On the Origins of Conditional Heteroscedasticity in Time Series
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 re- conceptualizing 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-step-ahead conditional heteroscedasticity arises â€“ necessarily and endogenously â€“ 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 â€˜tacking onâ€™ an ad hoc volatility model. Even where such nonlinear modeling is infeasible â€“ or where volatility is quantified using, say, a model-free implied volatility measure rather than squared returns â€“ 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.
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