Working Paper: NBER ID: w10009
Authors: Peter F. Christoffersen; Francis X. Diebold
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.
Keywords: financial asset returns; forecasting; volatility dynamics
JEL Codes: G1
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| volatility dependence (C69) | sign dependence (C29) |
| sign dependence is more likely to be present at intermediate return horizons (C29) | volatility forecastability and sign forecastability (G17) |
| expected returns are nonzero (G19) | volatility dependence produces sign dependence (C69) |
| little or no conditional mean dependence (C29) | sign dependence and volatility dependence (C46) |
| sign dependence is unlikely to be found through traditional tests (C46) | alternative methods are needed to detect sign forecastability (C53) |
| link between volatility forecastability and sign forecastability persists in conditionally non-Gaussian environments (G17) | robustness of findings (C90) |