Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2011-06-27 Number: 11-090/4 Author-Name: Geert Mesters Author-Workplace-Name: Netherlands Institute for the Study of Crime and Law Enforcement Author-Name: Siem Jan Koopman Author-Workplace-Name: VU University Amsterdam Author-Name: Marius Ooms Author-Workplace-Name: VU University Amsterdam Title: Monte Carlo Maximum Likelihood Estimation for Generalized Long-Memory Time Series Models 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.

Classification-JEL: C33, C43 Keywords: Fractional Integration, Importance Sampling, Kalman Filter, Latent Factors, Stochastic Volatility File-Url: https://papers.tinbergen.nl/11090.pdf File-Format: application/pdf File-Size: 597761 bytes Handle: RePEc:tin:wpaper:20110090