Design and performance evaluation of U-statistics-driven control charts for process monitoring: an application to financial process analysis

A statistical process monitoring technique requires robust procedures to detect changes other than mean shifts, especially in skewed and heavy tailed financial process. In this paper, the authors develop U-statistic based control charts to deal with complex distributional shifts in monitoring process. Such technique can be useful due to the distribution free property of U-statistics together with their well-established asymptotic properties. Based on these, the following distribution sensitive monitoring statistics have been constructed through Gini coefficient, log scale variability, Theil’s entropy measure, and Atkinson’s indices. To examine their behaviors, a comprehensive Monte Carlo simulation has been carried out by considering four distributions; Gamma, Weibull, Lognormal and Uniform distributions. According to the outcomes of the simulation, it was found that many statistics follow the normality in terms of their behaviors in relation to the sample size. On the contrary, systematic deviations were also found in some cases; mainly Atkinson type indices and entropy-based statistics were found to show the deviation depending upon the high sensitivity parameter and heavy tailenders, respectively. These results will be used to construct the control limits and probability limits by simulations in non-normal distributions. According to this knowledge, Shewhart-type control chart based on U-statistics is developed for detecting various types of distributional changes. By comparing with each other, it has been concluded that all of these statistics give good results in this case. Further, an example is also provided through financial process data.