Theory of spatio-temporal data analysis and its applications to environmental data

本研究提出了在观测点间距不规则时，对时空数据进行非平稳傅立叶分析的方法。非平稳傅立叶分析最初被提出用于非平稳时间序列局部周期图分析，以识别时间序列模型的时间依赖性。在这里，我们将时间序列的方法扩展到时空数据的方法，从而可以识别空间模型参数的局部依赖关系。用非平稳傅立叶方法证明了估计量的相合性。本文将该方法应用于关东地区的土地价格数据，并通过傅里叶分析检验了土地价格数据的非平稳行为。

This research has conducted a proposition of nonstationary Fourier analysis of spatio-temporal data when observation points are irregularly spaced. Originally nonstatinary Fourier analysis was proposed for nonstationary time series analysis by local periodogram in order to identify temporal dependencies of time series models. Here we extend the method for time series to that for spatio-temporal data that makes it possible to identify local dependencies of spatial model parameters. The consistency of the estimators by the nonstationary Fourier methods has been proved. We have applied the methodology to land price data in Kanto area and examined nonstationary behaviors of land price data by the Fourier analysis.