Empirical Economics

, Volume 54, Issue 3, pp 1237–1265 | Cite as

Copula-based nonlinear modeling of the law of one price for lumber products

  • Barry K. Goodwin
  • Matthew T. Holt
  • Gülcan Önel
  • Jeffrey P. Prestemon


This paper proposes an alternative and potentially novel approach to analyzing the law of one price in a nonlinear fashion. Copula-based models that consider the joint distribution of prices separated by space are developed and applied to weekly prices for lumber products. The copulas capture nonlinearities that arise in the extremes of the joint distributions of price differentials and suggest faster equilibrating adjustments when deviations from parity are extreme.


Law of one price Copulas Nonlinear time series models 

JEL Classification

F-020 C-580 


  1. Balcombe K, Bailey A, Brooks J (2007) Threshold effects in price transmission: the case of Brazilian wheat, maize, and soya prices. Am J Agric Econ 89:308–323CrossRefGoogle Scholar
  2. Benninga S, Protopapadakis A (1988) The equilibrium pricing of exchange rates and assets when trade takes time. J Int Money Financ 7:129–149CrossRefGoogle Scholar
  3. Berg D, Bakken H (2007) A copula goodness-of-fit approach based on the probability integral transform, unpublished working paper.
  4. Bessler DA, Fuller SW (1993) Cointegration between U.S. wheat markets. J Reg Sci 33:485–501CrossRefGoogle Scholar
  5. Buongiorno J, Uusivuori J (1992) The law of one price in the trade of forest products: co-integration tests for U.S. exports of pulp and paper. For Sci 38:539–553Google Scholar
  6. Cherubini U, Luciano E, Vecchiato W (2004) Copula methods in finance. John Wiley and Sons, ChichesterCrossRefGoogle Scholar
  7. Chvosta J, Erdman DJ, Little M (2011) Modeling financial risk factor correlation with the COPULA rocedure, SAS Global Forum, Paper 340–2011. SAS Institute Inc., CaryGoogle Scholar
  8. Czado C (2011) The world of vines. In: 4th Workshop on Vine Copula Distributions and Applications, Technische Universität München, Munich, Germany, May 2011. Accessed 31 March 2017
  9. Deheuvels P (1979) La Fonction de Dépendance Empirique et ses Propriétés: Un Test Non–Paramétrique d Indépendance. Académie Royale de Belgique. Bulletin de la Classe des Sciences, 5e Série 65:274–292Google Scholar
  10. De Lira Salvatierra I, Patton AJ (2015) Dynamic copula models and high frequency data. J Empir Financ 30:120–135CrossRefGoogle Scholar
  11. Demarta S, McNeil AJ (2005) The t copula and related copulas. Int Stat Rev 73:111–129CrossRefGoogle Scholar
  12. Dumas B (1992) Dynamic equilibrium and the real exchange rate in a spatially separated world. Rev Financ Stud 5:153–180CrossRefGoogle Scholar
  13. Embrechts P, McNeil A, Straumann D (2002) Correlation and dependence in risk management: properties and pitfalls. In: Dempster MAH (ed) Risk management: value at risk and beyond. Cambridge University Press, Cambridge, pp 176–223CrossRefGoogle Scholar
  14. Engle Robert F, Granger CWJ (1987) Co-integration and error correction: representation, estimation, and testing. Econometrica 55(2):251–276CrossRefGoogle Scholar
  15. Fackler PL, Goodwin BK (2001) Spatial Price Analysis. In: Rausser GC, Garnder BL (eds) Handbook of agricultural economics. Elsevier Science, New YorkGoogle Scholar
  16. Fang HB, Fang KT, Kotz S (2002) The meta-elliptical distributions with given marginals. J Multivar Anal 82:1–16CrossRefGoogle Scholar
  17. Genest C, Rivest L-P (1993) Statistical inference procedures for bivariate Archimedean copulas. J Am Stat Assoc 88(423):1034–1043CrossRefGoogle Scholar
  18. Genest C, Rémillard R, Beaudoin D (2009) Goodness of fit tests for copulas: a review and power study. Insur Math Econ 44:199–213CrossRefGoogle Scholar
  19. Giovannini A (1988) Exchange rates and traded goods prices. J Int Econ 24:45–68CrossRefGoogle Scholar
  20. Glasserman P (2004) Monte-Carlo methods in financial engineering. Springer-Verlag, New YorkGoogle Scholar
  21. Goodwin BK, Grennes TJ, Wohlgenant MK (1990) Testing the law of one price when trade takes time. J Int Money Financ 9:21–40CrossRefGoogle Scholar
  22. Goodwin BK, Holt MT, Prestemon JP (2011) North American oriented strand board markets, arbitrage activity, and market price dynamics: a smooth transition approach. Am J Agric Econ 93:993–1014CrossRefGoogle Scholar
  23. Goodwin BK, Piggott NE (2001) Spatial market integration in the presence of threshold effects. Am J Agric Econ 83:302–317CrossRefGoogle Scholar
  24. Heckscher EF (1916) Vaxelkursens Grundval vid Pappersmyntfot. Ekonomisk Tidskrift 18:309–312CrossRefGoogle Scholar
