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A Residual-Based LM Test for Fractional Cointegration

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  • Hassler, Uwe
  • Breitung, Jörg

Abstract

Nonstationary fractionally integrated time series may possibly be fractionally cointegrated. In this paper we propose a test for the null hypothesis of no cointegration. It builds on a static cointegration regression of the levels of the variables as a first step. In a second step, a univariate LM test is applied to the single equation regression residuals. However, it turns out that the application of the LM test to residuals without further modifications does not result in a limiting standard normal distribution, which contrasts with the situation when the LM test is applied to observed series. Therefore, we suggest a simple modification of the LM test that accounts for the residual effect. At the same time it corrects for eventual endogeneity of the cointegration regression. The proposed modification guarantees a limiting standard normal distribution of the test statistic. Our procedure is completely regression based and hence easy to perform. Monte Carlo experiments establish its validity for finite samples.

Suggested Citation

  • Hassler, Uwe & Breitung, Jörg, 2009. "A Residual-Based LM Test for Fractional Cointegration," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 77555, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    • Handle: RePEc:dar:wpaper:77555
    Note: for complete metadata visit http://tubiblio.ulb.tu-darmstadt.de/77555/
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    Cited by:

    1. Guglielmo Maria Caporale & Luis A. Gil‐Alana, 2005. "Fractional Cointegration And Aggregate Money Demand Functions," Manchester School, University of Manchester, vol. 73(6), pages 737-753, December.

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