Development of a General Framework for Nonlinear Prediction Using Auto-Cumulants: Theory, Methodology, and Computation

使用自累积量开发非线性预测的通用框架：理论、方法和计算

• 批准号: 2131233
• 负责人: Soumendra Lahiri
• 金额: $ 15万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-04-15 至 2022-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2131233&HistoricalAwards=false
• 关键词: Development; General; Framework; Nonlinear; Prediction

Data exhibiting nonlinear characteristics appear routinely in many areas of applications, such as weather forecasting, signal processing, etc. These features are also present in many economic and demographic time series collected by various national agencies for policy formulations that have important implications for the public and the society. However, the current methodology is heavily reliant upon linear approaches and some ad hoc methods are often used to handle nonlinear data, rendering the final results of analysis difficult to interpret. As a result, there is acute need for systematic development of new theoretical and methodological framework for improved prediction that takes into account the nonlinear features of the time series data. The proposed research seeks to address this need directly by developing new capabilities that will build on the existing linear theory for Gaussian and provide substantially improved prediction. In addition to advancing the statistical science and related scientific applications, it will also have potential impact on the practice of seasonal adjustments for better public policy formulation in the US and other nations.This project seeks to develop new theory and methodology for prediction for non-Gaussian, nonlinear processes, utilizing the tools of higher-order auto-cumulant functions and polyspectra. Specifically, the goals of the project include : (i) developing quadratic and higher order nonlinear predictors, with demonstrable improvements, (ii) extending forecasting approaches for a new class of so-called quadratically predictable processes; (iii) developing nonlinear models-fitting via an appropriate generalization of the Whittle likelihood, derived from the mean squared error of the one-step ahead quadratic forecasting filter, (iv) developing theoretical foundations of auto-cumulants for multi-linear forms that are paramount to derive third and higher order polynomial predictors,(v) developing algorithms and supporting software in R for implementation of the methodology. The results from the project are expected to provide tools for substantially improved forecasting and signal extraction for univariate and multivariate time series data exhibiting nonlinear characteristics that are prevalent in many areas of sciences (e.g., Astronomy, Atmospheric sciences, Finance, Signal Processing) and real life applications.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.

表现出非线性特性的数据经常出现在许多应用领域，如天气预报，信号处理等，这些功能也存在于许多经济和人口的时间序列收集的各种国家机构的政策制定，对公众和社会有重要影响。然而，目前的方法是严重依赖于线性的方法和一些特设的方法往往被用来处理非线性数据，使分析的最终结果难以解释。因此，迫切需要系统地发展新的理论和方法框架，以改善预测，考虑到时间序列数据的非线性特征。拟议的研究旨在通过开发新的能力来直接满足这一需求，这些能力将建立在现有的高斯线性理论基础上，并提供大幅改进的预测。除了促进统计科学和相关的科学应用，它也将对美国和其他国家更好地制定公共政策的季节调整实践产生潜在的影响。本项目旨在利用高阶自累积函数和多谱工具，为非高斯非线性过程的预测发展新的理论和方法。具体而言，该项目的目标包括：（一）开发二次和高阶非线性预测，具有明显的改进，（二）扩展预测方法的一类新的所谓的二次可预测的过程;（iii）通过从一步前二次预测滤波器的均方误差导出的Whittle似然的适当推广来开发非线性模型拟合，（iv）发展多线性形式的自累积量的理论基础，这对于导出三阶和更高阶多项式预测是至关重要的，（v）开发R中的算法和支持软件以实现该方法。预计该项目的结果将为显着改善单变量和多变量时间序列数据的预测和信号提取提供工具，这些数据表现出在许多科学领域普遍存在的非线性特征（例如，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。