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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.

得到了随机停止的独立正态分布随机变量序列的截尾停止时间的期望值和样本均值的渐近展开式。该结果可用于获得用于检测均值变化的累积检验的统计特性，例如误差概率和预期样本量。该结果可用于估计在拒绝了无平均变化的零假设之后发生变化的时间。我们还将累积检验应用于Gamma-Normal混合模型的均值变化的检测，该模型适用于尾部比正态分布更重的数据。最近对金融时间序列的实证研究表明，潜在分布往往具有更大的峰度。我们还应用该方法得到了类似的检测方差变化的序贯过程，因为在实际应用中，方差可能更重要。作为第一步，我们使用布朗运动近似来获得概率。我们现在正致力于通过使用(非线性)更新理论来获得更准确的结果，利用该理论，我们将评估边界上过剩的渐近分布。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程度上令人满意的结果。但对于时间序列数据的研究才刚刚起步，还没有取得令人满意的结果。虽然在方差变化的检测方面已经取得了一些成果，但我们离最终的目标还有很长的路要走。