Transcription of GENERALIZED AUTOREGRESSIVE CONDITIONAL …
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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.
p. (2) For p = 0 the process reduces to the ARCH(q) process, and for p = q = 0 E t is simply white noise. In the ARCH(q) process the conditional variance is specified as a linear function of past sample variances only, whereas the GARCH(p, q) process allows lagged conditional variances to …
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