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Empirical likelihood in long‐memory time series models
Author(s) -
Yau Chun Yip
Publication year - 2012
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2011.00756.x
Subject(s) - empirical likelihood , mathematics , autoregressive fractionally integrated moving average , series (stratigraphy) , likelihood function , autoregressive model , statistics , likelihood principle , likelihood ratio test , asymptotic distribution , econometrics , long memory , confidence interval , maximum likelihood , quasi maximum likelihood , volatility (finance) , paleontology , estimator , biology
This article studies the empirical likelihood method for long‐memory time series models. By virtue of the Whittle likelihood, one obtains a score function that can be viewed as an estimating equation of the parameters of a fractional integrated autoregressive moving average (ARFIMA) model. This score function is used to obtain an empirical likelihood ratio which is shown to be asymptotically chi‐square distributed. Confidence regions for the parameters are constructed based on the asymptotic distribution of the empirical likelihood ratio. Bartlett correction and finite sample properties of the empirical likelihood confidence regions are examined.