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Tests Based on Simplicial Depth for AR(1) Models With Explosion
Author(s) -
Kustosz Christoph P.,
Leucht Anne,
MÜller Christine H.
Publication year - 2016
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12186
Subject(s) - mathematics , outlier , consistency (knowledge bases) , test statistic , distribution (mathematics) , statistic , explosive material , asymptotic distribution , gaussian , statistics , statistical hypothesis testing , algorithm , mathematical analysis , geometry , chemistry , physics , organic chemistry , quantum mechanics , estimator
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.