Mathematical justification of a heuristic for statistical correlation of real-life time series

Many of the analyses of time series that arise in real-life situations require the adoption of various simplifying assumptions so as to cope with the complexity of the phenomena under consideration. Whilst accepting these simplifications lead to heuristics that provide less accurate, compared to the full analytical description, representation of the phenomena, the intelligent choice of the simplifications coupled with the empirical verification of the resulting heuristic results in a powerful heuristic modelling paradigm. In this study we look at the theoretical underpinning of our recent successful heuristic for estimation of urban travel times from lane-occupancy measurements. We show that that by interpreting time series as statistical processes with a known distribution it is possible to estimate travel time as a limit value of an appropriately defined statistical process. The proof of the theorem asserting the above supports the conclusion that it is possible to eliminate the adverse effect of spurious readings without the need for data averaging. At the same time, the complexity of the proof highlights the value of the heuristic modelling paradigm for real-life data processing.