Disentangling collective trends from local dynamics

TL;DR

This paper introduces a novel method based on independent component analysis to disentangle local dynamics from global trends in correlated time series, with applications to societal data like crime and obesity rates.

Contribution

The proposed method does not assume small local contributions and effectively separates local from global influences in societal time series data.

Findings

Crime rate fluctuations in the US and France reveal shifting influences of local and global factors.

Obesity rates in US states are mainly driven by external factors since 2000, with diverse local behaviors.

The method successfully distinguishes local from global components in synthetic and real societal data.

Abstract

A single social phenomenon (such as crime, unemployment or birth rate) can be observed through temporal series corresponding to units at different levels (cities, regions, countries...). Units at a given local level may follow a collective trend imposed by external conditions, but also may display fluctuations of purely local origin. The local behavior is usually computed as the difference between the local data and a global average (e.g. a national average), a view point which can be very misleading. We propose here a method for separating the local dynamics from the global trend in a collection of correlated time series. We take an independent component analysis approach in which we do not assume a small unbiased local contribution in contrast with previously proposed methods. We first test our method on synthetic series generated by correlated random walkers. We then consider crime rate series (in the US and France) and the evolution of obesity rate in the US, which are two important examples of societal measures. For crime rates, the separation between global and local policies is a major subject of debate. For the US, we observe large fluctuations in the transition period of mid-70's during which crime rates increased significantly, whereas since the 80's, the state crime rates are governed by external factors and the importance of local specificities being decreasing. In the case of obesity, our method shows that external factors dominate the evolution of obesity since 2000, and that different states can have different dynamical behavior even if their obesity prevalence is similar.