Mathematical Sciences: Walsh-Fourier Analysis and Categorical Time Series

首席研究员将发展统计理论 和分类时间序列的方法。 分类时间序列 出现在许多科学和工程环境中， 观测可以按类别分类（例如开或关）， 而不一定是数字规模。 主要研究者 将采用沃尔什-傅立叶变换的方法， 研究这些时间序列。 具体来说，调查员 将建立广泛的理论基础， 真实的平稳过程的Walsh-Fourier表示 此外，他还将制定合理的方法， 通过沃尔什-傅里叶变换的分类时间序列。 比例缩放将允许量化类别， 基于时域和频域的数据分析 技术.

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.