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Testing for Linearity in Regressions with I(1) processes

  • Yoichi Arai

    (Faculty of Economics, University of Tokyo)

In this paper we propose a generalized version of the RESET test for linearity in regressions with I(1) processes against various nonlinear alternatives and no cointegration. The proposed test statistic for linearity is given by the Wald statistic and its limiting distribution under the null hypothesis of linearity is shown to be a x2 distribution when a "leads and lags" estimation technique is employed to construct the test statistic. We show that the test is consistent against a class of nonlinear alternatives and no cointegration. This class includes polynomial functions of finite order, the logarithmic function, and the distribution function of any random variable and its scalar multiple. Finite?sample simulations show that the empirical size of the test is close to the nominal one and the test succeeds in detecting both nonlinearity in the class and no cointegration. We apply the test to see if relationships between exchange rates and fundamentals are linear and find significant evidence against linearity for all countries considered.

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File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2004/2004cf303.pdf
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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-303.

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Length: 45 pages
Date of creation: Oct 2004
Date of revision:
Handle: RePEc:tky:fseres:2004cf303
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  1. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  3. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
  4. Hong, Seung Hyun & Phillips, Peter C. B., 2010. "Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 96-114.
  5. Wooldridge, Jeffrey M. & White, Halbert, 1988. "Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 4(02), pages 210-230, August.
  6. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  7. repec:oup:restud:v:57:y:1990:i:1:p:99-125 is not listed on IDEAS
  8. Peter C.B. Phillips & Joon Y. Park, 1999. "Nonstationary Binary Choice," Cowles Foundation Discussion Papers 1223, Cowles Foundation for Research in Economics, Yale University.
  9. Corradi, V. & Swanson, N. & White, H., 1996. "Testing for Stationarity-Ergodicity and for Comovements Between Nonlinear Discrete Time Markov Processes," Papers 4-96-6, Pennsylvania State - Department of Economics.
  10. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-79, March.
  11. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  12. Hansen, Bruce E. & Seo, Byeongseon, 2002. "Testing for two-regime threshold cointegration in vector error-correction models," Journal of Econometrics, Elsevier, vol. 110(2), pages 293-318, October.
  13. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
  14. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, Oxford University Press, vol. 106(3), pages 669-682.
  15. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
  16. repec:oup:restud:v:58:y:1991:i:3:p:603-19 is not listed on IDEAS
  17. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
  18. Ogaki, Masao & Park, Joon Y., 1997. "A cointegration approach to estimating preference parameters," Journal of Econometrics, Elsevier, vol. 82(1), pages 107-134.
  19. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
  20. Meese, Richard A & Rose, Andrew K, 1990. "Nonlinear, Nonparametric, Nonessential Exchange Rate Estimation," American Economic Review, American Economic Association, vol. 80(2), pages 192-96, May.
  21. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  22. Ikeda, Shinsuke & Shibata, Akihisa, 1995. "Fundamentals uncertainty, bubbles, and exchange rate dynamics," Journal of International Economics, Elsevier, vol. 38(3-4), pages 199-222, May.
  23. Kurozumi, Eiji, 2002. "Testing for stationarity with a break," Journal of Econometrics, Elsevier, vol. 108(1), pages 63-99, May.
  24. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(01), pages 91-115, March.
  25. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  26. Ma, Yue & Kanas, Angelos, 2000. "Testing for a nonlinear relationship among fundamentals and exchange rates in the ERM," Journal of International Money and Finance, Elsevier, vol. 19(1), pages 135-152, February.
  27. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  28. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
  29. Yoosoon Chang & Joon Y. Park & Peter C.B. Phillips, 1999. "Nonlinear Econometric Models with Cointegrated and Deterministically Trending Regressors," Cowles Foundation Discussion Papers 1245, Cowles Foundation for Research in Economics, Yale University.
  30. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 473-495.
  31. Peter C.B. Phillips, 1987. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals via Martingale Approximations," Cowles Foundation Discussion Papers 846, Cowles Foundation for Research in Economics, Yale University.
  32. repec:oup:restud:v:53:y:1986:i:4:p:473-95 is not listed on IDEAS
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