Test and Estimation for the Structual Change in Econometric Model

计量经济模型结构变化的检验与估计

基本信息

批准号：
01530013
负责人：
TAKAHASHI Hajime
金额：
$ 1.09万
依托单位：
Hitotsubashi University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1989
资助国家：
日本
起止时间：
1989 至 1990
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-01530013/
关键词：
Structual change Sequential analysis Renewal theory Cusum test RENEWAL THEORY

项目摘要

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.

我们获得了截短的停止时间的预期值的渐近膨胀，以及独立正态分布随机变量的随机停止序列的样本均值。结果可以应用于获得Cusum测试的统计特征，以检测平均变化，例如误差概率和预期的样本量。结果可用于估计拒绝无均值变化的无效假设后发生变化的时间。我们还应用了Cusum测试将平均变化的检测到伽马正态分混合模型，该模型适用于比正态分布更重的数据。财务时间序列的最新经验研究表明，潜在的分布往往具有更大的峰度。我们还应用了该方法来获得类似的顺序程序来检测方差变化，因为在实践中，方差可能更重要。我们使用布朗运动近似作为第一步获得概率。我们现在正在努力通过使用（非线性）更新理论来获得更准确的结果，我们将通过这些理论评估过度界限的渐近分布。我们认为，我们以某种方式获得了独立随机变量序列的平均变化的令人满意的结果。但是，时间序列数据的情况才刚刚开始，尚未获得任何满意度。尽管获得了有关检测变化变化的一些结果，但我们仍然远至最终目标。