The effect of parameter estimation on Phase II control chart performance in monitoring financial GARCH processes with contaminated data

The application of control charts for monitoring financial processes has received a greater focus after recent global crisis. The Generelized AutoRegressive Conditional Heteroskedasticity (GARCH) time series model is widely applied for modelling financial processes. Therefore, traditional Shewhart control chart is developed to monitor GARCH processes. There are some difficulties in financial surveillance especially in the retrospective phase one of which being the posibility of existing outliers in the samples data. For this aim, in this paper some methods were proposed to estimate the parameters of the GARCH model based on maximum likelihood and robust estimation procedures. Then, the performance of Phase II residual Shewhart control chart with estimated parameters was evaluated according to in-control Average Run Length in the presence of outliers. The Monte Carlo simulation study was applied to evaluate the proposed methods considering different numerical examples. Finally, the US Dollar/Iran Rial (USD/IRR) exchange rate was considered for monitoring in which the results showed that the control chart was more sensitive when the robust methods were applied in the estimation procedure.