Statistical Inference for causal measures of long-memory cointegrated tme-series

为了扩展作者开发的经济时间序列之间因果关系度量的适用性，2001-2的研究通过开发基于惠特尔似然函数的估计和检验的可行的计算算法，使非平稳的长期相依协整时间序列的因果关系的统计推断成为可能。特别地，给出了分数布朗运动在一组弱条件下的极限定理，并在此基础上导出了极大似然估计量和怀特尔似然比统计量的极限理论。这些结果使得迄今已知的常规单位根协整计量分析得以扩展。在研究中，开发了一种统计推断的统一计算算法，并以日本和美国的宏观经济数据为例检验了该系统的性能。该算法基本上是一种改进的Hannan-Rissanen三步法，在第三步中使用惠特尔似然函数，并且比他们的方法有了改进。

In order to extend the applicability of the causal measures between economic time series the author developed, the research of 2001-2 made possible the statistical inference for causal measures on non-stationary long-range dependent cointegrated tome-series by developing feasible computational algorithm of estimating and testing for that purpose based on the whittle likelihood function. In particular, the research gave a limiting theorem of fractional Brownian motion under a set of weak conditions and on the basis of that theorem derived the limiting theory of the maximum Whittle likelihood estimator and the Whittle likelihood-ratio statistic. Those results enable extension of the conventional unit-root cointegration econometric analysis so far known. In the research a unified computation algorithm was developed for the statistical inference and the performance of the system was examined for Japan and U.S. macro economic data. The algorithm is basically a modified Hannan-Rissanen three-step method, using the Whittle likelihood function in the third step and is shown improvement over their method.