A profile Godambe information of power transformations for ARCH time series. Issue 14 (18th July 2017)

• Record Type: Journal Article
• Authors: Chung, Sunah; Hwang, S.Y.
• Is Part Of: Communications in statistics. Volume 46:Issue 14(2017)
• Page Start: 6899
• Page End: 6908
• Publication Date: 2017-07-18
• Subjects: ARCH -- power transformation -- profile Godambe information.; Primary 62M10; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2016.1139133
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: Due to Godambe (1985 ), one can obtain the Godambe optimum estimating functions (EFs) each of which is optimum (in the sense of maximizing the Godambe information) within a linear class of EFs. Quasi-likelihood scores can be viewed as special cases of the Godambe optimum EFs (see, for instance, Hwang and Basawa, 2011 ). The paper concerns conditionally heteroscedastic time series with unknown likelihood. Power transformations are introduced in innovations to construct a class of Godambe optimum EFs. A "best" power transformation for Godambe innovation is then obtained via maximizing the "profile" Godambe information. To illustrate, the KOrea Stock Prices Index is analyzed for which absolute value transformation and square transformation are recommended according to the ARCH(1) and GARCH(1, 1) models, respectively.