  25. Hu L (2006) Dependence patterns across financial markets: a mixed copula approach. Appl Financ Econ 10:717–729CrossRefGoogle Scholar
  26. Isard P (1977) How far can we push the “Law of One Price”? Am Econ Rev 67:942–948Google Scholar
  27. Joe H (1997) Multivariate models and dependence concepts. Chapman and Hall, LondonCrossRefGoogle Scholar
  28. Jondeau E, Rockinger M (2006) The Copula-GARCH model of conditional dependencies: an international stock-market application. J Int Money Financ 25:827–853CrossRefGoogle Scholar
  29. Jung C, Doroodian K (1994) The law of one price for U.S. softwood lumber: a multivariate cointegration test. For Sci 40:595–600Google Scholar
  30. Lo MC, Zivot E (2001) Threshold cointegration and nonlinear adjustment to the law of one price. Macroecon Dyn 5:533–576Google Scholar
  31. Michael P, Nobay AR, Peel D (1994) Purchasing power parity yet again: evidence from spatially separated markets. J Int Money Financ 13:637–657CrossRefGoogle Scholar
  32. Nelsen RB (2006) An introduction to copulas. Springer-Verlag, New YorkGoogle Scholar
  33. Oh DH, Patton AJ (2013) Time-varying systemic risk: evidence from a dynamic copula model of CDS spreads, (May 23, 2013). Economic Research Initiatives at Duke (ERID) Working Paper No. 167Google Scholar
  34. Park H, Mjelde JW, Bessler DA (2007) Time-varying threshold cointegration and the law of one price. Appl Econ 39:1091–1105CrossRefGoogle Scholar
  35. Patton AJ (2006) Modelling asymmetric exchange rate dependence. Int Econ Rev 47:527–556CrossRefGoogle Scholar
  36. Patton AJ (2009) Copula-based models for financial time series. In: Andersen TG, Davis RA, Kreiss J-P, Mikosch T (eds) Handbook of financial time series. Springer Verlag, BerlinGoogle Scholar
  37. Patton AJ (2012) A review of copula models for economic time series. J Multivar Anal 110:4–18CrossRefGoogle Scholar
  38. Patton AJ, Fan Y (2014) Copulas in econometrics. Annu Rev Econ 6:179–200CrossRefGoogle Scholar
  39. Reboredo JC (2011) How do crude oil prices co-move?: A copula approach. Energy Econ 33:948–955CrossRefGoogle Scholar
  40. Richardson DJ (1978) Some empirical evidence on commodity arbitrage and the law of one price. J Int Econ 8:341–351CrossRefGoogle Scholar
  41. Rodriguez JC (2003) Measuring financial contagion: a copula approach. J Empir Financ 14:401–423CrossRefGoogle Scholar
  42. Schepsmeier U, Stoeber J, Brechmann EC, Graeler B, Nagler T, Erhardt T (2012) Package VineCopula \(R\)-Project CRAN Repository, July 2015Google Scholar
  43. Schweizer B, Sklar A (1983) Probabilistic metric spaces. Elsevier Science, New YorkGoogle Scholar
  44. Sephton PS (2003) Spatial market arbitrage and threshold cointegration. Am J Agric Econ 85:1041–1046CrossRefGoogle Scholar
  45. Sklar A (1959) Fonctions de rèpartition àn dimensions et leurs marges. Publ Inst Stat Univ Paris 8:229–231Google Scholar
  46. Smith MS, Gan Q, Kohn RJ (2011) Modelling dependence using skew t copulas: Bayesian inference and applications. J Appl Econom 27:500–522CrossRefGoogle Scholar
  47. Taylor AM (2001) Potential pitfalls for the purchasing-power-parity puzzle? Sampling and specification biases in mean-reversion tests of the law of one price. Econometrica 69:473–498CrossRefGoogle Scholar
  48. Teräsvirta T (1994) Specification, estimation and evaluation of smooth transition autoregressive models. J Am Stat Assoc 89:208–218Google Scholar
  49. Thursby MC, Johnson PR, Grennes TJ (1986) The law of one price and the modelling of disaggregated trade flows. Econ Model 3:293–302CrossRefGoogle Scholar
  50. Wang W, Wells MT (2000) Model selection and semiparametric inference for bivariate failure-time data. J Am Stat Assoc 95(449):62–72CrossRefGoogle Scholar
  51. Yan J (2007) Enjoy the joy of copulas: with a package copula. J Stat Softw 21(4):1–21CrossRefGoogle Scholar
  52. Yan J, Kojadinovic I (2012) Package ‘copula,’: multivariate dependence with copulas, \(R\)-Project CRAN RepositoryGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Barry K. Goodwin
    • 1
  • Matthew T. Holt
    • 2
  • Gülcan Önel
    • 3
  • Jeffrey P. Prestemon
    • 4
  1. 1.Department of EconomicsNorth Carolina State UniversityRaleighUSA
  2. 2.Department of Economics, Finance, and Legal StudiesUniversity of AlabamaTuscaloosaUSA
  3. 3.Food and Resource Economics DepartmentUniversity of FloridaGainesvilleUSA
  4. 4.Forestry Sciences LaboratoryUSDA Forest ServiceResearch Triangle ParkUSA

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