Nonparametric Inference of Nonstationary Time Series

本研究项目旨在推动非平稳时间序列统计方法和理论的发展。非平稳时间序列是在连续时间点收集的数据点的序列，其中某些方面随着时间的推移而变化或是非平稳的。非平稳时间序列在经济、工程、环境科学、金融、医学等各个科学领域中出现的频率很高。忽略非平稳时间序列的两个重要特征--非平稳性和相依性，会导致错误的结论。因此，该研究项目不仅有望促进统计学领域的科学研究，还将促进涉及非平稳时间序列分析的其他学科的科学研究。为了捕捉由非平稳性引起的时间动力学，允许参数随时间变化，并将其建模为本质上无限维的确定性但未知的时间函数。为了避免参数模型可能的错误说明，非参数方法被用来估计和推断潜在的参数函数。所要进行的研究包括参数估计、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依过程，所发展的方法和所建立的渐近结果具有广泛的适用性，我们能够理解和量化非平稳性和相依对参数估计量和感兴趣的检验统计量的渐近行为的影响。

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.