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Rank tests for nonlinear cointegration

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  • Breitung, Jörg

Abstract

A test procedure based on ranks is suggested to test for nonlinear cointegration. For two (or more) time series it is assumed that there exist monotonic transformations such that the normalised series can asymptotically be represented by independent Brownian motions. Rank test procedures based on the difference between the sequences of ranks are suggested. If there is no cointegration between the time series, the sequences of ranks tend to diverge, whereas under cointegration the sequences of ranks evolve similarly. Monte Carlo simulations suggest that for a wide range of nonlinear models the rank tests perform better than their parametric competitors. To test for nonlinear cointegration a variable addition test based on ranks is suggested. As empirical illustrations we consider the term structure of interest rates. Only weak evidence for a nonlinear long run relationship between interest yields of bonds with different time to maturity is found. --

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Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 1998,65.

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Date of creation: 1998
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Handle: RePEc:zbw:sfb373:199865

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Keywords: unit roots; nonlinear cointegration; rank test; arcsine distribution;

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  1. G. Pfann & P. Schotman & R. Tschernig, 1994. "Nonlinear Interest Rate Dynamics and Implications for the Term Structure," SFB 373 Discussion Papers 1994,43, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 257-87, August.
  3. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-28, August.
  4. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
  5. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September.
  6. James H. Stock & Mark W. Watson, 1991. "A simple estimator of cointegrating vectors in higher order integrated systems," Working Paper Series, Macroeconomic Issues 91-3, Federal Reserve Bank of Chicago.
  7. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  9. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April.
  10. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  11. Campbell, Bryan & Galbraith, John W, 1993. "Inference in Expectations Models of the Term Structure: A Non-parametric Approach," Empirical Economics, Springer, vol. 18(4), pages 623-38.
  12. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-79, March.
  13. Granger, Clive W. J. & Terasvirta, Timo, 1993. "Modelling Non-Linear Economic Relationships," OUP Catalogue, Oxford University Press, number 9780198773207, September.
  14. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-74, January.
  15. Breitung, Jorg & Gourieroux, Christian, 1997. "Rank tests for unit roots," Journal of Econometrics, Elsevier, vol. 81(1), pages 7-27, November.
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