Volatility Library

Article by: Peter F. Christoffersen, Francis X. Diebold
Published by: Management Science
Date: 2006 August

“We consider three sets of phenomena that feature prominently in the financial economics literature: (1) conditional mean dependence (or lack thereof) in asset returns, (2) dependence (and hence forecastability) in asset return signs, and (3) dependence (and hence forecastability) in asset return volatilities. We show that they are very much interrelated and explore the relationships in detail. Among other things, we show that (1) volatility dependence produces sign dependence, so long as expected returns are nonzero, so that one should expect sign dependence, given the overwhelming evidence of volatility dependence; (2) it is statistically possible to have sign dependence without conditional mean dependence; (3) sign dependence is not likely to be found via analysis of sign autocorrelations, runs tests, or traditional market timing tests because of the special nonlinear nature of sign dependence, so that traditional market timing tests are best viewed as tests for sign dependence arising from variation in expected returns rather than from variation in volatility or higher moments; (4) sign dependence is not likely to be found in very high-frequency (e.g., daily) or very low-frequency (e.g., annual) returns; instead, it is more likely to be found at intermediate return horizons; and (5) the link between volatility dependence and sign dependence remains intact in conditionally.”

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Article by: Torben G. Andersen, Tim Bollerslev
Published by: International Economic Review
Date: 4 Nov 1998

“A voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using ARCH and stochastic volatility models. While most of these studies have documented highly significant in-sample parameter estimates and pronounced intertemporal volatility persistence, traditional ex post forecast evaluation criteria suggest that the models provide seemingly poor volatility forecasts. Contrary to this contention, the authors show that volatility models produce strikingly accurate interdaily forecasts for the latent volatility factor that would be of interest in most financial applications. New methods for improved ex post interdaily volatility measurements based on high-frequency intradaily data are also discussed. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.”

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