Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models
AbstractAn 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 InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 11-090/4.
Date of creation: 27 Jun 2011
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Fractional Integration; Importance Sampling; Kalman Filter; Latent Factors; Stochastic Volatility;
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-07-13 (All new papers)
- NEP-ECM-2011-07-13 (Econometrics)
- NEP-ETS-2011-07-13 (Econometric Time Series)
- NEP-ORE-2011-07-13 (Operations Research)
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