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

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  • 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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 51037.

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Date of creation: 29 Oct 2013
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Handle: RePEc:pra:mprapa:51037

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

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  1. Friedman, Moshe & Harris, Lawrence, 1998. "A Maximum Likelihood Approach for Non-Gaussian Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 16(3), pages 284-91, July.
  2. 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.
  3. Stephen Schilling & R. Bock, 2005. "High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature," Psychometrika, Springer, vol. 70(3), pages 533-555, September.
  4. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  5. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  6. 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, American Statistical Association, vol. 12(4), pages 413-17, October.
  7. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2002. "Reliable estimation of generalized linear mixed models using adaptive quadrature," Stata Journal, StataCorp LP, StataCorp LP, vol. 2(1), pages 1-21, February.
  8. Bartolucci, F. & De Luca, G., 2003. "Likelihood-based inference for asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 42(3), pages 445-449, March.
  9. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(1), pages 69-87, January.
  10. 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, Elsevier, vol. 128(2), pages 301-323, October.
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