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Break Detection for a Class of Nonlinear Time Series Models

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  • Richard A. Davis
  • Thomas C. M. Lee
  • Gabriel A. Rodriguez‐Yam

Abstract

. This article considers the problem of detecting break points for a nonstationary time series. Specifically, the time series is assumed to follow a parametric nonlinear time‐series model in which the parameters may change values at fixed times. In this formulation, the number and locations of the break points are assumed unknown. The minimum description length (MDL) is used as a criterion for estimating the number of break points, the locations of break points and the parametric model in each segment. The best segmentation found by minimizing MDL is obtained using a genetic algorithm. The implementation of this approach is illustrated using generalized autoregressive conditionally heteroscedastic (GARCH) models, stochastic volatility models and generalized state‐space models as the parametric model for the segments. Empirical results show good performance of the estimates of the number of breaks and their locations for these various models.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:5:p:834-867
    DOI: 10.1111/j.1467-9892.2008.00585.x
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    Cited by:

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    2. Badagian Baharian, Ana Laura & Kaiser Remiro, Regina & Peña, Daniel, 2013. "The change-point problem and segmentation of processes with conditional heteroskedasticity," DES - Working Papers. Statistics and Econometrics. WS ws131718, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Cardinali Alessandro & Nason Guy P, 2011. "Costationarity of Locally Stationary Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 2(2), pages 1-35, January.
    4. Borzykh, Dmitriy & Khasykov, Mikhail, 2018. "The refinement procedure of ICSS algorithm for structural breaks detection in GARCH-models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 51, pages 126-139.
    5. Georges Dionne & Olfa Maalaoui Chun, 2013. "Default and liquidity regimes in the bond market during the 2002-2012 period," Canadian Journal of Economics, Canadian Economics Association, vol. 46(4), pages 1160-1195, November.
    6. Cho, Haeran & Fryzlewicz, Piotr, 2023. "Multiple change point detection under serial dependence: wild contrast maximisation and gappy Schwarz algorithm," LSE Research Online Documents on Economics 120085, London School of Economics and Political Science, LSE Library.
    7. 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.
    8. Christopher S. Withers & Saralees Nadarajah, 2016. "Cusums for tracking arbitrary functionals," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(3), pages 193-228, August.
    9. Xinyu Kang & Apratim Ganguly & Eric D. Kolaczyk, 2022. "Dynamic Networks with Multi-scale Temporal Structure," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 218-260, June.
    10. Kim, Moosup & Lee, Taewook & Noh, Jungsik & Baek, Changryong, 2014. "Quasi-maximum likelihood estimation for multiple volatility shifts," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 50-60.
    11. Chun Yip Yau & Zifeng Zhao, 2016. "Inference for multiple change points in time series via likelihood ratio scan statistics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 895-916, September.
    12. Davis, Richard A. & Hancock, Stacey A. & Yao, Yi-Ching, 2016. "On consistency of minimum description length model selection for piecewise autoregressions," Journal of Econometrics, Elsevier, vol. 194(2), pages 360-368.
    13. Stefan Richter & Weining Wang & Wei Biao Wu, 2023. "Testing for parameter change epochs in GARCH time series," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 467-491.
    14. Borzykh, Dmitriy & Yazykov, Artem, 2019. "The new KS method for a structural break detection in GARCH(1,1) models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 54, pages 90-104.
    15. Chun Yip Yau & Chong Man Tang & Thomas C. M. Lee, 2015. "Estimation of Multiple-Regime Threshold Autoregressive Models With Structural Breaks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1175-1186, September.
    16. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    17. Georges Dionne & Olfa Maalaoui Chun, 2013. "Presidential Address: Default and liquidity regimes in the bond market during the 2002–2012 period," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 46(4), pages 1160-1195, November.

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