A Partial Review on Testing for Change Points in Autoregressive Time Series Models
Mohamed Salah Eddine Arrouch (),
Echarif Elharfaoui (),
Mohamed-Amine Elaafani () and
Sara Nejjam ()
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Mohamed Salah Eddine Arrouch: Chouaib Doukkali University
Echarif Elharfaoui: Chouaib Doukkali University
Mohamed-Amine Elaafani: Chouaib Doukkali University
Sara Nejjam: Chouaib Doukkali University
Methodology and Computing in Applied Probability, 2025, vol. 27, issue 3, 1-35
Abstract:
Abstract 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.
Keywords: Time series; Change-point; Score vector; Gaussian likelihood ratio; Mixing processes; 62F03; 62G10; 62F10; 62M10; 60G10; 60F17 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10185-3
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