Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics

40 Pages Posted: 5 Oct 2003 Last revised: 19 Sep 2009

See all articles by Peter Christoffersen

Peter Christoffersen

University of Toronto - Rotman School of Management; Copenhagen Business School; Aarhus University - CREATES

Francis X. Diebold

University of Pennsylvania - Department of Economics; National Bureau of Economic Research (NBER)

Multiple version iconThere are 3 versions of this paper

Date Written: October 2003

Abstract

We consider three sets of phenomena that feature prominently and separately in the financial economics literature: conditional mean dependence (or lack thereof) in asset returns, dependence (and hence forecastability) in asset return signs, and dependence (and hence forecastability) in asset return volatilities. We show that they are very much interrelated, and we explore the relationships in detail. Among other things, we show that: (a) 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; (b) The standard finding of little or no conditional mean dependence is entirely consistent with a significant degree of sign dependence and volatility dependence; (c) 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; (d) 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; (e) Sign dependence is very much present in actual U.S. equity returns, and its properties match closely our theoretical predictions; (f) The link between volatility forecastability and sign forecastability remains intact in conditionally non-Gaussian environments, as for example with time-varying conditional skewness and/or kurtosis.

Suggested Citation

Christoffersen, Peter and Diebold, Francis X., Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics (October 2003). NBER Working Paper No. w10009. Available at SSRN: https://ssrn.com/abstract=453803

Peter Christoffersen

University of Toronto - Rotman School of Management ( email )

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Copenhagen Business School

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Aarhus University - CREATES

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Francis X. Diebold (Contact Author)

University of Pennsylvania - Department of Economics ( email )

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