Detecting Changes in the Mean of an Integration and Fractionally Integrated MA Process on Double Modified EWMA Control Chart - Neammai, Julalak; Areepong, Yupaporn; Sukparungsee, Saowanit (Applied Science and Engineering Progress, 2026)
Stock market behavior is inherently volatile and sensitive to external influences, making effective monitoring tools essential for detecting shifts in financial time series. This study proposes a Double Modified Exponentially Weighted Moving Average (DMEWMA) control chart designed to improve the detection of small mean shifts in autocorrelated stock data modeled by Integrated Moving Average (IMA) and Fractionally Integrated Moving Average (FIMA) processes with exponential white noise. The Average Run Length (ARL) performance of the proposed chart is analytically derived using both an exact formula based on Fredholm integral equations and a Numerical Integral Equation (NIE) technique. The simulations confirm the accuracy of the analytical results. Comparative analysis demonstrates that the DMEWMA chart outperforms the Modified EWMA (MEWMA) chart across various shift magnitudes, exhibiting lower ARL₁, Relative Median Index (RMI), and Average Expected Quadratic Loss (AEQL) values. Real-world applications using Thai stock data further validate the practical utility of the proposed method, highlighting its superior sensitivity in detecting subtle process changes.