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Monitoring procedure for parameter change in causal time series

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  • Bardet, Jean-Marc
  • Kengne, William

Abstract

We propose a new sequential procedure to detect change in the parameters of a process X=(Xt)t∈Z belonging to a large class of causal models (such as AR(∞), ARCH(∞), TARCH(∞), or ARMA–GARCH processes). The procedure is based on a difference between the historical parameter estimator and the updated parameter estimator, where both these estimators are quasi-likelihood estimators. Unlike classical recursive fluctuation test, the updated estimator is computed without the historical observations. The asymptotic behavior of the test is studied and the consistency in power as well as an upper bound of the detection delay is obtained. Some simulation results are reported with comparisons to some other existing procedures exhibiting the accuracy of our new procedure. This procedure coupled with retrospective tests is applied to solve off-line multiple breaks detection in the daily closing values of the FTSE 100 stock index.

Suggested Citation

  • Bardet, Jean-Marc & Kengne, William, 2014. "Monitoring procedure for parameter change in causal time series," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 204-221.
    • Handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:204-221
    DOI: 10.1016/j.jmva.2013.12.004
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    Cited by:

    1. Kengne, William, 2021. "Strongly consistent model selection for general causal time series," Statistics & Probability Letters, Elsevier, vol. 171(C).
    2. Mamadou Lamine Diop & William Kengne, 2022. "Poisson QMLE for change-point detection in general integer-valued time series models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 373-403, April.
    3. William Kengne & Isidore S. Ngongo, 2022. "Inference for nonstationary time series of counts with application to change-point problems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 801-835, August.
    4. KUROZUMI, Eiji & 黒住, 英司, 2016. "Monitoring Parameter Constancy with Endogenous Regressors," Discussion Papers 2016-01, Graduate School of Economics, Hitotsubashi University.
    5. Joseph Ngatchou-Wandji & Echarif Elharfaoui & Michel Harel, 2022. "On change-points tests based on two-samples U-Statistics for weakly dependent observations," Statistical Papers, Springer, vol. 63(1), pages 287-316, February.
    6. Mohamed Salah Eddine Arrouch & Echarif Elharfaoui & Joseph Ngatchou-Wandji, 2023. "Change-Point Detection in the Volatility of Conditional Heteroscedastic Autoregressive Nonlinear Models," Mathematics, MDPI, vol. 11(18), pages 1-31, September.
    7. Pierre Perron & Eduardo Zorita & Eiji Kurozumi, 2017. "Monitoring Parameter Constancy with Endogenous Regressors," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(5), pages 791-805, September.

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