Likelihood-based Analysis of a Class of Generalized Long-Memory Time Series Models
AbstractThis article introduces a family of 'generalized long-memory time series models', in which observations have a specified conditional distribution, given a latent Gaussian fractionally integrated autoregressive moving-average (ARFIMA) process. The observations may have discrete or continuous distributions (or a mixture of both). The family includes existing models such as ARFIMA models themselves, long-memory stochastic volatility models, long-memory censored Gaussian models and others. Although the family of models is flexible, the latent long-memory process poses problems for analysis. Therefore, we introduce a Markov chain Monte Carlo sampling algorithm and develop a set of recursions which makes it feasible. This makes it possible, among other things, to carry out exact likelihood-based analysis of a wide range of non-Gaussian long-memory models without resorting to the use of likelihood approximations. The procedure also yields predictive distributions that take into account model parameter uncertainty. The approach is demonstrated in two case studies. Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.
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Bibliographic InfoArticle provided by Wiley Blackwell in its journal Journal of Time Series Analysis.
Volume (Year): 28 (2007)
Issue (Month): 3 (05)
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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782
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- Bos, Charles S. & Koopman, Siem Jan & Ooms, Marius, 2014. "Long memory with stochastic variance model: A recursive analysis for US inflation," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 76(C), pages 144-157.
- Tsyplakov, Alexander, 2010. "Revealing the arcane: an introduction to the art of stochastic volatility models," MPRA Paper 25511, University Library of Munich, Germany.
- C.S. Bos & S.J. Koopman & M. Ooms, 2007.
"Long Memory Modelling of Inflation with Stochastic Variance and Structural Breaks,"
Tinbergen Institute Discussion Papers
07-099/4, Tinbergen Institute.
- Charles S. Bos & Siem Jan Koopman & Marius Ooms, 2007. "Long memory modelling of inflation with stochastic variance and structural breaks," CREATES Research Papers 2007-44, School of Economics and Management, University of Aarhus.
- C.S. Bos & S.J. Koopman & M. Ooms, 2007. "Long Memory Modelling of Inflation with Stochastic Variance and Structural Breaks," Tinbergen Institute Discussion Papers 07-099/4, Tinbergen Institute.
- 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.
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