A new spectral model for binary or categorical-valued time series data

Abstract

The classical Fourier analysis of time series data can be used to detect periodic trends that are of sinusoidal shape. However, this analysis can be misleading when time series trends are not sinusoidal. In this article, using a sequence of periodic functions, we develop theory and methodology for modeling binary or categorical-valued data where patterns more naturally follow a rectangular shape. The theory parallels the Fourier theory and leads to a “Fourier-like” data transform that is specifically suited to the identification of rectangular trends.

Keywords:

• Frequency domain
• sequency domain
• periodic function