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Traffic systems are complex systems that exhibit non-stationarycharacteristics. Therefore, the identification of temporary traffic states issignificant. In contrast to the usual correlations of time series, here westudy those of position series, revealing structures in time, i.e. the richnon-Markovian features of traffic. Considering the traffic system of theCologne orbital motorway as a whole, we identify five quasi-stationary statesby clustering reduced rank correlation matrices of flows using the $k$-meansmethod. The five quasi-stationary states with nontrivial features include oneholiday state, three workday states and one mixed state of holidays andworkdays. In particular, the workday states and the mixed state exhibitstrongly correlated time groups shown as diagonal blocks in the correlationmatrices. We map the five states onto reduced-rank correlation matrices ofvelocities and onto traffic states where free or congested states are revealedin both space and time. Our study opens a new perspective for studying trafficsystems. This contribution is meant to provide a proof of concept and a basisfor further study.

Quasi-stationary states in temporal correlations for traffic systems: Cologne orbital motorway as an example