Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series B, Pt. 2, pp. 327--344

AN ARCH IN THE NONLINEAR MEAN\\ (ARCH-NM) MODEL

By

SAMARJIT DAS and NITYANANDA SARKAR, Indian Statistical Institute, Calcutta

SUMMARY. This paper suggests a class of ARCH in the nonlinear mean (ARCH-NM) models. This class of models generalizes the usual ARCH-M model by considering the Box-Cox power transformation of the conditional variance for representing the risk premium. Thus, this generalization provides an approach by which a flexible specification of time-varying risk premium in the nonlinear form for ARCH is possible. Properties of this model are studied and the estimation procedure is described. The proposed model is then applied to the daily closing prices on the Bombay Stock Exchange Sensitive Index and its performance compared with the standard ARCH-M model using proper diagnostic checks.

AMS (1991) subject classification. 62J02, 62P20.

Key words and phrases. ARCH, ARCH-M, Box-Cox power transformation, time-varying risk premium.

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