Seasonality and Anomaly Detection in Rare Data Using the Discrete Fourier Transformation

The discrete Fourier transform (DFT) algorithm is used for the detection of seasonality in discrete data. In most cases, event instances are common, which is to say that a discrete time series contains non-zero values at every time point. This paper explores how the DFT may be used with binary event data, defined as rare data in which instances occur at a low frequency and many time points contain a zero. The DFT has never been used in this context before. In addition to detecting the number of cycles, detecting the periods of those cycles, and detecting signal shifts, one method is developed and explained here as a successful way to identify anomalies in rare, binary data. As anomalies in binary, rare data are difficult to detect, the majority of this paper is focused on anomaly detection.