Generalized autoregressive conditional heteroskedasticity

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Abstract

A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented.

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I am grateful to David Hendry and Rob Engle for introducing me to this new idea, and to Rob Engle for many helpful discussions. I would also like to thank Sastry Pantula for suggesting the alternative parameterization, two anonymous referees for useful comments, and Kirsten Stentoft for typing the manuscript. The usual disclaimer applies.

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