Detecting at‐Most‐m Changes in Linear Regression Models
提出一种基于残差加权和的新统计检验方法，用于检测时间依赖线性回归模型中至多m个变化点，并通过蒙特卡洛模拟验证其在中小样本下的有效性，应用于无条件四因子资本资产定价模型。
In this article, we provide a new procedure to test for at‐most‐ changes in the time‐dependent regression model , that is, β 1 = β 2 = ⋯ = β T under the no‐change null hypothesis against the alternative if and β ( j ) ≠ β ( ℓ ) for some with . Our procedure is based on weighted sums of the residuals, incorporating the possibility of changes. The weak limit of the proposed test statistic is the sum of two double‐exponential random variables. A small Monte Carlo simulation illustrates the applicability of the limit results in case of small and moderate sample sizes. We compare the new method to the cumulative sum control chart (CUSUM) and standardized (weighted) CUSUM procedures and obtain the power curves of the test statistics under the alternative. We apply our method to find changes in the unconditional four‐factor capital asset pricing model.