Statistical Modeling, Adjustment and Inference for Seasonal Time Series

本计画研究季节性时间序列的新推论程序与模型。这项研究的结果将直接影响目前在美国人口普查局和其他定期公布季节调整的国内外机构实施的季节调整程序的诊断。人口普查局使用的“视觉显著性”方法缺乏严格的统计依据，新的光谱峰值检测方法将有助于以有纪律的方式量化I型和II型误差。虽然是受Census研究问题的启发，但新的方法和模型预计将有助于分析经济学、天文学、环境科学和大气科学等不同学科的时间序列。具体而言，该项目由三个相互关联的部分组成。在第一部分中，PI将开发两种新的光谱峰值检测方法，旨在为美国人口普查局使用的“视觉显著性”方法提供更有原则的方法。在第二部分中，PI将使用归一化周期图的平方积分来解决带限拟合优度检验。PI将使用新的Studentizer，而不是像文献中那样假设强高斯假设，因此基于自归一化的检验统计量的极限分布在不太严格的假设下是关键的。在第三部分中，PI将研究一种新的谱密度参数类，它可以用于基于模型的季节调整，以提高模型拟合和季节调整的质量。新的参数模型和相关的基于模型的季节性调整，如果开发成功，可能会提供一个更有效的建模和调整时间序列的手段。这项研究将通过对本科生和研究生的指导以及通过编写相关的讲义来促进教学和培训。

This project studies novel inference procedures and models for seasonal time series. The results of this research will have direct impact on the diagnostics of seasonal adjustment procedures that are currently implemented at the U.S. Census Bureau and other domestic or foreign agencies where seasonal adjustments are routinely published. The "Visual Significance" method used at the Census Bureau lacks a rigorous statistical justification and the new spectral peak detection methods will help to quantify type I and II errors in a disciplined fashion for a wide class of processes. Although motivated by research problems at Census, the new methodology and models are expected to be useful in the analysis of time series from various disciplines, including economics, astronomy, environmental science, and atmospheric sciences, among others.Specifically, the project consists of three interrelated parts. In the first part, the PI will develop two new methods of spectral peak detection, which are intended to provide more principled approaches to the "Visual Significance" method used at the U.S. Census Bureau. In the second part, the PI will address the band-limited goodness-of-fit testing using the integral of the square of the normalized periodogram. Instead of assuming the strong Gaussian-like assumption as done in the literature, the PI will use a new Studentizer, so that the limiting distribution of the self-normalization-based test statistic is pivotal under less stringent assumptions. In the third part, the PI will study a new parametric class of spectral density, which can be used in model-based seasonal adjustment to improve the quality of model fitting and seasonal adjustment. The new parametric models and related model-based seasonal adjustment, if successfully developed, may offer a more effective means of modeling and adjusting time series. The research will promote teaching and training through mentoring of undergraduate and graduate students and through the development of related lecture notes.