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A Residual-Based LM Test for Fractional Cointegration

Hassler, Uwe and Breitung, Jörg (2002):
A Residual-Based LM Test for Fractional Cointegration.
Darmstadt, In: Darmstadt Discussion Papers in Economics, [Online-Edition: http://econstor.eu/bitstream/10419/84848/1/ddpie_114.pdf],
[Report]

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
Erschienen: 2002
Creators: Hassler, Uwe and Breitung, Jörg
Title: A Residual-Based LM Test for Fractional Cointegration
Language: English
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.

Series Name: Darmstadt Discussion Papers in Economics
Volume: 114
Place of Publication: Darmstadt
Uncontrolled Keywords: Long memory, LM test, single equations
Divisions: 01 Department of Law and Economics
01 Department of Law and Economics > Volkswirtschaftliche Fachgebiete
Date Deposited: 04 Nov 2009 14:50
Official URL: http://econstor.eu/bitstream/10419/84848/1/ddpie_114.pdf
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