Examining the spatial periodicity of crime in South Africa using Fourier analysis

This paper analyses the periodicity of violent and property crimes committed in Tshwane, South Africa from 2001 to 2006. Conventional monthly, daily and hourly variations in these types of crime are highlighted and then Fourier analysis is introduced as an advanced mathematical technique which is able to identify periodic peaks or signals of crime contained within a large time-series crime data-set. Specifically, Fourier analysis is used to examine crime periodicities in Tshwane in neighbourhoods stratified by social deprivation. Across most neighbourhood quintiles, there is a notable peak in violent crimes every 7-10 days. That is, every 7-10 days over the 5 years, there is a peak in violent crimes in most neighbourhoods in Tshwane. There is also a marginal peak occurring roughly every 50-60 days in neighbourhood Quintiles 1 (most affluent) and 3 ('middle class'). Similar to violent crimes, the largest consistent periodicity for property crimes was observed across all five neighbourhood quintiles approximately every 7-10 days. A significant peak was also observed in property crime in Quintile 3 ('middle class') roughly every 75 days. Tentative explanations are provided for the results obtained.