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


  • The authors thank Giuseppe Cavaliere, Søren Johansen and Katarzyna Łasak for useful comments and suggestions. They also thank the participants to CREATES weekly seminars for helpful comments. Financial support from PRIN 2006 is gratefully acknowledged.

Correspondence author, Dipartimento di economia politica e metodi quantitativi, Via San Felice 5, University of Pavia, 27100 Pavia, Italy. Tel: 39-0382/986207, Fax: 39-0382/304226, e-mail:


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 33:77–102, 2013