高维时间序列的降维与建模

项目名称： 高维时间序列的降维与建模

项目编号： No.11501462

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 常晋源

作者单位： 西南财经大学

项目金额： 18万元

中文摘要： 随着科学技术的快速发展，高维时间序列数据随处可见，这给广大的统计工作者带来了前所未有的挑战与机遇。众所周知，直接使用已有参数模型对即便是维数不是很大的多维时间序列数据进行建模时通常都会遇到过度参数化和模型不可识别这两大问题。为了避免在分析高维时间序列数据时出现这样的问题，我们在这个项目中提出两种对高维时间序列进行降维的方法。通过这两种方法，我们可以将一个高维时间序列转化为多个低维时间序列，然后运用已有的模型对这些低维时间序列进行建模。这样的策略可以显著地缓解过度参数化和模型不可识别的问题。这为分析高维时间序列提出了一种有效而可行的方法。在研究所提方法的理论性质时，我们需要一些新的理论工具，这使得建立相应的理论结果非常具有挑战性。同时这个项目的完成将扩展当前我们对统计推断的理解和视角，并将在概念和方法上提出革新。

中文关键词： 高维时间序列；降维；高维数据分析；时间序列建模；时间序列预测

英文摘要： Lately, high-dimensional time series data have been encountered ubiquitously in a variety of practices that brings both opportunities and challenges to statisticians. It is well known that modeling a time series data even with moderate dimensionality via special parametric models will generate two issues: overparametrization and non-identification. To alleviate such issues in analyzing high-dimensional time series, we propose two approaches in the proposal to do dimension reduction for high-dimensional time series with reasonably unconstraint structure assumptions which will transfer the target time series to some low-dimensional time series. Then the conventional models in time series analysis can be applied to model such low-dimensional time series directly. Such strategy can significantly alleviate the issues of overparametrization and non-identification mentioned above and will pave an efficient road to analyze high-dimensional time series data. The theoretical studies for the new methods need some new technical tools that makes the construction of theoretical properties be challenging. The novelty of the proposal will extend the insights of modern statistical inference and brings innovations both conceptually and methodologically.

英文关键词： High dimensional time series;Dimension reduction;High dimensional data analysis;Time series modelling;Forecasting of time series