Abstract
This paper examines the causal structure among the daily corn futures and seven cash price series from Midwestern states from January 3, 2006, to March 24, 2011, through a rolling approach that takes into account window sizes of a half, one, one and a half, and two years. Except for some testing samples, all series are tied together through cointegration and adjust toward the long-run relationship(s). Considering different forecasting lengths, the out-of-sample Granger causality test for each window generally reveals that no series gains persistent forecastability from another. These results shed light on the evolving causal structure among the different series. Discussions of empirical findings at a more granular level also are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The recursive approach that continuously adds more observations to the sample for the model estimation until the end of time series also incorporates the idea of investigating potential time-varying relationships. It, however, is difficult to differentiate whether changing test statistics are due to changes in linkages among variables or increases in power of tests with observations added recursively. With the rolling approach of a given window size, the sample size for the model estimation is constant but the sample period evolves to reflect variations in relationships among variables arising from changing information embedded in series.
A bivariate system consisting of the futures and a cash series from one of the seven states is found to be not cointegrated. Details are available upon request.
For example, in December 2014, the nearby Chicago-delivery price for corn futures was close to $4.00 per bushel, while cash prices varied from $1.00 less than Chicago in interior producing locations such as South Dakota to more than $0.70 above the Chicago price in grain-importing regions such as North Carolina.
For example, Xu (2018c) presented empirical evidence of different causal relationships found based on data of different frequency.
The current study focuses on linear lead–lag causality. Another strand of the literature explores nonlinear relationships among time series, which might be ignored by linear causality tests. For example, for the crude oil market, Silvapulle and Moosa (1999) found that futures unidirectionally lead cash prices based on the linear causality test, while the bidirectional leadership is identified with the nonlinear test.
The asymptotic null distribution of \(LR_{Trace}(r)\) is a multivariate version of the Dickey–Fuller unit root distribution that depends on the dimension \(p-r\) and specification of the deterministic term.
This approach would be precisely correct for one-step ahead forecasts if \(d_{t}\) follows a normal distribution. While assuming normality will generally not be correct, it seems plausible to guess that the t critical value is appropriate as a comparison of the MDM test statistic (Harvey et al. 1997). A further simulation study reveals that the modified test statistic and using the t, rather than standard normal, critical value as a comparison of the statistic both contribute to the performance improvement—the former somewhat more than the latter (Harvey et al. 1997).
Results are available upon request.
Unless stated otherwise, we will refer to “log prices” as “prices” hereafter.
Results for other six states are available upon request.
The minimum, mean, median, and maximum for other six states and the skewness and kurtosis for all series are available upon request.
Results based on the ADF test with a trend, PP test with and without a trend, and KPSS test with and without a trend are available upon request.
We have tried calculating weekly averages of cash and futures prices to match weekly Midwest No 2 diesel retail prices from the US Energy Information Administration and retesting cointegration based on an ennea-variate system that further incorporates the diesel price. While diesel prices are nonstationary based on unit root tests, the cointegration rank is still found to be one or two for most of the rolling samples across window sizes. Actually, the absolute value of the correlation coefficient between the diesel price and cash-futures basis is smaller than 0.35, which is low, for almost all markets.
The cash-futures basis is defined as the price of the futures minus that of the cash.
Similar results were also found for financial index spot and futures series, e.g., Xu (2017b).
Detailed results are available upon request.
Results for other six states are available upon request.
The seven states cover seven of eight largest corn producing states in the US that contribute to 67.4% of the national harvest acres (National Agricultural Statistics Service 2010).
Results are available upon request.
