Study on long-range dependence and conditional heteroscedasticity in economic time-series

本研究发展了一种方法，以统计分析的各种特征的非平稳，长期依赖的多元时间序列过程。特别是，该研究表明，惠特尔似然方法可以对广泛的时间序列数据进行协整分析，将本研究与相关文献中的常规研究进行比较。本文建立了条件异方差平稳时间序列的泛函中心极限定理。利用这一定理，证明了各种检验统计量作为分数布朗运动的泛函渐近地执行。极限理论是协整秩检验的基础。这一结果将在2001年6月在京都举行的日美联合研讨会上报告。此外，研究提出了计算机算法的协整秩检验的趋势突变的存在下，也用于分析部分因果措施。前者扩展了Johansen检验，后者提供了一种处理由于第三级数的存在而引起的反馈失真的方法。

This study has developed an approach to statistical analysis of a variety of characteristics non-stationary, long-range dependent multivariate time-series processes. In particular, the study showed the Whittle likelihood method enables a cointegrated-analysis of a wide range of time-series data, comparing of this study conventional studies in the related literature. In this study we established a functional central limit theorem for conditional heteroscedestic stationary time-series. By means of this theorem, various test statistics are shown to perform asymptotically as functional of fractional Brownian motion. That limit theory is essential for cointegrated rank test. This result is to be reported at the Japan-U.S.joint seminar, which is held in Kyoto in June 2001. Moreover, the study produced computer algorithms for the cointegraion rank test in the presence of trend breaks and also for analyzing partial causal measure. The former extends the Johansen test and the latter provides a method to deal with feedback distortion due to the presence of a third series.