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Article

Multiscale Change Point Detection for Univariate Time Series Data with Missing Value

by
Tariku Tesfaye Haile
1,2,*,
Fenglin Tian
1,
Ghada AlNemer
3 and
Boping Tian
1,*
1
School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2
Department of Statistics, College of Natural and Computational Sciences, Arba Minch University, Arba Minch P.O. Box 21, Ethiopia
3
Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Mathematics 2024, 12(20), 3189; https://doi.org/10.3390/math12203189
Submission received: 21 August 2024 / Revised: 3 October 2024 / Accepted: 10 October 2024 / Published: 11 October 2024
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Abstract

This paper studies the autoregressive integrated moving average (ARIMA) state space model combined with Kalman smoothing to impute missing values in a univariate time series before detecting change points. We estimate a scale-dependent time-average variance constant that depends on the length of the data section and is robust to mean shifts under serial dependence. The consistency of the proposed estimator is shown under the assumption allowing heavy tailedness. Integrating the proposed estimator with the moving sum and wild binary segmentation procedures to determine the number and locations of change points is discussed. Furthermore, the performance of the proposed methods is evaluated through extensive simulation studies and applied to the Beijing multi-site air quality dataset to impute missing values and detect mean changes in the data.
Keywords: ARIMA; Kalman smoothing; time-average variance constant; robust estimation; moving sum; wild binary segmentation ARIMA; Kalman smoothing; time-average variance constant; robust estimation; moving sum; wild binary segmentation

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MDPI and ACS Style

Haile, T.T.; Tian, F.; AlNemer, G.; Tian, B. Multiscale Change Point Detection for Univariate Time Series Data with Missing Value. Mathematics 2024, 12, 3189. https://doi.org/10.3390/math12203189

AMA Style

Haile TT, Tian F, AlNemer G, Tian B. Multiscale Change Point Detection for Univariate Time Series Data with Missing Value. Mathematics. 2024; 12(20):3189. https://doi.org/10.3390/math12203189

Chicago/Turabian Style

Haile, Tariku Tesfaye, Fenglin Tian, Ghada AlNemer, and Boping Tian. 2024. "Multiscale Change Point Detection for Univariate Time Series Data with Missing Value" Mathematics 12, no. 20: 3189. https://doi.org/10.3390/math12203189

APA Style

Haile, T. T., Tian, F., AlNemer, G., & Tian, B. (2024). Multiscale Change Point Detection for Univariate Time Series Data with Missing Value. Mathematics, 12(20), 3189. https://doi.org/10.3390/math12203189

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