Periodicity Intensity Reveals Insights into Time Series Data: Three Use Cases

Abstract

Periodic phenomena are oscillating signals found in many naturally occurring time series. A periodogram can be used to measure the intensities of oscillations at different frequencies over an entire time series, but sometimes, we are interested in measuring how periodicity intensity at a specific frequency varies throughout the time series. This can be performed by calculating periodicity intensity within a window, then sliding and recalculating the intensity for the window, giving an indication of how periodicity intensity at a specific frequency changes throughout the series. We illustrate three applications of this, the first of which are the movements of a herd of new-born calves, where we show how intensity in the 24 h periodicity increases and decreases synchronously across the herd. We also show how changes in 24 h periodicity intensity of activities detected from in-home sensors can be indicative of overall wellness. We illustrate this on several weeks of sensor data gathered from each of the homes of 23 older adults. Our third application is the intensity of the 7-day periodicity of hundreds of University students accessing online resources from a virtual learning environment (VLE) and how the regularity of their weekly learning behaviours changes throughout a teaching semester. The paper demonstrates how periodicity intensity reveals insights into time series data not visible using other forms of analysis.