本文介紹一種快速且準確的變點估計方法，在傳統的金融實務上，主要方法通常僅依賴於每日收盤價來偵測結構變化的變點。在本研究中，考慮最高或最低價格的目的是提高參數估計的精確度，從而提高財務分析中識別變點的準確性。假設日內價格遵循幾何布朗運動，我們通過考慮收盤價和最高價，以及收盤價和最低價來提出變點模型。將輪廓似然應用於所提出的模型，我們使用最大似然估計（MLE）來估計參數和變點。通過模擬研究和對標準普爾500指數的實證分析，驗證了該方法的性能，分析的數據涵蓋了三個不同時期：2008年金融危機、2020年新冠疫情以及2022年俄羅斯入侵烏克蘭。此外，我們還分析了比特幣美元在2020年新冠疫情和2022年俄羅斯入侵烏克蘭的表現。;This paper introduces an approach for the rapid and accurate estimation for change-points. Within conventional finance practices, the predominant methodologies typically rely solely on daily closing prices for detecting change-points for structure change. In this study, the consideration of the highest or lowest prices aims to augment the precision of estimation with respect to parameters, consequently enhancing the accuracy of identifying change-points in financial analysis. Assuming that intra-daily price adheres to geometric Brownian motion, we propose change-point models by considering the closing price and the highest price, as well as the closing price and the lowest price. Applying the profile likelihood to the proposed model, we employ maximum likelihood estimation (MLE) to estimate parameters and the change-point. The performance of the methodology is verified by simulation studies and empirical analysis of the S&P 500 across three distinct periods: the 2008 financial crisis, the COVID-19 pandemic in 2020, and the Russian invasion of Ukraine in 2022. Furthermore, we analyze the performance of Bitcoin USD during the COVID-19 pandemic of 2020 and the Russian invasion of Ukraine in 2022.
