Inference in a nearly integrated autoregressive model with nonnormal innovations

Robust tests and estimators based on nonnormal quasi-likelihood functions are developed for autoregressive models with near unit root. Asymptotic power functions and power envelopes are derived for point-optimal tests of a unit root when the likelihood is correctly specified. The shapes of these power functions are found to be sensitive to the extent of nonnormality in the innovations. Power loss resulting from using least-squares unit-root tests in the presence of thick-tailed innovations appears to be greater than in stationary models.