Residual empirical processes and qualitatively robust GM-tests in autoregression

The local qualitative robustness of GM-tests against outliers in the autoregression model is studied in the paper. A local scheme of data contamination by independent outliers with the intensity O(n−1/2) is considered. The qualitative robustness in terms of power equicontinuity is obtained. The GM-tests asymptotically optimal in the maximin sense are constructed.