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

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  • G. Mesters
  • S. J. Koopman
  • M. Ooms

Abstract

An exact maximum likelihood method is developed for the estimation of parameters in a non-Gaussian nonlinear 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 autoregression obtained from minimizing mean squared prediction errors leads to an effective and feasible method. In our empirical study, we analyze ten daily log-return series from the S&P 500 stock index by univariate and multivariate long-memory stochastic volatility models. We compare the in-sample and out-of-sample performance of a number of models within the class of long-memory stochastic volatility models.

Suggested Citation

  • G. Mesters & S. J. Koopman & M. Ooms, 2016. "Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 659-687, April.
  • Handle: RePEc:taf:emetrv:v:35:y:2016:i:4:p:659-687
    DOI: 10.1080/07474938.2015.1031014
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    References listed on IDEAS

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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

    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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