Clipped self-normalized Max-CUSUM for sparse mean breaks in high-dimensional heavy-tailed locally stationary time series

Document Type : Original Scientific Paper

Author

Imam Reza International University‎, ‎Mashhad‎, ‎Iran

10.22034/jsmta.2026.24764.1222

Abstract

We develop a robust procedure for detecting and locating a single sparse mean break in high-dimensional‎, ‎locally stationary time series with heavy-tailed innovations and intermittent contamination‎. ‎The method combines coordinatewise clipping‎, ‎local self-normalization‎, ‎and a maximum cumulative sum scan‎. ‎In contrast with an oracle calibration‎, ‎the proposed implementation uses a locally centered block-multiplier bootstrap‎, ‎so it does not require a known covariance structure‎. ‎We establish negligible clipping bias under finite moments‎, ‎a Gaussian approximation for the scan statistic‎, ‎bootstrap validity under the null‎, ‎a sparse detection condition‎, ‎and a localization rate‎. ‎The theory is accompanied by sufficient conditions for time-varying linear and nonlinear filters‎. ‎A fully specified Monte Carlo study uses 250 replications per main design‎, ‎reports Wilson confidence intervals and Monte Carlo standard errors‎, ‎compares oracle and data-driven calibration‎, ‎and examines sensitivity to clipping‎, ‎window‎, ‎ridge‎, ‎scanning‎, ‎dimension‎, ‎and sparsity‎. ‎The proposed method is competitive with raw max scanning in clean settings and is particularly advantageous for sparse breaks under heavy tails and contamination; dense ℓ2 aggregation need not be dominated in clean‎, ‎dense-signal regimes.

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References

Bai, Q., Ling, S. and Zhu, K. (2025). Testing and estimation of change point in ARMA model with heavy-tailed G-GARCH noises. Journal of Time Series Analysis. doi: 10.1111/jtsa.70039.
Cao, Z., Seeuws, N., De Vos, M. and Bertrand, A. (2024). Change point detection in multi-channel time series via a time-invariant representation. IEEE Transactions on Knowledge and Data Engineering, 36(12):7743–7756.
Catoni, O. (2012). Challenging the empirical mean and empirical variance: A deviation study. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 48(4):1148–1185.
Chernozhukov, V., Chetverikov, D. and Kato, K. (2013). Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors. The Annals of Statistics, 41(6):2786–2819.
Cho, H. and Fryzlewicz, P. (2015). Multiple-change-point detection for high dimensional time series via sparsified binary segmentation. Journal of the Royal Statistical Society: Series B, 77(2):475–507.
Cho, H. and Fryzlewicz, P. (2023). Multiple change point detection under serial dependence: Wild contrast maximisation and gappy Schwarz algorithm. Journal of Time Series Analysis, 45(3):479–494.
Corradin, R., Danese, L. and Ongaro, A. (2022). Bayesian nonparametric change point detection for multivariate time series with missing observations. International Journal of Approximate Reasoning, 143:26–43.
Csörgő, M. and Horváth, L. (1997). Limit Theorems in Change-Point Analysis. Wiley.
Dahlhaus, R. (1997). Fitting time series models to nonstationary processes. The Annals of Statistics, 25(1):1–37.
Dehling, H., Fried, R. and Wendler, M. (2020). A robust method for shift detection in time series. Biometrika, 107(3):647–660.
Diop, M.L. and Kengne, W. (2022a). A general procedure for change-point detection in multivariate time series. TEST, 32(1):1–33.
Diop, M.L. and Kengne, W. (2022b). Epidemic change-point detection in general causal time series. Statistics & Probability Letters, 184:109416.
Gösmann, J., Stoehr, C., Heiny, J. and Dette, H. (2022). Sequential change point detection in high dimensional time series. Electronic Journal of Statistics, 16(1):3608–3671.
Guo, L. and Modarres, R. (2020). Nonparametric change point detection for periodic time series. Canadian Journal of Statistics, 48(3):518–534.
Gupta, M., Wadhvani, R. and Rasool, A. (2024). Comprehensive analysis of change-point dynamics detection in time series data: A review. Expert Systems with Applications, 248:123342.
He, Y., Kong, X., Trapani, L. and Yu, L. (2024). Online change-point detection for matrix-valued time series with latent two-way factor structure. The Annals of Statistics, 52(4):1646–1670.
Huber, P.J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1):73–101.
Kojadinovic, I. and Verdier, G. (2021). Nonparametric sequential change-point detection for multivariate time series based on empirical distribution functions. Electronic Journal of Statistics, 15(1):773–829.
Lee, S., Lee, S. and Moon, M. (2020). Hybrid change point detection for time series via support vector regression and CUSUM method. Applied Soft Computing, 89:106101.
Leyli-Abadi, M., Samé, A., Oukhellou, L., Cheifetz, N., Mandel, P., Féliers, C. and Heim, V. (2021). Online common change-point detection in a set of nonstationary categorical time series. Neurocomputing, 439:176–196.
Liu, B., Zhou, C., Zhang, X. and Liu, Y. (2020). A unified data-adaptive framework for high dimensional change point detection. Journal of the Royal Statistical Society Series B: Statistical Methodology, 82(4):933–963.
Ma, R. and Zhang, S. (2024). Multiplier subsample bootstrap for statistics of time series. Journal of Statistical Planning and Inference, 233:106183.
Tickle, S.O., Eckley, I.A. and Fearnhead, P. (2021). A computationally efficient, high-dimensional multiple changepoint procedure with application to global terrorism incidence. Journal of the Royal Statistical Society Series A: Statistics in Society, 184(4):1303–1325.
Wang, T. and Samworth, R.J. (2018). High dimensional change point estimation via sparse projection. Journal of the Royal Statistical Society: Series B, 80(1):57–83.
Wegner, L. and Wendler, M. (2024). Robust change-point detection for functional time series based on U-statistics and dependent wild bootstrap. Statistical Papers, 65(7):4767–4810.
Wu, W.B. (2005). Nonlinear system theory: Another look at dependence. Proceedings of the National Academy of Sciences, 102(40):14150–14154.
Yu, M. and Chen, X. (2020). Finite sample change point inference and identification for high-dimensional mean vectors. Journal of the Royal Statistical Society Series B: Statistical Methodology, 83(2):247–270.
Zhang, D. and Wu, W.B. (2017). Gaussian approximation for high dimensional time series. The Annals of Statistics, 45(5):1895–1919.
Zhang, X. and Chan, K.S. (2025). Spectral change point estimation for high-dimensional time series by sparse tensor decomposition. Journal of the Royal Statistical Society Series B: Statistical Methodology, 88(2):677–696.
Journal of Statistical Modelling: Theory and Applications
Volume 7, Issue 1
January 2026
Pages 113-127

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History

  • Receive Date: 16 June 2026
  • Revise Date: 05 August 2026
  • Accept Date: 25 September 2026
  • First Publish Date: 04 October 2026
  • Publish Date: 05 October 2026

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