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Feasible optimum Godambe scores for a semi-parametric GARCH time series

Authors
Hwang, S. Y.
Issue Date
Mar-2017
Publisher
KOREAN STATISTICAL SOC
Keywords
Feasible score; GARCH; Optimum Godambe score; Quasi-maximum likelihood
Citation
JOURNAL OF THE KOREAN STATISTICAL SOCIETY, v.46, no.1, pp 104 - 112
Pages
9
Journal Title
JOURNAL OF THE KOREAN STATISTICAL SOCIETY
Volume
46
Number
1
Start Page
104
End Page
112
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/8624
DOI
10.1016/j.jkss.2016.08.001
ISSN
1226-3192
1876-4231
Abstract
This paper concerns a semi-parametric GARCH time series for which the error distribution is unspecified. Godambe scores (GS) including quasi-likelihood scores are considered to estimate parameters of interest. Allowing the Godambe innovation to contain nuisance parameters associated with moments of the unknown error distribution, an optimum GS (oGS, for short) is obtained for each fixed nuisance parameters, and in turn the nuisance parameters are replaced by the quasi maximum likelihood (QML) residuals so that one can obtain computationally feasible zero of the oGS. It is verified under certain conditions that the solution of the feasible oGS continues to be asymptotically optimum, while extending the family of error distributions under consideration. (C) 2016 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.
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