search for


Monitoring anomaly for time series of volatility index (VIX)
Journal of the Korean Data & Information Science Society 2022;33:1153-61
Published online November 30, 2022;
© 2022 Korean Data and Information Science Society.

Min Jo Kim1 · Sangyeol Lee2

1 NH Investment & Securities Co., LTD
2 Department of Statistics, Seoul National University
Correspondence to: This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (No. 2021R1A2C1004009).
1 Deputy General Manager, NH Investment & Securities Co., LTD. Yeoui-daero Yeongdeungpo-gu, Seoul 07335, South Korea.
2 Corresponding author, Professor, Department of Statistics, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea. E-mail:
Received October 11, 2022; Revised October 26, 2022; Accepted October 27, 2022.
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.
This study investigates a monitoring procedure that aims to capture a change of model parameters in time series regarding the volatility index (VIX). To solve this problem, we harness a cumulative sum (CUSUM) process using residuals designed to simultaneously detect changes in both the conditional mean and variance of the time series. To obtain the control limits, limit theorems are used for the CUSUM monitoring process. Thereafter, the scheme of statistical process control (SPC) is applied to the time series of the log-returns of VIX by fitting it with an ARMA-GARCH model to obtain further knowledge regarding the financial market’s participants. Our study indicates the proposed monitoring process’ potential as a tool to allude to imminent significant market crashes.
Keywords : Monitoring parameter change, residual-based CUSUM monitoring, risk management, statistical process control, volatility index