Quantiles for t-statistics based on M-estimators of unit roots

We derive formulae for the asymptotic density and distribution functions of the t-statistic for autoregressive unit roots based on M-estimators. These formulae depend upon a nuisance parameter. Consequently, new critical valu es for this test would have to be generated for each different M-estimator that is used. We therefore provide a methodology for tractable and accurate analytic approximations of quantiles based on asymptotic expansions of fun ctions, We use it to derive simple yet accurate approximations for the asym ptotic distribution of these unit root M-tests. Using these asymptotic appr oximations, critical values of the tests can easily be obtained without eve n resorting to a computer. The approximation requires no new tabulation, an d the resulting cumulative distribution function (cdf) has a maximum absolu te error of 0.002 for typical quantiles (i.e. 1-10% quantiles). (C) 2000 El sevier Science S.A. All rights reserved. JEL classification: C22.