Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series B, Pt. 2, pp. 199--220

RANDOM COEFFICIENT FORMULATION OF CONDITIONAL HETEROSKEDASTICITY AND AUGMENTED ARCH MODELS

By

ANIL BERA, University of Illinois at Urbana-Champaign

MATTHEW L. HIGGINS, Western Michigan University

and

SANGKYU LEE, Kyung Hee University

SUMMARY.  In recent years, ARCH models have emerged as an indispensable tool for modeling the conditional second moment of economic variables, and therefore, proper formulation of the conditional variance function is of the utmost importance. In order to provide a unified approach to the problem of finding stationarity conditions and the test statistics for various specifications of conditional heteroskedasticity, we purpose a general random coefficient disturbance process which encompasses AR, ARCH and GARCH processes. Through the vector representation of the model, we use a new procedure to derive stationarity conditions for AR, ARCH, and GARCH models can be obtained as a special case of our result. Test statistics for conditional heteroskedasticity and autocorrelation are proposed. Through an illustrative example of estimating the variability of inflation, we show how misspecifying conditional heteroskedasticity or neglecting autocorrelation can affect inference about the conditional second moment of a random variable.

AMS (1980) subject classification.  62M10.

Key words and phrases. ARCH; augmented ARCH; autocorrelation, generalized ARCH; Lagrange multiplier test; random coefficient model; stationarity condition; variability of inflation.

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This article in Mathematical Reviews.