Exploring the correlation between temperature and crime: A case-crossover study of eight cities in America

Recent years have seen increasing academic interest in exploring the correlation between temperature and crime. However, it is uncertain whether similar long-term trends or seasonality (rather than causal effect) of temperature and crime is the major reason for the observed correlation between them. To explore whether there is still a correlation between temperature and crime when long-term trends and seasonal cycles are filtered out, we use the Kalman filter to decompose the time series of temperature and crimes, and then the fast Fourier transform is used to calculate the exact circle of their seasonality separately. Based on that, the box-plot method and linear regression are used to explore the correlation between temperature residuals and crime residuals. The results show that more than half of the crime types have similar seasonal cycles (approximately 1 year) to that of temperature. Moreover, the daily residual analyses show that temperature residuals have a positive correlation with assault and robbery residuals in all cities, whose average slopes are more than 0.1. The other four types of crimes vary greatly from case to case. The temperature residuals show a weak correlation with the residuals of some crime types.