# A Residual-Based LM Test for Fractional Cointegration

## 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.

Item Type: Report 2002 Hassler, Uwe ; Breitung, Jörg A Residual-Based LM Test for Fractional Cointegration English 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. Darmstadt Discussion Papers in Economics 114 Darmstadt Long memory, LM test, single equations 01 Department of Law and Economics01 Department of Law and Economics > Volkswirtschaftliche Fachgebiete 04 Nov 2009 14:50 http://econstor.eu/bitstream/10419/84848/1/ddpie_114.pdf ASCII CitationIBW_RDASimple MetadataEP3 XMLJSONHTML CitationAtomEndNoteRDF+XMLMultiline CSVMODSBibTeXReference ManagerT2T_XMLDublin Core TUfind oder in Google
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