IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/51037.html
   My bibliography  Save this paper

Adaptive quadrature for likelihood inference on dynamic latent variable models for time-series and panel data

Author

Listed:
  • Cagnone, Silvia
  • Bartolucci, Francesco

Abstract

Maximum likelihood estimation of dynamic latent variable models requires to solve integrals that are not analytically tractable. Numerical approximations represent a possible solution to this problem. We propose to use the Adaptive Gaussian-Hermite (AGH) numerical quadrature approximation for a class of dynamic latent variable models for time-series and panel data. These models are based on continuous time-varying latent variables which follow an autoregressive process of order 1, AR(1). Two examples of such models are the stochastic volatility models for the analysis of financial time-series and the limited dependent variable models for the analysis of panel data. A comparison between the performance of AGH methods and alternative approximation methods proposed in the literature is carried out by simulation. Examples on real data are also used to illustrate the proposed approach.

Suggested Citation

  • Cagnone, Silvia & Bartolucci, Francesco, 2013. "Adaptive quadrature for likelihood inference on dynamic latent variable models for time-series and panel data," MPRA Paper 51037, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:51037
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/51037/1/MPRA_paper_51037.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    3. 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.
    4. Frees,Edward W., 2004. "Longitudinal and Panel Data," Cambridge Books, Cambridge University Press, number 9780521828284, December.
    5. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    6. Rabe-Hesketh, Sophia & Skrondal, Anders & Pickles, Andrew, 2005. "Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects," Journal of Econometrics, Elsevier, vol. 128(2), pages 301-323, October.
    7. Silvia Cagnone & Paola Monari, 2013. "Latent variable models for ordinal data by using the adaptive quadrature approximation," Computational Statistics, Springer, vol. 28(2), pages 597-619, April.
    8. Francesco Bartolucci & Silvia Bacci & Fulvia Pennoni, 2014. "Longitudinal analysis of self-reported health status by mixture latent auto-regressive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(2), pages 267-288, February.
    9. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2002. "Reliable estimation of generalized linear mixed models using adaptive quadrature," Stata Journal, StataCorp LLC, vol. 2(1), pages 1-21, February.
    10. Francesco Bartolucci & Giovanni De Luca, 2001. "Maximum likelihood estimation of a latent variable time‐series model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 17(1), pages 5-17, January.
    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. Bartolucci, F. & De Luca, G., 2003. "Likelihood-based inference for asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 445-449, March.
    13. Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
    14. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    15. Frees,Edward W., 2004. "Longitudinal and Panel Data," Cambridge Books, Cambridge University Press, number 9780521535380, December.
    16. Stephen Schilling & R. Bock, 2005. "High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 533-555, September.
    17. J. C. Naylor & A. F. M. Smith, 1982. "Applications of a Method for the Efficient Computation of Posterior Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(3), pages 214-225, November.
    18. Tanizaki, Hisashi & Mariano, Roberto S., 1998. "Nonlinear and non-Gaussian state-space modeling with Monte Carlo simulations," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 263-290.
    Full references (including those not matched with items on IDEAS)

    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. Silvia Cagnone & Francesco Bartolucci, 2017. "Adaptive Quadrature for Maximum Likelihood Estimation of a Class of Dynamic Latent Variable Models," Computational Economics, Springer;Society for Computational Economics, vol. 49(4), pages 599-622, April.
    2. N. Balakrishna & Bovas Abraham & Ranjini Sivakumar, 2006. "Gamma stochastic volatility models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(3), pages 153-171.
    3. Siem Jan Koopman & Eugenie Hol Uspensky, 2000. "The Stochastic Volatility in Mean Model," Tinbergen Institute Discussion Papers 00-024/4, Tinbergen Institute.
    4. Antonis Demos, 2023. "Statistical Properties of Two Asymmetric Stochastic Volatility in Mean Models," DEOS Working Papers 2303, Athens University of Economics and Business.
    5. Antonis Demos, 2023. "Estimation of Asymmetric Stochastic Volatility in Mean Models," DEOS Working Papers 2309, Athens University of Economics and Business.
    6. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    7. repec:cte:wsrepe:ws131110 is not listed on IDEAS
    8. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    9. Silvia Cagnone & Paola Monari, 2013. "Latent variable models for ordinal data by using the adaptive quadrature approximation," Computational Statistics, Springer, vol. 28(2), pages 597-619, April.
    10. Motta, Anderson C. O. & Hotta, Luiz K., 2003. "Exact Maximum Likelihood and Bayesian Estimation of the Stochastic Volatility Model," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 23(2), November.
    11. Ben Tims & Ronald Mahieu, 2006. "A Range-Based Multivariate Stochastic Volatility Model for Exchange Rates," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 409-424.
    12. Michael Pitt & Sheheryar Malik & Arnaud Doucet, 2014. "Simulated likelihood inference for stochastic volatility models using continuous particle filtering," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 527-552, June.
    13. Siem Jan Koopman & Eugenie Hol Uspensky, 2002. "The stochastic volatility in mean model: empirical evidence from international stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 667-689.
    14. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    15. Björn Andersson & Tao Xin, 2021. "Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation," Journal of Educational and Behavioral Statistics, , vol. 46(2), pages 244-265, April.
    16. P. Girardello & Orietta Nicolis & Giovanni Tondini, 2002. "Comparing conditional variance models: Theory and empirical evidence," Departmental Working Papers 2002-08, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    17. repec:bla:jecsur:v:22:y:2008:i:4:p:711-751 is not listed on IDEAS
    18. Nelson, Daniel B., 1996. "Asymptotic filtering theory for multivariate ARCH models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 1-47.
    19. Willy Alanya & Gabriel Rodríguez, 2019. "Asymmetries in Volatility: An Empirical Study for the Peruvian Stock and Forex Markets," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 1-18, March.
    20. Bermudez, P. de Zea & Marín, J. Miguel & Rue, Håvard & Veiga, Helena, 2024. "Integrated nested Laplace approximations for threshold stochastic volatility models," Econometrics and Statistics, Elsevier, vol. 30(C), pages 15-35.
    21. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 328-352, July.
    22. Wang, Joanna J.J. & Chan, Jennifer S.K. & Choy, S.T. Boris, 2011. "Stochastic volatility models with leverage and heavy-tailed distributions: A Bayesian approach using scale mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 852-862, January.

    More about this item

    Keywords

    AR(1); categorical longitudinal data; Gaussian-Hermite quadrature; limited dependent variable models; stochastic volatility model;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal 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:pra:mprapa:51037. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.