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