Large deviations estimates for the multiscale analysis of traffic speed time series

Multifractal behavior is found in traffic speed time series and mostly measured around the concept of Legendre singularity spectrum. As one of the multifractal spectra, which is the probability distribution of roughness grain exponent, Legendre spectrum is structurally blind to subtle features like non-concavity or, to a certain extent non scaling of the distributions. In this article, we illustrate the large deviations spectrum on both artificial and traffic speed time series, and verify that this kind of approach is able to reveal significant information (represents some traffic characteristics here) that remains hidden with Legendre spectrum. In the mean time, the multiscale analysis of the large deviations spectrum was conducted to quantify the presence or absence of scale invariant phenomenon in the study of traffic speed signals.