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

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 11-090/4.

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Date of creation: 27 Jun 2011
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Handle: RePEc:dgr:uvatin:20110090

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Web page: http://www.tinbergen.nl

Related research

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

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  1. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
  2. Jurgen Doornik & Marius Ooms, 2001. "Computational Aspects of Maximum Likelihood Estimation of Autoregressive Fractionally Integrated Moving Average Models," Economics Series Working Papers 2001-W27, University of Oxford, Department of Economics.
  3. Deo, Rohit & Hurvich, Clifford & Lu, Yi, 2006. "Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 29-58.
  4. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
  5. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
  6. Koopman, Siem Jan & Shephard, Neil & Creal, Drew, 2009. "Testing the assumptions behind importance sampling," Journal of Econometrics, Elsevier, vol. 149(1), pages 2-11, April.
  7. Mark J. Jensen, 2004. "Semiparametric Bayesian Inference of Long-Memory Stochastic Volatility Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 895-922, November.
  8. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543.
  9. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
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Cited by:
  1. Siem Jan Koopman & Marcel Scharth, 2011. "The Analysis of Stochastic Volatility in the Presence of Daily Realised Measures," Tinbergen Institute Discussion Papers 11-132/4, Tinbergen Institute.

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