Test and Estimation for the Structual Change in Econometric Model

得到了独立正态分布随机变量序列的截尾停时和样本均值的期望值的渐近展开式。这些结果可用于获得用于检测均值变化的累积和检验的统计特性，例如错误概率和预期样本量。结果可用于估计在拒绝无均值变化的零假设后发生变化的时间。我们还应用了累积和检验的均值变化的伽玛-正态混合模型，这是适合于较重的尾部比正态分布的数据检测。而最近的金融时间序列的实证研究表明，潜在的分布往往有较大的峰度。我们还应用该方法得到了类似的检测方差变化的顺序过程，因为方差在实际中可能更重要。作为第一步，我们使用布朗运动近似来获得概率。我们现在正在努力得到更准确的结果，通过使用（非线性）更新理论，我们将评估超过边界的渐近分布。我们相信，对于独立随机变量序列的均值变化的检测，我们已经获得了某种令人满意的结果。但对于时间序列数据的案例研究才刚刚开始，还没有得到任何结果。虽然在方差变化的检测方面取得了一些成果，但离最终目标还有很长的路要走。

We obtained the asymptotic expansions of the expected values of the truncated stopping time and the sample mean of the randomly stopped sequence of independent normally distributed random variables. The results may be applied to obtain the statistical characteristics of the Cusum test for detecting the mean changes, such as error probabilities and the expected sample sizes. The results may be used to estimate the time at which the change occurs after having rejected the null hypothesis of no mean changes. We also applied the Cusum test for the detection of the mean change to the Gamma-mormal mixture model which is suitable for the data with heavier tail than that of the normal distribution. And recent empirical studies of the Financial Time Series show that the underlying distribution tends to have bigger kurtosis. We also applied the method to obtain the similar sequential procedure for detecting the variance change, for the variance may be more important in practice. We used Brownian motion approximation to obtain the probabilities as a first step. We are now working to get the more accurate results by using the (nonlinear) renewal theory with which we will evaluate the asymptotic distribution of the excess over the boundaries. We believe that we have obtained somehow satisfactory results for the detection of the mean change of the sequence of the independent random variables. But the case for the time series data is just started and have not got any satisfactoryresults yet. Although some results concerning the detection of the change of variance was obtained, we are still long way up to the final goal.