[Paper Review] Spatial concentration and temporal regularities in crime

Marcos Oliveira, Ronaldo Menezes|arXiv (Cornell University)|Jan 11, 2019

Crime Patterns and Interventions43 references4 citations

TL;DR

This paper investigates the spatial concentration and temporal regularities of crime using a complex-systems framework, demonstrating that crime clusters in specific urban micro-areas and exhibits circannual (yearly) cycles that are non-stationary at the local level. Despite city-wide stationarity, local crime rhythms shift over time, revealing dynamic, wave-like patterns across urban regions.

ABSTRACT

Though crime is linked to different socio-economic factors, it exhibits remarkable regularities regardless of cities' particularities. In this chapter, we consider two fundamental regularities in crime regarding two essential aspects of criminal activity: time and space. For more than one century, we know that (1) crime occurs unevenly within a city and (2) crime peaks during specific times of the year. Here we describe the tendency of crime to concentrate spatially and to exhibit temporal regularities. We examine these phenomena from the complex-system perspective of cities, accounting for the possibility of both spatial heterogeneity and non-stationarity in urban phenomena.

Motivation & Objective

• To understand the fundamental spatial and temporal regularities in urban crime across diverse cities.
• To investigate how spatial heterogeneity and non-stationarity affect the perception and modeling of crime dynamics.
• To assess whether crime patterns remain consistent across city sizes and types, independent of socio-economic idiosyncrasies.
• To develop a holistic, city-scale perspective on crime that integrates local-level variability with global regularities.
• To inform evidence-based policymaking by revealing dynamic, evolving crime patterns rather than static hotspots.

Proposed method

• Divides cities into equal-population spatial units to eliminate biases from varying urban geometries and block sizes.
• Applies continuous wavelet transform (CWT) to time series of crime data at the local level to detect periodicities, including circannual (1-year) cycles.
• Defines a composed scale-averaged power $ C^b(t) $ as the number of regions with statistically significant circannual periodicity at time $ t $, enabling city-wide monitoring of seasonal crime patterns.
• Measures the duration $ \Delta t $ of significant circannual bands per region to assess temporal stability and detect non-stationarity.
• Analyzes data from 12 U.S. cities to compare local dynamics with aggregated city-level patterns.
• Uses a bottom-up approach to study how local non-stationarity contributes to global, yet stable, city-level seasonal crime rhythms.

Experimental results

Research questions

• RQ1 To what extent is crime spatially concentrated across different urban areas, and does this concentration depend on city size or crime type?
• RQ2 How do circannual (yearly) crime patterns manifest at the local level, and are they stable or evolving over time?
• RQ3 What is the relationship between local non-stationarity and city-wide stationarity in crime rhythms?
• RQ4 How do local periodicities (e.g., biannual, triannual) contribute to or disappear from city-level crime patterns?
• RQ5 To what extent do dynamic, wave-like shifts in crime cycles challenge static hotspot-based crime models?

Key findings

• Crime exhibits strong spatial concentration, with a small number of micro-geographic units accounting for a disproportionate share of offenses, confirming the 'law of crime concentration'.
• Despite city-wide stationarity in circannual crime rhythms, individual regions show non-stationarity, with significant circannual periodicity appearing and disappearing over time.
• The number of regions with significant 1-year cycles ($ C^b(t) $) remains relatively stable over time across cities, indicating consistent city-scale seasonal patterns.
• The duration $ \Delta t $ of significant circannual bands per region decays faster than the full time series, indicating that local crime cycles are transient and not persistent.
• Crime patterns display wave-like dynamics across the city, with periodicities shifting across regions over time, suggesting a dynamic, evolving urban system.
• Spatial heterogeneity and non-stationarity at the local level obscure global regularities when only aggregated data are used, highlighting the need for multi-scale analysis.