The relationship between the speed in changing statistical structure and the accuracy in estimation of nonstationary spectrum

在这个研究项目中，我处理了非平稳时间序列的谱结构推断的统计考虑，其统计份额随着时间的推移而逐渐变化。该项目的目标是：1)对统计结构变化的速度与非平稳谱估计精度之间的关系进行数学评估；2)将(1)的概念应用于数据分析。在假定非平稳时间序列遵循振荡过程且具有非平稳谱密度结构的情况下，得到了一些关于非平稳谱估计误差的数学结果，并在2005年4月的ISI(国际统计学会)会议上公布。然而，该方法的缺点是不一定具有实际应用的灵活性。因此，我们还开发了一种新的方法论，可以在实际应用中使用。在这个项目中，作为一个案例，我们开发了一个基于观测卫星测量的包括不同结构变化速度的时空数据的时空模型。此外，通过应用该模型对预测性能进行评估，可以证明我们提出的统计结构在一定程度上是有效的。这篇论文发表在IEEE地球科学和遥感快报上。

In this research project, I have treated the statistical consideration on the inference of spectral structure of the nonstationary time series, whose statistical share changes gradually over time. The project has been proceeded with the goals that 1)mathematical evaluation on the relationship between the speed in changing statistical structure and the accuracy in estimating nonstationary spectrem, and 2)the application of the concept of (1) to the aspect of data analysisIn this project, under the assumption that the nonstationary time series follows an oscillatory process and it has a nonstationary spectral density structure, some mathematical results on the errors in estimating the nonstationary spectrum were obtained, and they were presented in the conference of ISI (International Statistical Institute), in Apr.,2005. The presented method has the disadvantage, however, that it is not necessarily flexible for the practical application. So, we also developed a new methodology, which is available for the application in the practical aspect. In this project, as a case, we developed a space-time model based on the space-time data, including different speeds in changing structure, measured by an observation satellite. Furthermore, we could show that the statistical structure we proposed is valid to some extent, via evaluation of forecasting performance by applying this model. The paper has been published in IEEE Geoscience and Remote Sensing Letters.