Analysis of stationary ans non-stationary economic time series with structural changes

本文的主要研究成果如下：(1)提出了I(1)和I(0)模型在结构变化的时间序列回归中断点的估计方法。仿真结果表明，本文方法优于现有方法。(2)提出了ARCH（∞）模型中方差方程结构变化的CUSUM检验，并推导了检验的渐近分布。我们还通过模拟展示了我们的测试的性能，并将测试应用于日元/美元汇率。(3)通过对经济时间序列的结构变化分析，我们经常遇到看似跳跃而非结构变化的情况。所以我们吸引了跳跃扩散过程。我们采用Kou的跳跃扩散模型和Barndorff-Nielsen和Shepard检验无跳跃的零值。结果我们发现在许多股票价格过程中都有跳跃。(4)处理日本股票数据高频数据。并发现了数据在一天内的固有运动，如季节变化、跳跃等。我们采用标记点过程对这些数据进行建模。通过仿真研究，比较了几种模型的性能。(5)将小波分析应用于包括股票数据在内的经济数据，发现小波分析在经济时间序列分析中比参数模型分析更有效、更灵活。

Our main research results are as follows :(1)We proposed a method of estimating break points in a time series regression with structural changes for I(1) and I(0) model By simulation it is shown that our method is superior to the existing methods.(2)We proposed a CUSUM test for structural change in variance equation in ARCH(∞)model and derived the asymptotic distribution of the test. We also showed performance of our test by simulation and applied the test to Yen/Doller exchange rate.(3)Through structural change analysis of economic time series we often encountered cases which seemed to have jump rather than structural changes. So we attracted jump diffusion process. We applied Kou's jump diffusion model and Barndorff-Nielsen and Shepard test for null of no jump. As the result we found that in many stock price processes there were jumps.(4)We dealt with high frequency data of Japanese stock data. and found inherent movement of the data such as seasonal change, jump, and so on within a day. We applied a marked point process to model such data. We compared performance of several models by simulation study.(5)We apply wavelet analysis to economic data including stock data and found that wavelet analysis were effective and more flexible than parametric model analysis in economic time series analysis.