Tests Based on Simplicial Depth for AR(1) Models With Explosion |
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Authors: | Christoph P Kustosz Anne Leucht Christine H MÜller |
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Affiliation: | 1. Fakult?t Statistik, Technische Universit?t Dortmund, Dortmund, Germany;2. Institut für Mathematische Stochastik, Technische Universit?t Braunschweig, Braunschweig, Germany |
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Abstract: | We propose outlier a robust and distribution‐free test for the explosive AR(1) model with intercept based on simplicial depth. In this model, simplicial depth reduces to counting the cases where three residuals have alternating signs. The asymptotic distribution of the test statistic is given by a specific Gaussian process. Conditions for the consistency are given, and the power of the test at finite samples is compared with alternative tests. The new test outperforms these tests in the case of skewed errors and outliers. Finally, we apply the method to crack growth data and compare the results with an OLS approach. |
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Keywords: | Alternating sign autoregression distribution‐free test robustness simplicial depth consistency JEL 62M10 62G10 62G35 62F05 |
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