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.

The views expressed are those of the authors and do not necessarily re ect those of the Bank of England. Cameron's research was funded by the ESRC (grant no. R000234954) and Proudman and Redding's by the Bank of England. We are enormously grateful to Steve Bond for his insightful comments, advice and suggestions. We are also very grateful to Philippe Aghion, Andrew