2003, Volume 65, Pt. 4 , 744--762

ESTIMATION FOR NONLINEAR AUTOREGRESSIVE MODELS GENERATED BY BETA-ARCH PROCESSES

By

S.Y. HWANG, Sookmyung Women's University, Seoul, Korea and I.V. BASAWA, University of Georgia, Athens, USA

SUMMARY. Two methods of parameter estimation for a general nonlinear autoregressive process with beta-ARCH innovations are discussed and the large sample properties of the estimators for each method are derived.  The first method is based on iterated least squares which is also related to the quasilikelihood method.  The maximum likelihood method is discussed next, via the local asymptotic normality and its connection to optimal estimating functions is explained.

AMS (1991) subject classification. Primary 62M10; secondary 91B84.

Key words and phrases. ARCH models, nonlinear time series, ergodicity, asymptotic normality, LAN property, maximum likelihood estimation, quasilikelihood.

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