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Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models

Author

Listed:
  • Geert Mesters

    (Netherlands Institute for the Study of Crime and Law Enforcement)

  • Siem Jan Koopman

    (VU University Amsterdam)

  • Marius Ooms

    (VU University Amsterdam)

Abstract

An exact maximum likelihood method is developed for the estimation of parameters in a non-Gaussian nonlinear log-density function that depends on a latent Gaussian dynamic process with long-memory properties. Our method relies on the method of importance sampling and on a linear Gaussian approximating model from which the latent process can be simulated. Given the presence of a latent long-memory process, we require a modification of the importance sampling technique. In particular, the long-memory process needs to be approximated by a finite dynamic linear process. Two possible approximations are discussed and are compared with each other. We show that an auto-regression obtained from minimizing mean squared prediction errors leads to an effective and feasible method. In our empirical study we analyze ten log-return series from the S&P 500 stock index by univariate and multivariate long-memory stochastic volatility models.

Suggested Citation

  • Geert Mesters & Siem Jan Koopman & Marius Ooms, 2011. "Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models," Tinbergen Institute Discussion Papers 11-090/4, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20110090
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Antonello D’Agostino & Domenico Giannone & Michele Lenza & Michele Modugno, 2016. "Nowcasting Business Cycles: A Bayesian Approach to Dynamic Heterogeneous Factor Models," Advances in Econometrics,in: Dynamic Factor Models, volume 35, pages 569-594 Emerald Publishing Ltd.
    2. Tobias Hartl & Roland Weigand, 2018. "Multivariate Fractional Components Analysis," Papers 1812.09149, arXiv.org, revised Jan 2019.
    3. Tobias Hartl & Roland Weigand, 2018. "Approximate State Space Modelling of Unobserved Fractional Components," Papers 1812.09142, arXiv.org, revised Mar 2019.
    4. Siem Jan Koopman & Marcel Scharth, 2012. "The Analysis of Stochastic Volatility in the Presence of Daily Realized Measures," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(1), pages 76-115, December.

    More about this item

    Keywords

    Fractional Integration; Importance Sampling; Kalman Filter; Latent Factors; Stochastic Volatility;

    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation

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