傳統的統計製程管制(Statistical Process Control, SPC)方法，如CUSUM或EWMA管制圖，早期多應用於工業製造領域，近年來已逐漸擴展至生醫、資訊、氣候與金融等非工業領域。本研究旨在將管制圖應用於股價變動異常監控，以提供金融市場中更具統計基礎之監測工具。然而現有應用於金融資料之管制圖多建立在常態分配假設下，但股價波動資料通常具有厚尾與高狹峰特性，使傳統方法容易產生誤警，或低估極端風險；此外，傳統管制圖多著重於平均數或變異數之偏移偵測，較難掌握由尾部風險變動所引起之整體分配型態改變。為克服上述限制，本研究基於Kullback-Leibler資訊理論(KLI)建構半柯西分配管制圖，用以監測股價變動之異常。本文所定義之股價變動，是指相鄰兩交易日收盤價差之絕對值，並進一步加以標準化。於方法上，本研究以KLI作為檢定統計量，以衡量當前觀測資料分配與在管制狀態下理論分配之差異程度，使其對整體分配型態變化具有較高敏感性。研究中並推導半柯西分配下之KLI統計量，探討最大概似估計法(MLE)與百分位距法(Interpercentile Range, IPR)在尺度參數估計上之應用，並利用KLI統計量近似服從卡方分配之性質建立管制界限。最後，本研究將所建構之管制圖應用於實際股價資料，並與既有方法進行比較，以評估其在股價異常監控上的適用性與偵測效能。期望本研究所發展之方法能提供一套較穩健且具即時性的股價異常監控工具，作為金融風險管理之決策輔助依據。

Conventional statistical process control (SPC) methods, such as CUSUM and EWMA control charts, were originally developed for industrial manufacturing applications. In recent years, their applications have gradually expanded to non-industrial fields, including healthcare, information systems, meteorology, and finance. This study applies a control chart to the monitoring of anomalous stock price fluctuations in order to provide a more statistically grounded monitoring tool for financial markets. However, existing control charts for financial data are commonly constructed under normality assumptions, whereas actual stock price fluctuations often exhibit heavy- tailed and leptokurtic characteristics. As a result, conventional methods may generate false alarms or underestimate extreme risks. In addition, traditional control charts mainly focus on shifts in the mean or variance and may not adequately capture changes in the overall distribution caused by tail risk. Accordingly, this study develops a Half-Cauchy distribution-based control chart using Kullback–Leibler information (KLI) to monitor anomalous stock price fluctuations. The monitored variable is defined as the absolute percentage change between the clos- ing prices of two consecutive trading days. The proposed KLI statistic measures the discrepancy between the distribution of observed data and the in-control distribution, thereby increasing sensitivity to changes in the overall distributional pattern. This study further investigates the application of maximum likelihood estimation (MLE) and the interpercentile range (IPR) estimator for scale-parameter estimation under the Half-Cauchy distribution and establishes control limits using the chi-square approximation of the KLI statistic. Finally, the proposed control chart is applied to actual stock price data and compared with existing methods to evaluate its applicability and detection performance in monitoring stock price anomalies. The proposed method is expected to provide a robust and timely monitoring tool to support financial risk management and decision making.

劉乙力. (2025). 應用具有快速初始反應機制之指數Kullback-Leibler 資訊管制圖監控分散式阻斷服務攻擊. 國立成功大學
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