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<p>This review discusses the detection of a single change-point in autoregressive models of order <i>p</i>. It begins by outlining parameter estimation. Subsequently, two common robust testing methods are considered: the Efficient Score Test (EST) and the Likelihood Ratio Test (LRT). The limiting distributions of the test statistics under the null hypothesis of no change, along with methods for pinpointing the location of the change-point, are presented. Both methods are backed by theoretical justifications. To illustrate the performance, a summary of a comprehensive simulation experiment under various change scenarios is included, confirming the convergence and performance of the discussed methods. Finally, an application of these techniques to real-world data, specifically analyzing changes in volatility is described. These findings are placed in context with recent algorithms in the literature, highlighting their comparative efficacy and reliability.</p>

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A Partial Review on Testing for Change Points in Autoregressive Time Series Models

  • 期刊论文

  • 发表日期：

    2025年7月2日

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  • Mohamed Salah Eddine Arrouch,
  • Echarif Elharfaoui,
  • Mohamed-Amine Elaafani,
  • Sara Nejjam

摘要

This review discusses the detection of a single change-point in autoregressive models of order p. It begins by outlining parameter estimation. Subsequently, two common robust testing methods are considered: the Efficient Score Test (EST) and the Likelihood Ratio Test (LRT). The limiting distributions of the test statistics under the null hypothesis of no change, along with methods for pinpointing the location of the change-point, are presented. Both methods are backed by theoretical justifications. To illustrate the performance, a summary of a comprehensive simulation experiment under various change scenarios is included, confirming the convergence and performance of the discussed methods. Finally, an application of these techniques to real-world data, specifically analyzing changes in volatility is described. These findings are placed in context with recent algorithms in the literature, highlighting their comparative efficacy and reliability.