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On the Origins of Conditional Heteroscedasticity in Time Series

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  • Richard Ashley

Abstract

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 – 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.

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File URL: ftp://repec.econ.vt.edu/Papers/Ashley/origins_of_conditional_heteroscedasticity.pdf
File Function: First version, 2010
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Bibliographic Info

Paper provided by Virginia Polytechnic Institute and State University, Department of Economics in its series Working Papers with number e07-23.

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Length: 32 pages
Date of creation: 2010
Date of revision:
Handle: RePEc:vpi:wpaper:e07-23

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Keywords: nonlinearity; nonlinear serial dependence; conditional heteroscedasticity; ARCH models; GARCH models.;

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  1. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S119-36, Suppl. De.
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Cited by:
  1. Catherine Kyrtsou & Michel Terraza, 2008. "Seasonal Mackey-Glass-GARCH process and short-term dynamics," Discussion Paper Series 2008_09, Department of Economics, University of Macedonia, revised Sep 2008.
  2. Malliaris, A.G. & Kyrtsou, C., 2009. "Editorial introduction of the special issue: "Energy sector pricing and macroeconomic dynamics"," Energy Economics, Elsevier, vol. 31(6), pages 825-826, November.

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