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，我对非平稳时间序列的谱结构推断进行了统计考虑，非平稳时间序列的统计份额是随着时间逐渐变化的。本课题的目标是：1)对统计结构变化速度与非平稳谱估计精度之间的关系进行数学评价；2)将(1)的概念应用于数据分析方面。本课题假设非平稳时间序列遵循振荡过程，具有非平稳谱密度结构。得到了一些估计非平稳谱误差的数学结果，并在2005年4月国际统计学会（ISI）会议上发表。然而，所提出的方法的缺点是，它不一定是灵活的，为实际应用。因此，我们也开发了一种新的方法，可用于实际方面的应用。在这个项目中，作为一个案例，我们基于观测卫星测量的时空数据，包括不同速度的结构变化，建立了一个时空模型。此外，我们可以通过应用该模型对预测性能的评价来证明我们提出的统计结构在一定程度上是有效的。该论文发表在《IEEE地球科学与遥感快报》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.