On the power of Pearson’s test under local alternatives in autoregression with outliers. (English) Zbl 1418.62189
Summary: We consider a stationary linear AR(\(p\)) model with contamination (gross errors in the observations). The autoregression parameters are unknown, as well as the distribution of innovations. Based on the residuals from the parameter estimates, an analog of the empirical distribution function is defined and a test of Pearson’s chi-square type is constructed for testing hypotheses on the distribution of innovations. We obtain the asymptotic power of this test under local alternatives and establish its qualitative robustness under the hypothesis and alternatives.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62G10 | Nonparametric hypothesis testing |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62G35 | Nonparametric robustness |
Keywords:
autoregression; outliers; residuals; empirical distribution function; Pearson’s chi-square test; robustness; local alternativesReferences:
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