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

本研究发展了一种统计分析多种特征的非平稳、长程相关的多变量时间序列过程的方法。特别是，研究表明，怀特尔似然方法能够对广泛的时间序列数据进行协整分析，并与相关文献中的常规研究进行比较。在本研究中，我们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具有渐近性质。这一极限理论对于协整检验是必不可少的。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，这项研究还提出了在存在趋势突变的情况下进行协积等级检验的计算机算法，以及用于分析部分因果度量的计算机算法。前者扩展了Johansen检验，后者提供了一种处理由于第三序列的存在而导致的反馈失真的方法。

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.