Estimation of Long-Memory Time Series Models: a Survey of Different Likelihood-Based Methods

Ngai Hang Chan; Wilfredo Palma

doi:10.1016/S0731-9053(05)20023-3

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Advances in Econometrics

ISSN: 0731-9053
Series editor(s): Thomas B. Fomby, R. Carter Hill, Ivan Jeliazkov, Juan Carlos Escanciano and Eric Hillebrand

Subject Area: Economics

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Estimation of Long-Memory Time Series Models: a Survey of Different Likelihood-Based Methods

Document Information:
Title:	Estimation of Long-Memory Time Series Models: a Survey of Different Likelihood-Based Methods
Author(s):	Ngai Hang Chan, Wilfredo Palma
Volume:	20 Editor(s): Thomas B. Fomby, Dek Terrell ISBN: 978-0-76231-273-3 eISBN: 978-1-84950-388-4
Citation:	Ngai Hang Chan, Wilfredo Palma (2006), Estimation of Long-Memory Time Series Models: a Survey of Different Likelihood-Based Methods, in Thomas B. Fomby, Dek Terrell (ed.) Econometric Analysis of Financial and Economic Time Series (Advances in Econometrics, Volume 20), Emerald Group Publishing Limited, pp.89-121
DOI:	10.1016/S0731-9053(05)20023-3 (Permanent URL)
Publisher:	Emerald Group Publishing Limited
Article type:	Chapter Item
Abstract:	Since the seminal works by Granger and Joyeux (1980) and Hosking (1981), estimations of long-memory time series models have been receiving considerable attention and a number of parameter estimation procedures have been proposed. This paper gives an overview of this plethora of methodologies with special focus on likelihood-based techniques. Broadly speaking, likelihood-based techniques can be classified into the following categories: the exact maximum likelihood (ML) estimation (Sowell, 1992; Dahlhaus, 1989), ML estimates based on autoregressive approximations (Granger & Joyeux, 1980; Li & McLeod, 1986), Whittle estimates (Fox & Taqqu, 1986; Giraitis & Surgailis, 1990), Whittle estimates with autoregressive truncation (Beran, 1994a), approximate estimates based on the Durbin–Levinson algorithm (Haslett & Raftery, 1989), state-space-based maximum likelihood estimates for ARFIMA models (Chan & Palma, 1998), and estimation of stochastic volatility models (Ghysels, Harvey, & Renault, 1996; Breidt, Crato, & de Lima, 1998; Chan & Petris, 2000) among others. Given the diversified applications of these techniques in different areas, this review aims at providing a succinct survey of these methodologies as well as an overview of important related problems such as the ML estimation with missing data (Palma & Chan, 1997), influence of subsets of observations on estimates and the estimation of seasonal long-memory models (Palma & Chan, 2005). Performances and asymptotic properties of these techniques are compared and examined. Inter-connections and finite sample performances among these procedures are studied. Finally, applications to financial time series of these methodologies are discussed.