Nonparametric Inference of Nonstationary Time Series

非平稳时间序列的非参数推理

• 批准号: 1405685
• 负责人: Ting Zhang
• 金额: $ 12万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-15 至 2014-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1405685&HistoricalAwards=false
• 关键词: Nonparametric; Inference; Nonstationary; Time; Series

This research project aims to advance the development of statistical methodology and theory for analyzing nonstationary time series. A nonstationary time series is a sequence of data points collected at successive time points with certain aspects changing over time or being nonstationary. Nonstationary time series appear very frequently in various scientific fields including economics, engineering, environmental science, finance, and medical science among others. Ignoring nonstationarity and dependence, two important features of nonstationary time series, can lead to erroneous conclusions. Therefore, the research project is expected to promote scientific research in not only statistics but also other disciplines that involve the analysis of nonstationary time series. In order to capture the temporal dynamics resulting from the nonstationarity, the parameters are allowed to change over time and modeled as deterministic but unknown functions of time, which are intrinsically infinite dimensional. To avoid potential misspecifications of parametric models, nonparametric methods are used to estimate and make inference about the underlying parameter functions. The research to be performed involves parameter estimation, hypothesis testing, and variable selection for regression models with time-varying parameters. By allowing a general class of nonstationary and dependent processes, the methods to be developed and the asymptotic results to be established can be widely applicable, and we are able to understand and quantify the effect of nonstationarity and dependence on the asymptotic behavior of parameter estimators and test statistics of interest.

本研究项目旨在促进非平稳时间序列分析的统计方法和理论的发展。非平稳时间序列是在连续时间点上收集的数据点序列，其中某些方面随时间变化或是非平稳的。非平稳时间序列在包括经济学、工程学、环境科学、金融学和医学等各个科学领域中出现得非常频繁。忽略非平稳时间序列的两个重要特征——非平稳性和相关性，可能会导致错误的结论。因此，该研究项目不仅可以促进统计学的科学研究，还可以促进其他涉及非平稳时间序列分析的学科的科学研究。为了捕捉由非平稳性引起的时间动态，允许参数随时间变化，并将其建模为确定性但未知的时间函数，其本质上是无限维的。为了避免参数模型可能出现的错误规范，采用非参数方法对底层参数函数进行估计和推断。研究涉及参数估计、假设检验和时变参数回归模型的变量选择。通过允许一类一般的非平稳和相关过程，所要开发的方法和所要建立的渐近结果可以广泛适用，并且我们能够理解和量化非平稳和依赖对参数估计量和感兴趣的检验统计量的渐近行为的影响。