Capability of New Modified EWMA Control Chart for Integrated and Fractionally Integrated Time-Series: Application to US Stock Prices

Among various statistical process -control (SPC) methods, control charts are widely employed as essential instruments for monitoring and improving process quality. This study focuses on a new modified exponentially weighted moving-average (New Modified EWMA) control chart that enhances detection capability under integrated and fractionally integrated time-series processes. Special attention is given to the effect of symmetry on the chart structure and performance. The proposed chart preserves a symmetric monitoring configuration, in which the two-sided design ($\mathrm{LCL}>0$) establishes control limits that are equally spaced around the center line, enabling balanced detection of both upward and downward shifts. Conversely, the one-sided version ($\mathrm{LCL}=0$) introduces a deliberate asymmetry to increase sensitivity to upward mean shifts, which is particularly useful when downward deviations are physically implausible or less critical. The efficacy of the control chart utilizing both models is assessed through Average Run Length (ARL). Herein, the explicit formula of ARL is derived and compared to the ARL obtained from the Numerical Integral Equation (NIE) in terms of both accuracy and computational time. The accuracy of the analytical ARL expression is validated by its negligible percentage difference ($\%diff$) in comparison to the results derived using the NIE approach, and the display processing time not exceeding 3 s. To confirm the highest capability, the suggested method is compared to both the classic EWMA and the modified EWMA charts using evaluation metrics such as ARL and SDRL (standard deviation run length), as well as RMI (relative mean index) and PCI (performance comparison index). Since asset values are volatile due to positive and negative market influences, symmetry is crucial in financial monitoring. Thus, symmetric control-chart structures reduce directional bias and better portray financial market activity by balancing upward and downward movements. Finally, examination of US stock prices illustrates performance, employing a symmetrical two-sided control chart for the rapid detection of changes through the new modified EWMA, in contrast to standard EWMA and modified EWMA charts.