We argue that the predictive regression between implied volatility (regressor) and realized volatility over the remaining life of a European option (regressand) is likely to be a fractional cointegrating relation. Because cointegration is associated with long-run comovements, this classical...

We view economic time series as the result of a cascade of shocks occurring at different times and different frequencies (scales). We suggest that economic relations that are found to be elusive when using raw data may hold true for different layers (details) in the cascade of economic shocks....