References
Amato, J.D., Swanson, N.R.: The real-time predictive content of money for output. J. Monet. Econ, 48, 3–24 (2001). https://doi.org/10.1016/s0304-3932(01)00070-8
Ashley, R.A., Tsang, K.P.: Credible Granger-causality Inference with modest sample lengths: a cross-sample validation approach. Econometrics 2, 72–91 (2014). https://doi.org/10.3390/econometrics2010072
Bessler, D.A., Fuller, S.W.: Railroad wheat transportation markets in the central plains: modeling with error correction and directed graphs. Transport. Res. Part E: Logist. Transport. Rev. 36, 21–39 (2000). https://doi.org/10.1016/S1366-5545(99)00015-0
Bessler, D., Yang, J., Wongcharupan, M.: Price dynamics in the international wheat market: modeling with error correction and directed acyclic graphs. J. Reg. Sci. 43, 1–33 (2003). https://doi.org/10.1111/1467-9787.00287
Bossaerts, P., Hillion, P.P.: Implementing statistical criteria to select return forecasting models: what do we learn? Rev. Financ. Stud. 12, 405–428 (1999). https://doi.org/10.1093/rfs/12.2.405
Bierens, H.J., Martins, L.F.: Time-varying cointegration. Econom. Theory 26, 1453–1490 (2010). https://doi.org/10.1017/S0266466609990648
Campbell, J.Y.: Stock returns and the term structure. J. Financ. Econ. 18, 373–399 (1987). https://doi.org/10.1016/0304-405x(87)90045-6
Carter, C.A., Mohapatra, S.: How reliable are hog futures as forecasts? Am. J. Agric. Econ. 90, 367–378 (2008). https://doi.org/10.1111/j.1467-8276.2007.01122.x
Chao, J., Corradi, V., Swanson, N.R.: Out-of-sample Tests for Granger causality. Macroecon. Dyn. 5, 598–620 (2001)
Colino, E.V., Irwin, S.H.: Outlook vs. futures: three decades of evidence in hog and cattle markets. Am. J. Agric. Econ. 92, 1–15 (2010). https://doi.org/10.1093/ajae/aap013
Dickey, D., Fuller, W.: Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49, 1057–1072 (1981). https://doi.org/10.2307/1912517
Diebold, F.X., Mariano, R.S.: Comparing predictive accuracy. J. Bus. Econ. Stat. 13, 253–263 (1995). https://doi.org/10.2307/1392185
Engle, R., Granger, C.W.J.: Co-integration and error correction: representation, estimation and testing. Econometrica 55, 251–276 (1987). https://doi.org/10.2307/1913236
Ferraro, D., Rogoff, K., Rossi, B.: Can oil prices forecast exchange rates? An empirical analysis of the relationship between commodity prices and exchange rates. J. Int. Money Finance 54, 116–141 (2015). https://doi.org/10.1016/j.jimonfin.2015.03.001
Garbade, K.D., Silber, W.L.: Price movements and price discovery in futures and cash markets. Rev. Econ. Stat. 65, 289–297 (1983). https://doi.org/10.2307/1924495
Garcia, P., Irwin, S.H., Smith, A.: Futures market failure? Am. J. Agric. Econ. 97, 40–64 (2014). https://doi.org/10.1093/ajae/aau067
Granger, C.W.J.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424–438 (1969). https://doi.org/10.2307/1912791
Haigh, M.S., Holt, M.T.: Hedging multiple price uncertainty in international grain trade. Am. J. Agric. Econ. 82, 881–896 (2000). https://doi.org/10.1111/0002-9092.00088
Harvey, D., Leybourne, S., Newbold, P.: Testing the equality of prediction mean squared errors. Int. J. Forecast. 13, 281–291 (1997). https://doi.org/10.1016/s0169-2070(96)00719-4
Hernandez, M., Torero, M.: Examining the dynamic relationship between spot and future prices of agricultural commodities. International Food Policy Research Institute (IFPRI) Discussion Paper 00988 (2010)
Hill, J.B.: Efficient tests of longrun causation in trivariate VAR processes with a rolling window study of the money-income relationship. J. Appl. Econ. 22, 747–765 (2007). https://doi.org/10.1002/jae.925
Hoffman, L.A., Aulerich, N.: Recent Convergence Performance of Futures and Cash Prices for Corn, Soybeans, and Wheat. Economic Research Service/USDA. FDS-13L-01 (2013)
Johansen, S.: Statistical analysis of cointegration vectors. J. Econ. Dyn. Control 12, 231–254 (1988). https://doi.org/10.1016/0165-1889(88)90041-3
