Stochastic Inequalities for the Run Length of the EWMA Chart for Long-Memory Processes

In this paper the properties of the modified EWMA control chart for detecting changes in the mean of an ARFIMA process are discussed. The central question is related to the false alarm probability and its behavior for different autocorrelation structures and parameters of the underlying process. It is shown under which conditions the false alarm probability of an ARFIMA(p,d,q) process is larger than that of the pure ARFIMA(0,d,0) process. Furthermore, it is shown that the false alarm probability for ARFIMA(0,d,0) and ARFIMA(1,d,1) is monotonic in d for common parameter values of the processes.