Mathematical Sciences: Walsh-Fourier Analysis and Categorical Time Series

数学科学：沃尔什-傅里叶分析和分类时间序列

• 批准号: 9000522
• 负责人: David Stoffer
• 金额: $ 3.8万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1992-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9000522&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Walsh; Fourier; Analysis

The principal investigator will develop statistical theory and methods for categorical time series. Categorical time series arise in many scientific and engineering settings in which the observations can be classified by category (e.g. on or off) and not necessarily by a numerical scale. The principal investigator will employ the method of the Walsh-Fourier transform to investigate these time series. Specifically, the investigator will establish a broad theoretical basis for the application of Walsh-Fourier representation for real time stationary processes. Furthermore, he will develop sound methodologies for the scaling of categorical time series via the Walsh-Fourier transform. Scaling would allow the quantification of the categories and analysis of the data based on both time and frequency domain techniques.

首席研究员将发展分类时间序列的统计理论和方法。分类时间序列出现在许多科学和工程环境中，其中观测可以按类别(例如，开或关)分类，而不一定按数字尺度分类。首席调查员将使用沃尔什-傅立叶变换的方法来研究这些时间序列。具体地说，研究人员将为沃尔什-傅立叶表示在实时平稳过程中的应用奠定广泛的理论基础。此外，他还将开发可靠的方法，通过沃尔什-傅立叶变换对分类时间序列进行标度。比例尺将允许根据时间域和频域技术对类别进行量化和数据分析。