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Unbalanced Fractional Cointegration and the No-Arbitrage Condition on Commodity Markets

Author

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  • Gilles De Truchis

    () (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)

  • Florent Dubois

    () (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)

Abstract

Technical abstract: A necessary condition for two time series to be nontrivially cointegrated is the equality of their respective integration orders. Nonetheless, in some cases, the apparent unbalance of integration orders of the observables can be misleading and the cointegration theory applies all the same. This situation refers to unbalanced cointegration in the sense that balanced long run relationship can be recovered by an appropriate filtering of one of the time series. In this paper, we suggest a local Whittle estimator of bivariate unbalanced fractional cointegration systems. Focusing on a degenerating band around the origin, it estimates jointly the unbalance parameter, the long run coefficient and the integration orders of the regressor and the cointegrating errors. Its consistency is demonstrated for the stationary regions of the parameter space and a finite sample analysis is conducted by means of Monte Carlo experiments. An application to the no-arbitrage condition between crude oil spot and futures prices is proposed to illustrate the empirical relevance of the developed estimator. Non-technical abstract: The no-arbitrage condition between spot and future prices implies an analogous condition on their underlying volatilities. Interestingly, the long memory behavior of the volatility series also involves a long-run relationship that allows to test for the no-arbitrage condition by means of cointegration techniques. Unfortunately, the persistent nature of the volatility can vary with the future maturity, thereby leading to unbalanced integration orders between spot and future volatility series. Nonetheless, if a balanced long-run relationship can be recovered by an appropriate filtering of one of the time series, the cointegration theory applies all the same and unbalanced cointegration operates between the raw series. In this paper, we introduce a new estimator of unbalanced fractional cointegration systems that allows to test for the no-arbitrage condition between the crude oil spot and futures volatilities.

Suggested Citation

  • Gilles De Truchis & Florent Dubois, 2014. "Unbalanced Fractional Cointegration and the No-Arbitrage Condition on Commodity Markets," Working Papers halshs-01065775, HAL.
  • Handle: RePEc:hal:wpaper:halshs-01065775
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01065775
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    References listed on IDEAS

    as
    1. Guglielmo Maria Caporale & Davide Ciferri & Alessandro Girardi, 2014. "Time-Varying Spot and Futures Oil Price Dynamics," Scottish Journal of Political Economy, Scottish Economic Society, vol. 61(1), pages 78-97, February.
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    3. Chakraborty, Avik & Evans, George W., 2008. "Can perpetual learning explain the forward-premium puzzle?," Journal of Monetary Economics, Elsevier, vol. 55(3), pages 477-490, April.
    4. Baillie, Richard T. & Bollerslev, Tim, 2000. "The forward premium anomaly is not as bad as you think," Journal of International Money and Finance, Elsevier, vol. 19(4), pages 471-488, August.
    5. Chevillon, Guillaume & Mavroeidis, Sophocles, 2011. "Learning generates Long Memory," ESSEC Working Papers WP1113, ESSEC Research Center, ESSEC Business School.
    6. Karim Abadir & Gabriel Talmain, 2002. "Aggregation, Persistence and Volatility in a Macro Model," Review of Economic Studies, Oxford University Press, vol. 69(4), pages 749-779.
    7. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-112, January.
    8. Brenner, Robin J. & Kroner, Kenneth F., 1995. "Arbitrage, Cointegration, and Testing the Unbiasedness Hypothesis in Financial Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(01), pages 23-42, March.
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    More about this item

    Keywords

    unbalanced cointegration; fractional cointegration; no-arbitrage condition; local Whittle likelihood; commodity markets;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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