Johansen, S.: Determination of cointegration rank in the presence of a linear trend. Oxf. Bull. Econ. Stat. 54, 383–397 (1992). https://doi.org/10.1111/j.1468-0084.1992.tb00008.x
Karali, B., McNew, K., Thurman, W.N.: Price discovery and the basis effects of failures to converge in soft red winter wheat futures markets. J. Agric. Resour. Econ. 43, 1–17 (2018)
Kawaller, I.G., Koch, P.D., Koch, T.W.: The relationship between the S&P 500 Index and the S&P 500 index futures prices. Fed. Reserve Bank Atlanta Econ. Rev. 73, 2–10 (1988)
Koop, G., Leon-Gonzalez, R., Strachan, R.W.: Bayesian inference in a time varying cointegration model. J. Econom. 165, 210–220 (2011). https://doi.org/10.1016/j.jeconom.2011.07.007
Kroner, K.F., Sultan, J.: Time-varying distributions and dynamic hedging with foreign currency futures. J. Financ. Quantit. Anal. 28, 535–551 (1993). https://doi.org/10.2307/2331164
Kwiatkowski, D., Phillips, P., Schmidt, P., Shin, Y.: Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root? J. Econom. 54, 159–178 (1992). https://doi.org/10.1016/0304-4076(92)90104-Y
Li, S., Thurman, W.: Grain Transport on the Mississippi River and Spatial Corn Basis. Selected Paper prepared for Presentation at the Southern Agricultural Economics Association SAEA Annual Meeting, Orlando, Florida, 35 February 2013 (2013)
Meese, R., Rogoff, K.S.: Exchange rate models of the seventies. Do they fit out of sample? J. Int. Econ. 14, 3–24 (1983). https://doi.org/10.1016/0022-1996(83)90017-X
Moosa, I.A.: An econometric model of price determination in the crude oil futures markets. Proc. Econom. Soc. Australas. Meet. 3, 373–402 (1996)
National Agricultural Statistics Service. Field Crops Usual Planting and Harvesting Dates. (2010). Available at http://usda.mannlib.cornell.edu/usda/current/planting/planting-10-29-2010.pdf. Accessed 3 Sept 2014
Phillips, P., Perron, P.: Testing for a unit root in time series regression. Biometrica 75, 335–346 (1988). https://doi.org/10.2307/2336182
Rosenberg, J.V., Traub, L.G.: Price Discovery in the Foreign Currency Futures and Spot Market. Federal Reserve Bank of New York Staff Reports, No. 262 (2006). https://doi.org/10.2139/ssrn.922317
Sarno, L., Valente, G.: Exchange rates and fundamentals: footloose or evolving relationship? J. Eur. Econ. Assoc. 7, 786–830 (2009). https://doi.org/10.1162/jeea.2009.7.4.786
Schroeder, T.C., Goodwin, B.K.: Price discovery and cointegration for live hogs. J. Futures Markets 11, 685–696 (1991). https://doi.org/10.1002/fut.3990110604
Silvapulle, P., Moosa, I.A.: The relationship between spot and futures prices: evidence from the crude oil market. J. Futures Markets 19, 175–193 (1999). https://doi.org/10.1002/(sici)1096-9934(199904)19:2<175::aid-fut3>3.3.co;2-8
Silvapulle, P.S., Podivinsky, J.M.: The effect of non-normal disturbances and conditional heteroskedasticity on multiple cointegration tests. J. Stat. Comput. Simul. 65, 173–189 (2000). https://doi.org/10.1080/00949650008811997
Swanson, N.R.: Money and output viewed through a rolling window. J. Monet. Econ. 41, 455–473 (1998). https://doi.org/10.1016/S0304-3932(98)00005-1
Swanson, N.R., White, H.: A model-selection approach to assessing the information in the term structure using linear models and artificial neural networks. J. Bus. Econ. Stat. 13, 265–275 (1995). https://doi.org/10.2307/1392186
Swanson, N.R., White, H.: A model selection approach to real-time macroeconomic forecasting using linear models and artificial neural networks. Rev. Econ. Stat. 79, 540–550 (1997). https://doi.org/10.1162/003465397557123
Tang, C.F., Abosedra, S.: Tourism and growth in Lebanon: new evidence from bootstrap simulation and rolling causality approaches. Empir. Econ. 50, 679–696 (2016). https://doi.org/10.1007/s00181-015-0944-9
