Crompton, P. and I. Xiarchos, 2008, “Metal Prices and the Supply of Storage”, Commodity modeling and pricing: methods for analyzing resource market behavior, edited by Schaeffer, Peter, p 108-116.
Deaton A. and G. Laroque, 1997, “Competitive Storage and Commodity Price Dynamics”, Journal of Political Economy, Vol. 104 No. 5.
Enders, W. and P. Siklos, 2001, “Cointegration and Threshold Adjustment,” Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pp. 166-76.
Heaney, R. A, 1998, “A test of the cost-of-carry relationship using the London Metal Exchange lead contract”, The Journal of Futures Markets 18, pp. 177–200.
Johansen, S., 1988, ‘Statistical Analysis of Cointegration Vectors,’ _Journal of Economic Dynamics and Control,_v. 12, pp. 231-254.
Kouassi, Eugene, 2008, “Testing for Temporal Asymmetry In the Metal Price-Stock Relationship”, Commodity modeling and pricing: methods for analyzing resource market behavior, edited by Schaeffer, Peter, p 118-134
Martens, M., Kofman, P. and Vorst, A.C.F., 1998, “A Threshold Error Correction Model for Intraday Futures and Index Returns,” Journal of Applied Econometrics, 13, pp. 245-263.
Markert, V. and H. Zimmermann, 2008, Chapter 5, “The Relationship Between Risk Premium and Convenience Yield Models’ in Handbook of Commodity Investing by Dieter G. Kaiser, Frank J. Fabozzi, Roland Fuss
Tsay, R. S., 1989, “Testing and modeling threshold autoregressive processes”, Journal of the American Statistical Association, 84, pp. 231-240, 1989.
Watkins, C. and M. McAleer, 2006. “Pricing of non-ferrous metals futures on the London Metal Exchange,” Applied Financial Economics, Taylor and Francis Journals, vol. 16(12), pp 853-880.
Wu, Yangru, and Hua Zhang, 1997, “Do Interest Rates Follow Unit-Root Processes? Evidence from Cross-Maturity Treasury Bill Yields,” Review of Quantitative Finance & Accounting, Vol. 8, Issue 1, pp. 69-81.
We would like to thank Thomas Helbling and Research Department seminar participants at the IMF for useful comments and suggestions. The usual disclaimer applies.
Mabro (2009) provides an example in oil markets where ample oil supplies in August 1997 and in 2008 moved the term structure of futures prices into a very steep contango. The increasing differential between spot and futures contracts gave sufficient incentives for traders to buy physical oil to add to inventories and sell a futures contract. This resulted in an inventory build-up subsequently pressuring prices flattening the term structure in 1998 and 2009, respectively.
We also ran the threshold identification procedure for AR(3) processes, consistent with Aikaike information criteria, and found that the results were mostly identical (or very close) to those obtained from an AR(1).
We supplement this approach less formal analysis of AR(1) coefficient t-ratio scatter plots, obtained from recursive least squares regressions. This yielded less clear-cut conclusions, but tended to support the number and location of the thresholds obtained from the formal methods described. Details are available on request from the authors.