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A profile Godambe information of power transformations for ARCH time series

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  • Sunah Chung
  • S.Y. Hwang

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.

Suggested Citation

  • Sunah Chung & S.Y. Hwang, 2017. "A profile Godambe information of power transformations for ARCH time series," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 6899-6908, July.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:14:p:6899-6908
    DOI: 10.1080/03610926.2016.1139133
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