Tang, Y.N., Mak, S.C., Choi, D.F.S.: The causal relationship between stock index futures and cash index prices in Hong Kong. Appl. Financ. Econ. 2, 187–190 (1992). https://doi.org/10.1080/758527099
Wang, Z., Yang, J., Li, Q.: Interest rate linkages in the eurocurrency market: contemporaneous and out-of-sample granger causality tests. J. Int. Money Finance 26, 86–103 (2007). https://doi.org/10.1016/j.jimonfin.2006.10.005
Xu, X.: Price Discovery in U.S. Corn Cash and Futures Markets: The Role of Cash Market Selection. Selected Paper prepared for presentation at the Agricultural & Applied Economics Association’s 2014 AAEA Annual Meeting, Minneapolis, MN, July 27–29 (2014a)
Xu, X.: Causality and Price Discovery in U.S. Corn Markets: An Application of Error Correction Modeling and Directed Acyclic Graphs. Selected Paper prepared for presentation at the Agricultural & Applied Economics Association’s 2014 AAEA Annual Meeting, Minneapolis, MN, July 27–29 (2014b)
Xu, X.: Cointegration among regional corn cash prices. Econ. Bull. 35, 2581–2594 (2015)
Xu, X.: Contemporaneous causal orderings of US Corn cash prices through directed acyclic graphs. Empir. Econ. 52, 731–758 (2017a). https://doi.org/10.1007/s00181-016-1094-4
Xu, X.: The rolling causal structure between the Chinese stock index and futures. Financ. Markets Portf. Manag. 31, 491–509 (2017b). https://doi.org/10.1007/s11408-017-0299-7
Xu, X.: Short-run price forecast performance of individual and composite models for 496 corn cash markets. J. Appl. Stat. 44, 2593–2620 (2017c). https://doi.org/10.1080/02664763.2016.1259399
Xu, X.: Causal structure among US Corn Futures and regional cash prices in the time and frequency domain. J. Appl. Stat. 45, 2455–2480 (2018a). https://doi.org/10.1080/02664763.2017.1423044
Xu, X.: Cointegration and price discovery in US Corn cash and futures markets. Empir. Econ. 55, 1889–1923 (2018b). https://doi.org/10.1007/s00181-017-1322-6
Xu, X.: Intraday price information flows between the CSI300 and futures market: an application of wavelet analysis. Empir. Econ. 54, 1267–1295 (2018c). https://doi.org/10.1007/s00181-017-1245-2
Xu, X.: Linear and nonlinear causality between corn cash and futures Prices. J. Agric. Food Ind. Organ. 16, Article 20160006 (2018d). https://doi.org/10.1515/jafio-2016-0006
Xu, X.: Using local information to improve short-run corn price forecasts. J. Agric. Food Ind. Organ. 16, Article 20170018 (2018e). https://doi.org/10.1515/jafio-2017-0018
Xu, X.: Contemporaneous and Granger causality among US Corn cash and futures prices. Eur. Rev. Agric. Econ. (forthcoming). https://doi.org/10.1093/erae/jby036
Xu, X., Thurman, W.N.: Using local information to improve short-run corn cash price forecasts. In: Proceedings of the NCCC-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management. St. Louis, MO (2015a)
Xu, X., Thurman, W.: Forecasting local grain prices: An evaluation of composite models in 500 corn cash markets. Selected Poster prepared for presentation at the 2015 Agricultural & Applied Economics Association and Western Agricultural Economics Association Joint Annual Meeting, San Francisco, CA, July 26–28 (2015b)
Yang, J., Bessler, D.A., Leatham, D.J.: Asset storability and price discovery in commodity futures markets: a new look. J. Futures Markets 21, 279–300 (2001). https://doi.org/10.1002/1096-9934(200103)21:3<279::aid-fut5>3.0.co;2-l
Acknowledgements
The author acknowledges Kevin McNew and Geograin, Inc of Bozeman, Montana, for generously providing the data used in the analysis in this paper. The author thanks two anonymous referees and Markus Schmid (editor) for their helpful comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Xu, X. Price dynamics in corn cash and futures markets: cointegration, causality, and forecasting through a rolling window approach. Financ Mark Portf Manag 33, 155–181 (2019). https://doi.org/10.1007/s11408-019-00330-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11408-019-00330-7