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

Tariku Tesfaye Haile (), Fenglin Tian, Ghada AlNemer and Boping Tian ()
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Tariku Tesfaye Haile: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Fenglin Tian: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Ghada AlNemer: Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Boping Tian: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Mathematics, 2024, vol. 12, issue 20, 1-22

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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