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<p>This paper investigates the issue of testing for a change point in persistence under heavy-tailed sequences with infinite variance. To mitigate the impact of outliers on persistence change detection, a robust ratio-typed test based on the Least Absolute Deviations (LAD) estimation is provided to test the process of a sequence shifting from stationarity (<i>I</i>(0)) to nonstationarity (<i>I</i>(1)) or vice versa. This approach extends the scope of change point analysis in heavy-tailed series with the applicable range of tail index <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\kappa\)</EquationSource> </InlineEquation> from (1,&#xa0;2) to (0,&#xa0;2). We establish the consistency of the LAD-estimator under the null hypothesis and demonstrate that asymptotic distribution of the proposed test is a functional of Brownian motion. Under the alternative hypothesis, we prove the robust ratio-typed test’s divergence and derive the convergent rate of change point estimator. Numerical simulations reveal that compared to the LS-based test, the LAD-based test exhibits more robustness under heavy-tailed circumstance. Moreover, the empirical size distortions are absent and empirical power is satisfactory. Finally, two practical applications are presented to demonstrate the effectiveness of these proposed test procedures.</p>

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LAD estimates-based change point detection for persistence in heavy-tailed sequences

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Yao Li,
  • Hao Jin,
  • Yan Xu

摘要

This paper investigates the issue of testing for a change point in persistence under heavy-tailed sequences with infinite variance. To mitigate the impact of outliers on persistence change detection, a robust ratio-typed test based on the Least Absolute Deviations (LAD) estimation is provided to test the process of a sequence shifting from stationarity (I(0)) to nonstationarity (I(1)) or vice versa. This approach extends the scope of change point analysis in heavy-tailed series with the applicable range of tail index \(\kappa\) from (1, 2) to (0, 2). We establish the consistency of the LAD-estimator under the null hypothesis and demonstrate that asymptotic distribution of the proposed test is a functional of Brownian motion. Under the alternative hypothesis, we prove the robust ratio-typed test’s divergence and derive the convergent rate of change point estimator. Numerical simulations reveal that compared to the LS-based test, the LAD-based test exhibits more robustness under heavy-tailed circumstance. Moreover, the empirical size distortions are absent and empirical power is satisfactory. Finally, two practical applications are presented to demonstrate the effectiveness of these proposed test procedures.