Geodesic
Robust sign test for the unit root hypothesis of autoregression
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 3, pp. 431-446 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An $\operatorname{AR}(1)$-model is considered with autoregression observations that contain gross errors (contaminations) with unknown arbitrary distribution. The unit root hypothesis for autoregression is tested. A special sign test is proposed as an alternative to the least-square test (the latter test is not applicable in this setting). The sign test is shown to be locally qualitatively robust in terms of the equicontinuity of the power.
Keywords: hypotheses testing, unit root, sign tests, qualitative robustness.
Mots-clés : autoregression, contaminations 
@article{TVP_2018_63_3_a1,
     author = {M. V. Boldin},
     title = {Robust sign test for the unit root hypothesis of autoregression},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {431--446},
     year = {2018},
     volume = {63},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2018_63_3_a1/}
}
TY  - JOUR
AU  - M. V. Boldin
TI  - Robust sign test for the unit root hypothesis of autoregression
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2018
SP  - 431
EP  - 446
VL  - 63
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TVP_2018_63_3_a1/
LA  - ru
ID  - TVP_2018_63_3_a1
ER  - 
%0 Journal Article
%A M. V. Boldin
%T Robust sign test for the unit root hypothesis of autoregression
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2018
%P 431-446
%V 63
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_2018_63_3_a1/
%G ru
%F TVP_2018_63_3_a1
M. V. Boldin. Robust sign test for the unit root hypothesis of autoregression. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 3, pp. 431-446. http://geodesic.mathdoc.fr/item/TVP_2018_63_3_a1/

[1] M. V. Boldin, “Sign tests in the simplest auto-regression with coefficient from $\mathbb R^1$”, Russian Math. Surveys, 52:3 (1997), 607–608 | DOI | DOI | MR | Zbl

[2] M. V. Boldin, “Local robustness of sign tests in $\operatorname{AR}(1)$ against outliers”, Math. Methods Statist., 20:1 (2011), 1–13 | DOI | MR | Zbl

[3] M. V. Boldin, “Robustness of sign tests for testing hypotheses about order of autoregression”, Theory Probab. Appl., 57:4 (2013), 663–670 | DOI | DOI | MR | Zbl

[4] M. V. Boldin, G. I. Simonova, Yu. N. Tyurin, Sign-based methods in linear statistical models, Transl. Math. Monogr., 162, Amer. Math. Soc., Providence, RI, 1997, xii+234 pp. | MR | Zbl | Zbl

[5] N. H. Chan, C. Z. Wei, “Asymptotic inference for nearly nonstationary $\operatorname{AR}(1)$ processes”, Ann. Statist., 15:3 (1987), 1050–1063 | DOI | MR | Zbl

[6] D. A. Dickey, W. A. Fuller, “Distribution of the estimators for autoregressive time series with a unit root”, J. Amer. Statist. Assoc., 74:366, part 1 (1979), 427–431 | DOI | MR | Zbl

[7] G. B. A. Evans, N. E. Savin, “The calculation of the limiting distribution of the least squares estimator of the parameter in a random walk model”, Ann. Statist., 9:5 (1981), 1114–1118 | DOI | MR | Zbl

[8] J. Hájek, Z. Šidák, Theory of rank tests, Academic Press, New York–London; Academia, Publishing House of the Czechoslovak Academy of Sciences, Prague, 1967, 297 pp. | MR | Zbl

[9] R. D. Martin, V. J. Yohai, “Influence functionals for time series”, Ann. Statist., 14:3 (1986), 781–818 | DOI | MR | Zbl

[10] H. Rieder, “Qualitative robustness of rank tests”, Ann. Statist., 10:1 (1982), 205–211 | DOI | MR | Zbl

[11] A. Steland, “Weighed Dickey–Fuller processes for detecting stationarity”, J. Statist. Plann. Inference, 137:12 (2007), 4011–4030 | DOI | MR | Zbl