On the Origins of Conditional Heteroscedasticity in Time Series
AbstractThe 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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Bibliographic InfoPaper provided by Virginia Polytechnic Institute and State University, Department of Economics in its series Working Papers with number e07-23.
Length: 32 pages
Date of creation: 2010
Date of revision:
nonlinearity; nonlinear serial dependence; conditional heteroscedasticity; ARCH models; GARCH models.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-10-23 (All new papers)
- NEP-ECM-2010-10-23 (Econometrics)
- NEP-ETS-2010-10-23 (Econometric Time Series)
- NEP-ORE-2010-10-23 (Operations Research)
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