Online monitoring of process variance drifts for leptokurtic and heavy‐tailed data

Abstract

AbstractIn many applications, monitoring the variance of a process online is very important. For example, in industrial and medical fields and weather and ocean research, monitoring the variance drift in processes can effectively reduce losses. This monitoring is especially important in finance because data tend to have leptokurtic and heavy‐tailed characteristics and there are few control charts for the online monitoring of variance drifts. Therefore, we develop a new exponentially weighted moving average control chart based on the sample quantiles of all pairwise differences: the EWMA control chart. This control chart shows a good performance in the online monitoring of variance drifts when the distribution is leptokurtic and heavy‐tailed, as is the case with the Student's t‐distribution, the Pareto distribution, and the generalized error distribution. To visually explain the EWMA control chart for monitoring the effect of variance drifts, we compare the monitoring efficiency of the EWMA control chart with that of two other control charts (the MDEWMA control chart and the GVA control chart) using Monte Carlo simulations and the RMI. The results show that the EWMA control chart is the most effective for monitoring the variance drifts of data with leptokurtic and heavy‐tailed distributions. Additionally, we use these three control charts to monitor the variance drifts of the weekly return rate of gold (data from Yahoo Finance) to illustrate the application of the EWMA control chart in practical cases.