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Testing for Linearity in Regressions with I (1) processes

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  • Yoichi Arai

    (Faculty of Economics, University of Tokyo)

Abstract

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 x^2 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.carf.e.u-tokyo.ac.jp/pdf/workingpaper/fseries/21.pdf
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Bibliographic Info

Paper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-014.

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Length: 45 pages
Date of creation: Oct 2004
Date of revision:
Handle: RePEc:cfi:fseres:cf014

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  1. Peter C.B. Phillips & Joon Y. Park, 1999. "Nonstationary Binary Choice," Cowles Foundation Discussion Papers 1223, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. 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.
  4. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  5. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
  6. Corradi, Valentina & Swanson, Norman R. & White, Halbert, 2000. "Testing for stationarity-ergodicity and for comovements between nonlinear discrete time Markov processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 39-73, May.
  7. Meese, Richard A & Rose, Andrew K, 1991. "An Empirical Assessment of Non-linearities in Models of Exchange Rate Determination," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 603-19, May.
  8. G. William Schwert, 1988. "Tests For Unit Roots: A Monte Carlo Investigation," NBER Technical Working Papers 0073, National Bureau of Economic Research, Inc.
  9. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
  10. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  11. Phillips, P.C.B., 1988. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals Via Martingale Approximations," Econometric Theory, Cambridge University Press, vol. 4(03), pages 528-533, December.
  12. Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers 768, Cowles Foundation for Research in Economics, Yale University.
  13. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  14. Kurozumi, Eiji, 2002. "Testing for stationarity with a break," Journal of Econometrics, Elsevier, vol. 108(1), pages 63-99, May.
  15. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  16. Krugman, Paul R, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, MIT Press, vol. 106(3), pages 669-82, August.
  17. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  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. 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.
  20. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  21. 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.
  22. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-79, March.
  23. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
  24. 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.
  25. 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.
  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. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
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Cited by:
  1. Yoichi Arai & Eiji Kurozumi, 2005. "Testing for the Null Hypothesis of Cointegration with Structural Breaks (Subsequently published in "Econometric Reviews", Volume 26, Issue 6 November 2007, pages 705 - 739. )," CARF F-Series CARF-F-022, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  2. Yoichi Arai & Eiji Kurozumi, 2005. "Testing for the Null Hypothesis of Cointegration with Structural Breaks," CIRJE F-Series CIRJE-F-319, CIRJE, Faculty of Economics, University of Tokyo.

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