Nonparametric Inference of Nonstationary Time Series

本研究计画旨在推动非平稳时间序列分析之统计方法与理论之发展。非平稳时间序列是在连续时间点收集的数据点序列，其某些方面随时间变化或非平稳。非平稳时间序列经常出现在经济学、工程学、环境科学、金融学、医学等各个科学领域。忽略非平稳性和相关性这两个非平稳时间序列的重要特征，会导致错误的结论。因此，该研究项目预计将不仅促进统计学的科学研究，而且促进涉及非平稳时间序列分析的其他学科的科学研究。为了捕捉非平稳性导致的时间动态，允许参数随时间变化，并建模为确定性但未知的时间函数，其本质上是无限维的。为了避免参数模型的潜在误设定，使用非参数方法来估计和推断潜在的参数函数。研究内容包括时变参数回归模型的参数估计、假设检验和变量选择。通过允许一般类的非平稳和相关过程，方法开发和渐近结果建立可以广泛适用，我们能够理解和量化的非平稳性和相关性的影响的渐近行为的参数估计和测试统计的利益。

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.