Residual empirical processes and qualitatively robust GM-tests in autoregression

The article deals with the local qualitative robustness of GM-tests against outliers in the autoregression model. We consider a local scheme of data contamination by independent outliers with the intensity $O(n^{-1/2}).$ The qualitative robustness in terms of power equicontinuity is obtained. The asymptotically optimal in maximin sense GM-tests are constructed.