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Maximum likelihood estimation of a latent variable time‐series model

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  • Francesco Bartolucci
  • Giovanni De Luca

Abstract

Recently, Fridman and Harris proposed a method which allows one to approximate the likelihood of the basic stochastic volatility model. They also propose to estimate the parameters of such a model maximising the approximate likelihood by an algorithm which makes use of numerical derivatives. In this paper we propose an extension of their method which enables the computation of the first and second analytical derivatives of the approximate likelihood. As will be shown, these derivatives may be used to maximize the approximate likelihood through the Newton–Raphson algorithm, with a saving in the computational time. Moreover, these derivatives approximate the corresponding derivatives of the exact likelihood. In particular, the second derivative may be used to compute the standard error of the estimator and confidence intervals for the parameters. The paper presents also the results of a simulation study which allows one to compare our approach with other existing approaches. Copyright © 2001 John Wiley & Sons, Ltd.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:apsmbi:v:17:y:2001:i:1:p:5-17
    DOI: 10.1002/asmb.426
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    Cited by:

    1. Maddalena Cavicchioli, 2017. "Estimation and asymptotic covariance matrix for stochastic volatility models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 437-452, August.
    2. Roland Langrock & Théo Michelot & Alexander Sohn & Thomas Kneib, 2015. "Semiparametric stochastic volatility modelling using penalized splines," Computational Statistics, Springer, vol. 30(2), pages 517-537, June.
    3. Michels, Rouven & Ötting, Marius & Langrock, Roland, 2023. "Bettors’ reaction to match dynamics: Evidence from in-game betting," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1118-1127.
    4. Luca De Angelis & Leonard J. Paas, 2013. "A dynamic analysis of stock markets using a hidden Markov model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(8), pages 1682-1700, August.
    5. 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.
    6. Carlos A. Abanto‐Valle & Roland Langrock & Ming‐Hui Chen & Michel V. Cardoso, 2017. "Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(4), pages 394-408, August.
    7. 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.
    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.

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