The volatility clustering frequently observed in financial/economic time series is often
ascribed to GARCH and/or stochastic volatility models. This paper demonstrates the
usefulness of reconceptualizing the usual definition of conditional heteroscedasticity as the (h
= 1) special case of h-step-ahead conditional heteroscedasticity, where the conditional
volatility in period t depends on observable variables up through period t – h. Here it is
shown that, for h > 1, h-stepahead conditional heteroscedasticity arises – necessarily and
endogenously - from nonlinear serial dependence in a time series; whereas one-step-ahead
conditional heteroscedasticity (i.e., h = 1) requires multiple and heterogeneously-skedastic
innovation terms. Consequently, the best response to observed volatility clustering may often
be to model the nonlinear serial dependence which is likely causing it, rather than ‘tacking
on’ an ad hoc volatility model. Even where such nonlinear modeling is infeasible – or where
volatility is quantified using, say, a model-free implied volatility measure rather than
squared returns – these results suggest a re-consideration of the usefulness of lag-one terms in
volatility models. An application to observed daily stock returns is given.