Analysis of Time Series Data: Theory and its Applications

本项目的研究成果涉及以下三个方面：（1）时间序列分析中的渐近展开，（2）经济时间序列中的特殊问题，（3）渐近展开的基本问题。按照上述分类，我们描述了我们的项目的主要结果。(1)Maekawa推导了ARMAX模型中OLS估计量的Edgeworth展开式，并对所得公式进行了分析。并给出了AR（p）过程中四种预报量的展开式，比较了它们的有限样本性质。Taniguchi发展了高斯阿尔马过程中极大似然估计的三阶渐近有效性理论，并发现D类中的修改的MLE在这个意义上是有效的。(2)Okamoto将西姆斯的非因果关系推广到更一般的情形，提出了VAR模型中因果关系检验的多元相对功率贡献（MRPC）。Kitaoka在各种条件下通过模拟方法比较了几种因果关系的测试程序，发现RPC是其中最鲁棒的。(3)藤越调查基本问题的渐近展开。他的结果似乎与时间导数分析中的渐近展开非常相关。例如，他在估计近似误差界的方法将适用于时间序列分析。

The results of this projects are associated with the following three area: (1) Asymptotic expansion in time series analysis, (2) Special problems in economic time series, (3) Basic problems in asymptotic expansion. Following the above classification, we describe the main results of our projects.(1) Maekawa derived the Edgeworth expansion for the OLS estimator in a ARMAX model and analyzed the resulting formulas. He also obtained the expansion for the four predictors in AR(p) process and compared the finite sample properties of them. Taniguchi developed the theory of the third order asymptotic efficiency of the maximum likelihood estimator in the Gaussian ARMA process and found that a modified MLE in the class D was efficient in that sense.(2) Okamoto extended the Sims' noncausality to a more general case and proposed the multivariate relative powe contribution(MRPC) for the causality test in VAR model. Kitaoka compared several test procedures for causality by simulation method under various conditions and found that RPC was the most robust among them.(3) Fujikoshi investigated basic problems in the asymptotic expansion. His results seems to be very relevant to the asymptotic expansion in time deries analysis. For example, his method in evaluating the error bound in approximations will be applicable to the time series analysis.