A No-Arbitrage Fractional Cointegration Model for Futures and Spot Daily Ranges

The no-arbitrage relation between futures and spot prices implies an analogous relation between futures and spot daily ranges. The long-memory features of the range-based volatility estimators are analyzed, and fractional cointegration is tested in a semi-parametric framework. In particular, the no-arbitrage condition is used to derive a long-run relationship between volatility measures and to justify the use of a fractional vector error correction model (FVECM) to study their dynamic relationship. The out-of-sample forecasting superiority of FVECM, with respect to alternative models, is documented. The results highlight the importance of incorporating the long-run equilibrium in volatilities to obtain better forecasts, given the information content in the volatility of futures prices. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark Published online November 30, 2011 in Wiley Online Library (wileyonlinelibrary.com) 33:77–102, 2013