We study the optimal choice of quasi-likelihoods for nearly integrated, possibly non-normal, autoregressive models. It turns out that the two most natural candidate criteria, minimum Mean Squared Error (MSE) and maximum power against the unit root null, give rise to different optimal...

We study the optimal choice of quasi-likelihoods for nearly integrated, possibly non-normal, autoregressive models. It turns out that the two most natural candidate criteria, minimum Mean Squared Error (MSE) and maximumpower against the unit root null, give rise to different...

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...