Time Series and Spectral Methods for Imputation, Regression, and Environmental Health

用于插补、回归和环境健康的时间序列和谱方法

• 批准号: RGPIN-2017-04741
• 负责人: Burr, Wesley
• 金额: $ 1.02万
• 依托单位: Trent University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=675449
• 关键词: Time; Series; Spectral; Methods; Imputation

Progress in statistical methods is vital for making sense of an ever-increasing flow of data. Time series are a type of data consisting of repeated observations of a physical phenomena, indexed by a common factor. The proposed research deals with the reconstruction of missing samples in such time series, the estimation of the spectra of them, and the use of both in regression models. The research falls within two distinct statistical areas, both dealing with data: the first in the pre-analysis stage (interpolating raw time series), and the second in the analysis stage (development of models for analysis).***The analysis of time series in the natural sciences is a key element in the interpretation of real-world phenomena. These analyses have increasing value and predictive power as the length of the data series increases. Unfortunately, such series are often plagued by missing records. Interpolation allows for the reconstruction of values for missing records, extending the inferential power of the overall series. One prong of the proposed research centres on the development of algorithms and theory for the interpolation of time series. The challenge with such algorithms is the complex nature of real-world time series, and developing models which allow for violations of simplistic assumptions is the primary objective of the research. ***The proposed research on model development consists of application of time series spectral methods to two problems: the estimation of limited timescale associations in additive models, and the estimation of lagged associations. The first of these is a problem of mixed data, with both predictor and response having elements driven by long-term effects (e.g., mortality records vary annually), but with the inference desired being that of the short-term effects: careful work is required to separate the two. The second of these problems is that of delayed effects, where predictors have time delayed associations with responses. The research proposed develops a novel modelling framework for estimation of these delayed effects, eliminating an identifiability issue of previous solutions.***The work proposed here will address these problems relating to time series data, and lead to original research that will further the scientific use of complex time series. The work on time series interpolation will be of value to researchers seeking to analyze long time series, while the work on additive models will be of value to researchers for whom these models are a primary working tool for estimation of timescale-limited associations. A further impact will be to refine and improve the reliability of risk estimation for population health, which ultimately will affect the policies made by our government that pertain to the health of Canadians. Training is a major component of this research program, which will support 1 Phd and 7 MSc graduate students, as well as 8 undergraduate summer research students.

统计方法的进步对于理解不断增长的数据流至关重要。时间序列是一种由对物理现象的重复观察组成的数据，由公共因子索引。所提出的研究涉及此类时间序列中缺失样本的重建、它们的频谱的估计以及两者在回归模型中的使用。该研究属于两个不同的统计领域，都涉及数据：第一个是预分析阶段（插入原始时间序列），第二个是分析阶段（开发分析模型）。***自然科学中的时间序列分析是解释现实世界现象的关键要素。随着数据系列长度的增加，这些分析的价值和预测能力不断增加。不幸的是，此类系列经常受到记录缺失的困扰。插值允许重建缺失记录的值，从而扩展整个系列的推理能力。拟议研究的一个方面集中在时间序列插值算法和理论的开发上。此类算法面临的挑战是现实世界时间序列的复杂性，开发允许违反简单假设的模型是研究的主要目标。 ***拟议的模型开发研究包括将时间序列谱方法应用于两个问题：加法模型中有限时间尺度关联的估计和滞后关联的估计。第一个是混合数据的问题，预测因素和响应因素都具有由长期影响驱动的因素（例如，死亡率记录每年都会变化），但所需的推论是短期影响：需要仔细工作才能将两者分开。第二个问题是延迟效应，即预测变量与响应的关联存在时间延迟。拟议的研究开发了一种新颖的建模框架来估计这些延迟效应，消除了先前解决方案的可识别性问题。***此处提出的工作将解决与时间序列数据相关的这些问题，并引发原创性研究，进一步促进复杂时间序列的科学使用。时间序列插值的工作对于寻求分析长时间序列的研究人员来说是有价值的，而加性模型的工作对于那些将这些模型作为估计时间尺度有限关联的主要工作工具的研究人员来说是有价值的。进一步的影响将是完善和提高人口健康风险评估的可靠性，这最终将影响我国政府制定的有关加拿大人健康的政策。培训是该研究计划的主要组成部分，将支持 1 名博士生和 7 名硕士研究生以及 8 名本科生暑期研究生。