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Testing a Class of Piece-Wise CHARN Models with Application to Change-Point Study

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  • Youssef Salman

    (Mines Saint-Etienne, CNRS, UMR 6158 LIMOS, Institut Henri Fayol, University Clermont Auvergne, 42023 Saint-Etienne, France
    Department of Applied Mathematics, Faculty of Sciences, Lebanese University, Beirut 2038 1003, Lebanon
    These authors contributed equally to this work.)

  • Joseph Ngatchou-Wandji

    (EHESP Rennes and Institut Élie Cartan de Lorraine, CEDEX, 54506 Vandoeuvre-lès-Nancy, France
    These authors contributed equally to this work.)

  • Zaher Khraibani

    (Department of Applied Mathematics, Faculty of Sciences, Lebanese University, Beirut 2038 1003, Lebanon)

Abstract

We study a likelihood ratio test for testing the conditional mean of a class of piece-wise stationary CHARN models. We establish the locally asymptotically normal (LAN) structure of the family of likelihoods under study. We prove that the test is asymptotically optimal, and we give an explicit form of its asymptotic local power. We describe an algorithm for detecting change points and estimating their locations. The estimates are obtained as time indices, maximizing the estimate of the local power. The simulation study we conduct shows the good performance of our method on the examples considered. This method is also applied to a set of financial data.

Suggested Citation

  • Youssef Salman & Joseph Ngatchou-Wandji & Zaher Khraibani, 2024. "Testing a Class of Piece-Wise CHARN Models with Application to Change-Point Study," Mathematics, MDPI, vol. 12(13), pages 1-40, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2092-:d:1428441
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    References listed on IDEAS

    as
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    2. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    3. Ruggieri, Eric & Antonellis, Marcus, 2016. "An exact approach to Bayesian sequential change point detection," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 71-86.
    4. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    5. Vogelsang, Timothy J., 1997. "Wald-Type Tests for Detecting Breaks in the Trend Function of a Dynamic Time Series," Econometric Theory, Cambridge University Press, vol. 13(6), pages 818-848, December.
    6. Richard A. Davis & Thomas C. M. Lee & Gabriel A. Rodriguez‐Yam, 2008. "Break Detection for a Class of Nonlinear Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 834-867, September.
    7. Chen, Kuo-mei & Cohen, Arthur & Sackrowitz, Harold, 2011. "Consistent multiple testing for change points," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1339-1343, November.
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