Mathematical Sciences: Walsh-Fourier Analysis and Categorical Time Series

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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.