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.

表现出非线性特征的数据在许多应用领域（例如天气预报，信号处理等）中常规出现。这些特征也存在于各个国家机构收集的许多经济和人口统计学时间序列中，这些特征针对对公众和社会具有重要意义的政策制定。但是，当前的方法在很大程度上依赖于线性方法，并且某些临时方法通常用于处理非线性数据，从而使分析的最终结果难以解释。结果，急需系统地开发新的理论和方法论框架以改进预测，以考虑时间序列数据的非线性特征。拟议的研究旨在通过开发将基于高斯现有线性理论并提供大幅改进的预测来直接解决这一需求。除了推进统计科学及相关科学应用外，它还将对美国和其他国家的季节性调整实践产生潜在的影响。该项目旨在利用非高斯，非线性流程的预测新理论和方法论，利用高级自动兼容功能和polysprectra的工具。具体而言，该项目的目标包括：（i）开发二次和高阶非线性预测因子，并具有可证明的改进，（ii）扩展了一系列新类似的四二次可预测过程的预测方法； (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.预计该项目的结果将提供工具，以实质上改进的预测和信号提取，用于单变量和多变量时间序列数据，这些数据在许多科学领域（例如，天文学，大气科学，财务，财务，融资，信号处理）和现实生活中的授权和实际启用nsf deem deem deem dee eym dee eym dee eym apportiation the Science conciences中普遍存在的非线性特征。更广泛的影响审查标准。