近四十年来，变点问题在统计学领域一直是研究的热点问题之一。若忽略结构变点的影响，则会导致不准确的预测和错误的统计分析，故在建立模型之前有效地检验结构变点就显得尤为必要。研究发现：一方面许多金融时序数据不是简单的服从某个独立的分布，序列之间往往存在着一定的相依性；另一方面均值作为金融数据的重要数值特征，能很好地刻画时间序列的水平变化。因此，本文围绕相依序列均值变点检验问题展开研究，具体内容如下：
       相较于经典的累积和统计量，采用比值检验统计量研究了相依序列均值变点的检验问题。在均值变点模型中，理论上证明了比值统计量在原假设下的极限分布是一个标准布朗运动的泛函，并在备择假设下证明了该统计量的一致性。数值模拟结果表明：经验水平值在检验显著性水平附近波动；经验势函数值随着样本容量和均值变化幅度的增加而增加，且均值变点位置在样本中间的经验势函数值会显著高于均值变点位置在样本两端的经验势函数值。
       鉴于许多金融数据具有非平稳的波动性，讨论了异方差情形下相依序列均值变点的检验问题。基于广义的中心极限定理，分别推导了异方差情形下比值统计量在原假设和备择假设下的极限分布。原假设下的渐近分布不再是标准布朗运动的泛函，而是取决于方差函数的具体表达形式。研究发现异方差下的经验水平值会出现严重的扭曲现象，不再逼近检验显著性水平。针对此缺陷，本文提出了修正的比值检验统计量以实现异方差下均值变点的有效检验。数值模拟结果表明：修正的比值检验统计量能很好的改善了经验水平值扭曲和经验势函数值损失的现象。
       最后，选取了上海浦东开发银行股票价格和尼罗河最低水位两组时序数据进行实证分析。结果显示：本文所提出的修正比值检验方法是有效且可行的。基于比值统计量研究时变波动情形下的均值变点在计量经济领域具有重要的理论意义和应用价值。
 

      For the past four decades, the problem of change point has been one of the hot issues in the field of statistical research. Ignoring the influence of structural changes will lead to inaccurate predictions and incorrect statistical analysis, so it is especially necessary to effectively test structural changes before building a model. The study found that: on the one hand, many financial time series data do not simply obey an independent distribution, and there are often certain dependencies between sequences; on the other hand, the mean value, as an important numerical feature of financial data, can well describe the level change of the time series. Therefore, this article mainly focuses on the test of the change point of the mean change point of the dependent sequence. The specific research content is as follows:
       Compared with the classical cumulative sum statistics, the ratio test statistic is used to study the test of the change point of the mean of the dependent series. In the mean change point model, it is theoretically proved that the limit distribution of the ratio statistic under the null hypothesis is a functional of the standard Brownian motion, and the consistency of the statistic is proved under the alternative hypothesis. Numerical simulation results show that the empirical size fluctuates around the testing significant level; the empirical potential power increases with the increase of sample size and the jump size of the mean change; the empirical potential power of the mean change point in the middle of the sample is significantly higher than the value of the empirical potential power at the previous and later periods of the mean change point.
       In view of the fact that many financial data have non-stationary volatility, the problem of testing the mean change points of dependent series in the case of heteroscedasticity is discussed. Based on the generalized central limit theorem, the limit distributions of the ratio statistic in the case of heteroscedasticity under the null hypothesis and the alternative hypothesis are deduced respectively. The asymptotic distribution under the null hypothesis is no longer a functional of the standard Brownian motion, but depends on the specific expression of the variance function. The study found that the empirical size under heteroscedasticity will be severely distorted, and the testing significant level is no longer approached. In response to this defect, this article proposes a modified ratio test statistic to achieve an effective test of the mean change point under heteroscedasticity. Numerical simulation results show that the modified ratio test statistics can improve the distortion of empirical size and the loss of empirical potential power.
        Finally, two sets of time series data of Shanghai Pudong Development Bank stock price and the lowest water level of the Nile River are selected for empirical analysis. The results show that the modified ratio test method proposed in this article is effective and feasible. The study of the mean change point under time-varying fluctuations based on ratio statistics has important theoretical significance and application value in the field of econometrics.
 

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