Causes and Consequences of Police Capture in Colombia around Personal Injuries and Intrafamily Violence Using Signal Processing Techniques

This article searched causality between four national daily time series including Colombian Police operatives of capture since 2011 to 2015: first series was is the representative market rate, in Colombian pesos per US dollar, TRM; second, potential criminals captured by the Colombian National Police Force for two crimes: personal injuries and violence inside family and the final series was inpatients to health emergency services. These four daily time series are was compared in six pairwise; This six-time series pairwise was evaluated using five techniques: sperman correlation coefficient, determination coefficient, spectral analysis, wavelet coherence and the statistical causality in Granger sense in search of causality relationship. As result was obtained: first, behavioral similarity degree of each pair of time series; second, simultaneity degree; also, improvements in the simultaneity coefficient using wavelet; and finally, the frequency or cyclicity repetition of each of the variables, and the causality direction. Here was found seven relationships in the statistical sense of granger causality, among twelve possible; first the TRM causes the operational capture for personal injuries; the mutual causality between capture for personal injuries; fourth and fifth, the simultaneous causality between access to the emergency room and capture for personal injuries; and between access to emergencies and captures by violence inside family. Also was find the evolution of the police captures in every day, those was represented in heat map in time and frequency.