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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
    4. 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.
    5. 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.
    6. 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.
    7. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2002. "Reliable estimation of generalized linear mixed models using adaptive quadrature," Stata Journal, StataCorp LP, vol. 2(1), pages 1-21, February.
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    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. 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.
    11. 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.
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    13. 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.
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    More about this item

    Keywords

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

    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

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