Monitoring long-memory air quality data using ARFIMA model

Statistical control chart is commonly used in the industry to help ensure stability of manufacturing process and it can also be used to monitor the environmental data, such as industrial waste or effluent of manufacturing process. However, control chart needs to be modified if the set of environmental data exhibits the property of long memory. In this paper, a control chart for autocorrelated data using autoregressive fractionally integrated moving-average (ARFIMA) model is proposed to monitor the long-memory air quality data. Finally, we use the air quality data of Taiwan as examples to compare the difference between ARFIMA and autoregressive integrated moving-average (ARIMA) models. The results show mat residual control charts using ARFIMA models are more appropriate than those using ARIMA models.