{"title":"Asymptotic Properties of Residual Based Tests for Cointegration","authors":"P. Phillips, S. Ouliaris","doi":"10.2307/2938339","DOIUrl":null,"url":null,"abstract":"This paper develops an asymptotic theory for residual based tests for cointegration. Attention is given to the augmented Dickey-Fuller (ADF) test and the Z(subscript \"alpha\") and Z(subscript \"t\") unit root tests. Two new tests are also introduced. The tests are shown to be asymptotically similar, and simple representations of their limiting distributions are given and asymptotic critical values are tabulated. The ADF and Z(subscript \"t\") tests are asymptotically equivalent. Power properties of the test are also studied. The tests are consistent if suitably constructed, but the ADF and Z(subscript \"t\") tests have slower rates of divergence under cointegration than the other tests. Copyright 1990 by The Econometric Society.","PeriodicalId":50556,"journal":{"name":"Econometrica","volume":"58 1","pages":"165-193"},"PeriodicalIF":7.1000,"publicationDate":"1990-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2307/2938339","citationCount":"2018","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Econometrica","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.2307/2938339","RegionNum":1,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 2018
Abstract
This paper develops an asymptotic theory for residual based tests for cointegration. Attention is given to the augmented Dickey-Fuller (ADF) test and the Z(subscript "alpha") and Z(subscript "t") unit root tests. Two new tests are also introduced. The tests are shown to be asymptotically similar, and simple representations of their limiting distributions are given and asymptotic critical values are tabulated. The ADF and Z(subscript "t") tests are asymptotically equivalent. Power properties of the test are also studied. The tests are consistent if suitably constructed, but the ADF and Z(subscript "t") tests have slower rates of divergence under cointegration than the other tests. Copyright 1990 by The Econometric Society.
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Econometrica publishes original articles in all branches of economics - theoretical and empirical, abstract and applied, providing wide-ranging coverage across the subject area. It promotes studies that aim at the unification of the theoretical-quantitative and the empirical-quantitative approach to economic problems and that are penetrated by constructive and rigorous thinking. It explores a unique range of topics each year - from the frontier of theoretical developments in many new and important areas, to research on current and applied economic problems, to methodologically innovative, theoretical and applied studies in econometrics.
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