Multifractal cross-correlation analysis of traffic time series based on large deviation estimates

Abstract

Multiscale analysis of cross-correlation between traffic signals is a developing research area, which helps to better understand the characteristics of traffic systems. Multifractal analysis is a multiscale analysis and almost exclusively develops around the concept of Legendre singularity spectrum, but which is structurally blind to subtle features like non-concavity or nonscaling of the distributions in some degree. Large deviations theory overcomes these limitations, and recently, performing estimators were proposed to reliably compute the corresponding large deviations singularity spectrum. In this paper, we apply the large deviations spectrum based on detrend cross-correlation analysis roughness exponent to both artificial and traffic time series and verify that this kind of approach is able to reveal significant information that remains hidden with Legendre spectrum. Meanwhile, we illustrate the presence of non-concavities in the spectra of cross-correlation between traffic series by the presence or absence of accidents and quantify the presence or absence of scale invariance and the generating mechanism of multifractality for cross-correlation between traffic signals.