随着数据时代的到来，基于高斯序列的检测方法已有局限，许多时间序列数据呈现厚尾和尖峰特征，需要探索更加鲁棒、高效的变点检验方法。尤其是在金融和经济数据中，现有方法基于弱相依性和条件异方差假设，未能考虑时变方差的影响。因此，时变方差波动下的相依序列的结构变点检测很有意义，选取最小绝对离差估计（LAD）方法，研究结构变点的线下检测和在线监测，具体内容如下：

在时变方差模型下，使用LAD估计的比值型统计量来检测均值变点。该统计量通过对数据减去样本中位数后的差值进行计算，消除了方差波动对统计量的影响，因此无需估计时变方差函数。在理论分析中，在原假设下证明了统计量渐近服从维纳过程的泛函，在备择假设下证明了该方法的一致性。在数值模拟中，验证了该统计量的临界值不受时变方差影响，其经验水平和经验功效均表现良好。基于LAD估计的比值型统计量相比Wild Bootstrap检验方法能够有效控制异常值的影响，提高变点检测的准确性。在实证分析中，基于一组股票数据和一组水文数据，验证了所提方法的有效性与实用价值。

数据规模的持续扩大使得传统线下变点检测方法面临挑战，尤其是在处理动态和实时数据时，线下检测方法无法及时反馈数据结构的变化。因此，针对实时变化数据的在线变点监测研究很有必要。在理论分析中，将线下变点的统计量与滑动窗口和带宽参数相结合，能够实时监测数据中的变点。在原假设下证明了统计量的渐近分布，在备择假设下证明该方法的相合性。在数值模拟中，验证了变点位置和样本容量对监测效果的影响，结果表明该方法在厚尾情形下更具鲁棒性，并且具有较短的平均运行长度，表现出较强的实时监测能力。在实证分析中，基于两组金融数据，验证了所提方法的有效性与实用价值。

With the advent of the era of big data, detection methods based on Gaussian sequences have limitations. Many time series data show thick tails and peak characteristics, and it is necessary to explore more robust and efficient change point detection methods. Especially in financial and economic data, existing methods are based on weak dependence and conditional heteroskedasticity assumptions and fail to consider the impact of time-varying variance. Therefore, it is very meaningful to detect structural change points in dependent sequences under time-varying variance fluctuations. The Least Absolute Deviations Estimation method, which is robust in thick-tailed sequences, is selected to study the offline detection and online monitoring of structural change points. The specific contents are as follows:

Under the time-varying variance model, the ratio statistic of LAD estimation is used to detect mean change points. The statistic is calculated by subtracting the sample median from the data, eliminating the effect of variance instability on the statistic, so there is no need to estimate the time-varying variance function. Under the null hypothesis, it is proved that the statistic asymptotically obeys the functional of the Wiener process and is consistent under the alternative hypothesis. Through numerical simulation, it is verified that the critical value of the statistic is not affected by the time-varying variance, and its size and power are both good. In addition, for data with fat-tailed distribution, the ratio statistic based on LAD estimation can effectively control the influence of outliers and improve the accuracy of change point detection compared with the Wild Bootstrap test method. Finally, based on a set of stock data and a set of hydrological data, the effectiveness and practical value of the proposed method are verified through empirical research.

With the continuous increase in the amount of data, offline change point detection methods face severe challenges, especially when dealing with dynamic and real-time data, offline detection methods cannot timely feedback the changes in data structure. Therefore, it is necessary to study online change point monitoring for real-time changing data. Combining the statistics of offline change points with sliding windows and bandwidth parameters can monitor the change points in data in real time. Under the null hypothesis, the limiting distribution of the statistics and the consistency under the alternative hypothesis are proved. Secondly, numerical simulation verifies the influence of change point location and sample size on the monitoring effect. The results show that the method is more robust in the case of fat tails and has a shorter average run length, showing a strong real-time monitoring ability. Finally, based on two sets of financial data, the effectiveness and practical value of the proposed method are verified through empirical research.

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