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Outlier detection for long memory processes
Journal of the Korean Data & Information Science Society 2021;32:1205-18
Published online November 30, 2021;
© 2021 Korean Data and Information Science Society.

Kyeongmin Lee1 · Changryong Baek2

1Department of Fintech, Sungkyunkwan University
12Department of Statistics, Sungkyunkwan University
Correspondence to: 1 Graduate student, Department of Statistics, Department of Fintech, Sungkyunkwan University, Seoul 03063, Korea.
2 Corresponding author: Professor, Department of Statistics, Sungkyunkwan University, Seoul 03023, Korea. E-mail:
This work was supported by the Basic Science Research Program from the National Research Foundation of Korea(NRF-2019R1F1A1057104).
Received September 17, 2021; Revised October 19, 2021; Accepted October 19, 2021.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Autoregressive moving average (ARMA) model is widely used to detect outliers in time series data. However, if the time series is known to have very strong correlations for large lags, also known as long memory, ARMA model is no longer suitable. This paper proposes outlier detection method based on heterogeneous autoregressive (HAR) model. Simulations study shows that our propose method performs well for long memory time series by producing larger test statistic. Our method is also illustrated to the realized volatility of S&P 500 index and electricity data.
Keywords : Heterogeneous autoregressive model, long memory, outliers, robust regression.