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GENERALIZED AUTOREGRESSIVE CONDITIONAL …

Journal of Econometrics 31 (1986) 307-327. North-Holland GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY Tim BOLLERSLEV* University of California at San Diego, La Jolla, CA 92093, USA Institute of Economics, University of Aarhus, Denmark Received May 1985, final version received February 1986 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. 1. Introduction While conventional time series and econometric models operate under an assumption of constant variance, the ARCH ( AUTOREGRESSIVE CONDITIONAL Heteroskedastic) process introduced in Engle (1982) allows the CONDITIONAL variance to change over time as a function bf past errors leaving the uncondi- tional variance constant.

0304-4076/86/$3.50© 1986, Elsevier Science Publishers B.V. (North-Holland) 308 T. Bollerslev, Generalization of A R C H process tional variance equation to take account of the long memory typically found in empirical work, since estimating a totally free lag distribution often will lead to violation of the non-negativity constraints. ...

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