Statistical Modeling, Adjustment and Inference for Seasonal Time Series

季节性时间序列的统计建模、调整和推断

• 批准号: 1407037
• 负责人: Xiaofeng Shao
• 金额: $ 22万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1407037&HistoricalAwards=false
• 关键词: Statistical; Modeling; Adjustment; Inference; Seasonal

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.

该项目研究了季节性时间序列的新型推理程序和模型。这项研究的结果将直接影响美国人口普查局以及其他常规发布季节性调整的季节性调整程序的诊断。人口普查局使用的“视觉意义”方法缺乏严格的统计依据，而新的光谱峰检测方法将有助于以纪律处分的方式量化I型和II型错误，以进行广泛的过程。尽管受到人口普查的研究问题的激励，但新方法和模型预计将在分析来自各个学科的时间序列的分析中很有用，包括经济学，天文学，环境科学和大气科学等。特别是，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检测方法，这些方法旨在为美国人口普查局使用的“视觉意义”方法提供更多原则性的方法。在第二部分中，PI将使用标准化期刊的正方形的积分来解决带限值的拟合测试。 PI不再假设文献中强烈的高斯式假设，而是使用新的Studentizer，因此在不太严格的假设下，基于自分裂的测试统计量的限制分布至关重要。在第三部分，PI将研究新的光谱密度参数类别，可用于基于模型的季节性调整，以提高模型拟合和季节性调整的质量。新的参数模型和相关的基于模型的季节性调整（如果成功开发）可能会提供更有效的建模和调整时间序列的方法。这项研究将通过指导本科和研究生的指导以及开发相关讲义，从而促进教学和培训。