Mathematical Sciences: Developing a Bispectral-Based Test for Gaussianity and Linearity of a Time Series

数学科学：开发基于双谱的时间序列高斯性和线性检验

• 批准号: 9631326
• 负责人: Jane Harvill
• 金额: $ 1.8万
• 依托单位: Bowling Green State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 1998-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9631326&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Developing; Bispectral; Based

Correct model specification is arguably the most critical aspect of reliable time series analysis. In the past decade, significant advances have been made so it is now possible to analyze a time series as non-gaussian or non-linear. Therefore, it is desirable to have reliable tests for determining linearity or non-linearity and to have comprehensive tools for performing proper analysis. An initial investigation of existing bispectral-based tests for gaussianity and linearity of a time series revealed many areas for study. Examinations of different functions of the bispectrum and normalized bispectrum for various types of non-linearity will be conducted. A second area of investigation is the development of a test statistic that will not result in vastly different values when different smoothing procedures are used in estimating spectral quantities. It is the hope of the principal investigator that after such examinations are conducted, a test statistic will be developed that not only reliably tests for linearity, but will aid in diagnosing the type of non-linearity when rejecting the null hypothesis. A second goal of this research is to continue to develop a time series analysis package in S-Plus which will include devices for analyzing non-linear time series. The package will have functions that may be used for linear and non-linear time series analysis. Since the package is in S-Plus, graphical examination of relevant time series quantities is a "built-in feature." Documentation will also be developed. When complete, the package, along with documentation, will be submitted to statlib for public use.

正确的模型规范可以说是可靠时间序列分析的最关键方面。 在过去的十年中，已经取得了重大进展，因此现在可以将时间序列分析为非高斯或非线性。 因此，需要有可靠的测试来确定线性或非线性，并有全面的工具来执行正确的分析。 对现有基于双谱的时间序列高斯性和线性检验的初步调查揭示了许多需要研究的领域。 将检查双谱的不同函数和归一化双谱的各种类型的非线性。 研究的第二个领域是开发一种测试统计量，当使用不同的平滑程序来估计光谱量时，该统计量不会产生截然不同的值。 主要研究者希望在进行此类检查后，将开发出检验统计量，该检验统计量不仅可以可靠地检验线性度，而且可以在拒绝原假设时帮助诊断非线性类型。 这项研究的第二个目标是继续在 S-Plus 中开发时间序列分析包，其中包括用于分析非线性时间序列的设备。 该软件包将具有可用于线性和非线性时间序列分析的功能。 由于该软件包位于 S-Plus 中，因此相关时间序列量的图形检查是一项“内置功能”。 还将开发文档。 完成后，该包以及文档将提交给 statlib 供公众使用。