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

Abstract

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 that these simplifications lead to heuristics providing less accurate processing of information compared to the solution of analytical equations, the intelligent choice of the simplifications coupled with the empirical verification of the resulting heuristic has proven itself to be a powerful systems modelling paradigm. In this study, we look at the theoretical underpinning of a successful heuristic for estimation of urban travel times from lane occupancy measurements. We show 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 design a heuristic that eliminates the adverse effect of spurious readings without loosing temporal resolution of data (as implied by the standard method of data averaging). The original contribution of the paper concerning the link between the analytical modelling and the design of heuristics is general and relevant to a broad spectrum of applications.