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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 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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Bibliographic Info

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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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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