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Monitoring parameter change in time series models

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  • Gombay, Edit
  • Serban, Daniel

Abstract

Sequential tests that are generalizations of Page's CUSUM tests are proposed for detecting an abrupt change in any parameter, or in any collection of parameters of an autoregressive time series model. These tests accommodate nuisance parameters. They are based on large sample approximations to the efficient score vector under the null hypothesis of no change and under the alternative. The empirical power of the tests is evaluated in a simulation study. The new method performs better than the existing ones found in the literature if the criterion is the type I error probability, which can be unacceptably high for methods that minimize the expected value of the reaction time.

Suggested Citation

  • Gombay, Edit & Serban, Daniel, 2009. "Monitoring parameter change in time series models," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 715-725, April.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:4:p:715-725
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    References listed on IDEAS

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    1. Gombay, Edit & Horváth, Lajos, 1994. "An application of the maximum likelihood test to the change-point problem," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 161-171, March.
    2. Gombay, Edit, 2008. "Change detection in autoregressive time series," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 451-464, March.
    3. Alwan, Layth C & Roberts, Harry V, 1988. "Time-Series Modeling for Statistical Process Control," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 87-95, January.
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    Citations

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    Cited by:

    1. 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.
    2. Chen Fuqi & Nkurunziza Sévérien, 2014. "Constrained inference in multiple regression with structural changes," Statistics & Risk Modeling, De Gruyter, vol. 31(3-4), pages 237-257, December.
    3. Sven Knoth & Marianne Frisén, 2012. "Minimax optimality of CUSUM for an autoregressive model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(4), pages 357-379, November.
    4. Zhanshou Chen & Yanting Xiao & Fuxiao Li, 2021. "Monitoring memory parameter change-points in long-memory time series," Empirical Economics, Springer, vol. 60(5), pages 2365-2389, May.
    5. Christopher Dienes & Alexander Aue, 2014. "On-Line Monitoring Of Pollution Concentrations With Autoregressive Moving Average Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 239-261, May.
    6. Sévérien Nkurunziza & Pei Patrick Zhang, 2018. "Estimation and testing in generalized mean-reverting processes with change-point," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 191-215, April.
    7. Huh, Jaewon & Oh, Haejune & Lee, Sangyeol, 2017. "Monitoring parameter change for time series models with conditional heteroscedasticity," Economics Letters, Elsevier, vol. 152(C), pages 66-70.
    8. Li Zhaoyuan & Tian Maozai, 2017. "Detecting Change-Point via Saddlepoint Approximations," Journal of Systems Science and Information, De Gruyter, vol. 5(1), pages 48-73, February.
    9. Chen, Zhanshou & Tian, Zheng & Wei, Yuesong, 2010. "Monitoring change in persistence in linear time series," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1520-1527, October.
    10. 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.
    11. Zdeněk Hlávka & Marie Hušková & Claudia Kirch & Simos Meintanis, 2012. "Monitoring changes in the error distribution of autoregressive models based on Fourier methods," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 605-634, December.

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