{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T16:42:38Z","timestamp":1790613758195,"version":"4.1.0"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"unspecified","delay-in-days":5124,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1995,2]]},"abstract":"<jats:p>This paper considers unit root tests based on M estimators. The asymptotic theory for these tests is developed. It is shown how the asymptotic distributions of the tests depend on nuisance parameters and how tests can be constructed that are invariant to these parameters. It is also shown that a particular linear combination of a unit root test based on the ordinary least-squares (OLS) estimator and on an M estimator converges to a normal random variate. The interpretation of this result is discussed. A simulation experiment is described, illustrating the level and power of different unit root tests for several sample sizes and data generating processes. The tests based on M estimators turn out to be more powerful than the OLS-based tests if the innovations are fat-tailed.<\/jats:p>","DOI":"10.1017\/s0266466600009191","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T11:41:32Z","timestamp":1236685292000},"page":"331-346","source":"Crossref","is-referenced-by-count":71,"title":["Unit Root Tests Based on M Estimators"],"prefix":"10.1017","volume":"11","author":[{"given":"Andr\u00e9","family":"Lucas","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,2,11]]},"reference":[{"key":"S0266466600009191_ref001","doi-asserted-by":"publisher","DOI":"10.2307\/2951574"},{"key":"S0266466600009191_ref011","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600013189"},{"key":"S0266466600009191_ref016","doi-asserted-by":"publisher","DOI":"10.2307\/3315522"},{"key":"S0266466600009191_ref013","volume-title":"Working paper TI 94\u20133","author":"Hoek","year":"1994"},{"key":"S0266466600009191_ref008","volume-title":"Working paper 93\/16","author":"Franses","year":"1993"},{"key":"S0266466600009191_ref009","volume-title":"Introduction to Statistical Time Series","author":"Fuller","year":"1976"},{"key":"S0266466600009191_ref006","first-page":"3","article-title":"Unit roots in economic time series: A selective survey","volume":"8","author":"Diebold","year":"1990","journal-title":"Advances in Econometrics"},{"key":"S0266466600009191_ref017","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600004400"},{"key":"S0266466600009191_ref023","doi-asserted-by":"publisher","DOI":"10.2307\/1913237"},{"key":"S0266466600009191_ref005","first-page":"427","article-title":"Distribution of estimators for autoregressive time series with a unit root","volume":"74","author":"Dickey","year":"1979","journal-title":"Journal of the American Statistical Association"},{"key":"S0266466600009191_ref022","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600013402"},{"key":"S0266466600009191_ref021","doi-asserted-by":"publisher","DOI":"10.2307\/1913610"},{"key":"S0266466600009191_ref003","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348240"},{"key":"S0266466600009191_ref010","volume-title":"Robust Statistics. 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