Geodesic
Unit root test under innovation outlier contamination small sample case
Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 1, pp. 5-17.

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The two sided unit root test of a first-order autoregressive model in the presence of an innovation outlier is considered. In this paper, we present three tests; two are usual and one is new. We give formulas computing the size and the power of the three tests when an innovation outlier (IO) occurs at a specified time, say k. Using a comparative study, we show that the new statistic performs better under contamination. A Small sample case is considered only.
Keywords: autoregressive process, Dickey-Fuller test, innovation outlier, power, size 
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Atil, Lynda; Fellag, Hocine; Nouali, Karima. Unit root test under innovation outlier contamination small sample case. Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 1, pp. 5-17. http://geodesic.mathdoc.fr/item/DMPS_2006_26_1_a0/

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