Regression with Time Series Regressors

使用时间序列回归器进行回归

• 批准号: 1812054
• 负责人: Suhasini Subba Rao
• 金额: $ 12万
• 依托单位: Texas A&M University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-08-01 至 2022-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1812054&HistoricalAwards=false
• 关键词: Regression; Time; Series; Regressors

The projects to be investigated are motivated by the following two different problems. It is well known that sea ice in the Arctic is receding. Changes in climate are thought to be a contributing factor. Therefore, it is important to understand if, when, and how daily temperatures in the Arctic region are impacting sea ice. The second motivation comes from neuroscience. Is it possible to predict the decision a person makes based on biometric and neurophysiological responses, such as eye dilation observed over time or an EEG? The objectives in both examples are very different, however they are bound by a common theme; to understand how data observed over time (usually called a time series) affects an outcome of interest. These problems fall under the canopy of regression (a broad topic in statistics), which is a widely researched area in statistics. However, what distinguishes these problems from the classical regression framework is that the regressors have a well-defined structure, which is rarely exploited in most classical regression techniques. By modelling the time series, methods will be developed that exploit the structure of the time series. This will facilitate estimation in models that otherwise would not be possible. The approach will be used to identify salient periods in the time series that have the greatest impact on the outcome and can be used to physically interpret the data. In recent years, there has been a growing number of data sets, from a wide spectrum of applications ranging from the neurosciences to the geosciences, where an outcome is observed together with a time series that is believed to influence the outcome. Despite the clear need in applications, there exists surprisingly few results that exploit the properties of a time series in the prediction of outcomes. This project will bridge this gap by developing regression methods that utilize the fact that the regressors are a time series or are spatially dependent. To achieve these aims, many new statistical methods will be developed. In signal processing, deconvolution methods are often used to estimate the parameters of a two-sided linear filter. This is because the deconvolution is computationally very fast to implement. However, there has been very little exploration on the use of deconvolution methods within the framework of estimating regression parameters. This project will develop deconvolution techniques for (i) linear regression models, and (ii) generalized linear models and when the regressors are stationary and locally stationary. The focus will be on the realistic situation where the time series or spatial data is far larger than the number of responses. Besides the computational simplicity of deconvolution, by isolating the Fourier transform of the regression coefficients, diagnostic tools to understand the nature of the underlying regression coefficients will be developed. For example, the methods can tell whether the coefficients are smooth, contain periodicities, or are sparse. The project will develop inferential methods for parameter estimators that allow for uncertainty quantification, construction of confidence intervals, and tests for linear dependence. Included is a new technique for estimating the variance of the regression coefficients.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

要调查的项目是由以下两个不同的问题引起的。 众所周知，北极的海冰正在消退。气候变化被认为是一个促成因素。 因此，重要的是要了解北极地区的每日温度是否、何时以及如何影响海冰。 第二个动机来自神经科学。是否有可能根据生物特征和神经生理反应（例如随着时间的推移观察到的眼睛扩张或EEG）来预测一个人做出的决定？这两个例子的目标非常不同，但它们都有一个共同的主题：了解随着时间的推移观察到的数据（通常称为时间序列）如何影响感兴趣的结果。这些问题属于回归（统计学中的一个广泛主题）的范畴，这是统计学中广泛研究的领域。然而，这些问题与经典回归框架的区别在于回归变量具有定义良好的结构，这在大多数经典回归技术中很少被利用。通过对时间序列建模，将开发利用时间序列结构的方法。这将有助于在模型中进行估计，否则是不可能的。该方法将用于确定时间序列中对结果影响最大的突出时期，并可用于对数据进行物理解释。近年来，有越来越多的数据集，从神经科学到地球科学的广泛应用，其中结果与被认为会影响结果的时间序列一起观察。 尽管在应用中有明确的需求，但令人惊讶的是，很少有结果利用时间序列的属性来预测结果。该项目将通过开发回归方法来弥补这一差距，该方法利用回归量是时间序列或空间依赖性这一事实。 为了实现这些目标，将开发许多新的统计方法。在信号处理中，反卷积方法经常被用来估计双边线性滤波器的参数。这是因为去卷积在计算上实现起来非常快。然而，在估计回归参数的框架内，对使用反卷积方法的探索很少。本项目将为（i）线性回归模型和（ii）广义线性模型以及回归量平稳和局部平稳时开发反卷积技术。重点将放在时间序列或空间数据远远大于答复数量的现实情况上。 除了反卷积的计算简单性之外，通过隔离回归系数的傅里叶变换，将开发诊断工具来理解潜在回归系数的性质。例如，这些方法可以判断系数是否平滑、包含周期性或稀疏。 该项目将开发参数估计的推理方法，允许不确定性量化，置信区间的构建和线性相关性的测试。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。