Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis


  • Michael Jansson,

    1. Dept. of Economics, University of California, Berkeley, 530 Evans Hall #3880, Berkeley, CA 94720, U.S.A. and CREATES;
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  • Morten Ørregaard Nielsen

    1. Dept. of Economics, Queen's University, Kingston, Ontario, K7L 3N6, Canada and CREATES;
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    • We are grateful to Jim Stock, the referees, Peter Boswijk, Niels Haldrup, Søren Johansen, Tom Rothenberg, and seminar participants at the University of Aarhus, Cornell University, the Econometric Society World Congress in Shanghai, the HEC Montréal-CIRPÉE Applied Financial Time Series Workshop, the CREATES conference on Periodicity, Non-stationarity, and Forecasting of Economic and Financial Time Series, the 2011 NBER-NSF Time Series Conference, the 2011 Canadian Econometric Study Group conference, and the 2011 CIREQ Time Series Conference for comments and discussion, and to the Danish Social Sciences Research Council (FSE Grant 275-05-0220), the Social Sciences and Humanities Research Council of Canada (SSHRC Grant 410-2009-0183), and the Center for Research in Econometric Analysis of Time Series (CREATES, funded by the Danish National Research Foundation) for financial support.


Seemingly absent from the arsenal of currently available “nearly efficient” testing procedures for the unit root hypothesis, that is, tests whose asymptotic local power functions are virtually indistinguishable from the Gaussian power envelope, is a test admitting a (quasi-)likelihood ratio interpretation. We study the large sample properties of a quasi-likelihood ratio unit root test based on a Gaussian likelihood and show that this test is nearly efficient.