG Discussion Papers 113, Graduate School of Economics and Management, Tohoku University, revised Aug 2013.
    11. Harvey, Andrew, 2010. "Tracking a changing copula," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 485-500, June.
    12. Svetunkov, Ivan & Boylan, John E., 2023. "iETS: State space model for intermittent demand forecasting," International Journal of Production Economics, Elsevier, vol. 265(C).
    13. Shang, Zuofeng, 2012. "On latent process models in multi-dimensional space," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1259-1266.
    14. Robert Jung & A. Tremayne, 2011. "Useful models for time series of counts or simply wrong ones?," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(1), pages 59-91, March.
    15. Shirozhan, M. & Bakouch, Hassan S. & Mohammadpour, M., 2023. "A flexible INAR(1) time series model with dependent zero-inflated count series and medical contagious cases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 216-230.
    16. Ki Hong Kim & Young Jae Han & Sugil Lee & Sung Won Cho & Chulung Lee, 2019. "Text Mining for Patent Analysis to Forecast Emerging Technologies in Wireless Power Transfer," Sustainability, MDPI, vol. 11(22), pages 1-24, November.
    17. Ord, J. Keith & Koehler, Anne B. & Snyder, Ralph D. & Hyndman, Rob J., 2009. "Monitoring processes with changing variances," International Journal of Forecasting, Elsevier, vol. 25(3), pages 518-525, July.
    18. Axel Groß‐KlußMann & Nikolaus Hautsch, 2013. "Predicting Bid–Ask Spreads Using Long‐Memory Autoregressive Conditional Poisson Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(8), pages 724-742, December.
    19. Boris Aleksandrov & Christian H. Weiß, 2020. "Testing the dispersion structure of count time series using Pearson residuals," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 325-361, September.
    20. Nobuhiko Terui & Masataka Ban & Toshihiko Maki, 2010. "Finding market structure by sales count dynamics—Multivariate structural time series models with hierarchical structure for count data—," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(1), pages 91-107, February.

    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:stapro:v:45:y:1999:i:4:p:325-333. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.