  Traffic systems are complex systems that exhibit non-stationary
characteristics. Therefore, the identification of temporary traffic states is
significant. In contrast to the usual correlations of time series, here we
study those of position series, revealing structures in time, i.e. the rich
non-Markovian features of traffic. Considering the traffic system of the
Cologne orbital motorway as a whole, we identify five quasi-stationary states
by clustering reduced rank correlation matrices of flows using the $k$-means
method. The five quasi-stationary states with nontrivial features include one
holiday state, three workday states and one mixed state of holidays and
workdays. In particular, the workday states and the mixed state exhibit
strongly correlated time groups shown as diagonal blocks in the correlation
matrices. We map the five states onto reduced-rank correlation matrices of
velocities and onto traffic states where free or congested states are revealed
in both space and time. Our study opens a new perspective for studying traffic
systems. This contribution is meant to provide a proof of concept and a basis
for further study.
