Approximate Normality of T-Ratios Based on M-Estimators for the Unit Root

We derive formulae for the asymptotic density and distribution functions of the t-statistic for autoregressive unit roots based on M-estimators. The distribution depends upon a nuisance parameter. Consequently, new critical values for this test have to be generated for each new estimator that is used. We therefore also derive simple yet accurate normal approximations to the asymptotic distribution of these unit root M-tests. Using these asymptotic approximations, critical values of the tests can easily be obtained without resorting to extensive simulation experiments. The approximation requires no new tabulation, and the resulting distribution function has a maximum absolute error of 0.002 for typical quantiles