Analytical explicit formulas of average run length for long memory process with ARFIMA model on CUSUM control chart

• Main Authors: Wilasinee Peerajit, Yupaporn Areepong, Saowanit Sukparungsee
• Format: Article
• Language: English
• Published: Prince of Songkla University 2017-12-01
• Series: Songklanakarin Journal of Science and Technology (SJST)
• Subjects: ARFIMA(p; d; q) process; numerical integral equation (NIE) method; exponential white noise
• Online Access: http://rdo.psu.ac.th/sjstweb/journal/39-6/39-6-11.pdf

This paper proposes the explicit formulas for the derivation of exact formulas from Average Run Lengths (ARLs) using integral equation on CUSUM control chart when observations are long memory processes with exponential white noise. The authors compared efficiency in terms of the percentage of absolute difference to a similar method to verify the accuracy of the ARLs between the values obtained by the explicit formulas and numerical integral equation (NIE) method. The explicit formulas were based on Banach fixed point theorem which was used to guarantee the existence and uniqueness of the solution for ARFIMA(p,d,q). Results showed that the two methods are similar in good agreement with the percentage of absolute difference at less than 0.23%. Therefore, the explicit formulas are an efficient alternative for implementation in real applications because the computational CPU time for ARLs from the explicit formulas are 1 second preferable over the NIE method.