Stochastic Projection-Factoring Method Based on Piecewise Stationary Renewal Processes for Mid- and Long-Term Traffic Flow Modeling and Forecasting

Abstract

Forecasting traffic over a long period of time is of considerable interest and usefulness, but accurate forecasting is very difficult. Traditional projection and factoring methods for mid- and long-term cumulative traffic forecasting are deterministic and only provide a point prediction without specifying a statistical measure of prediction reliability. This paper constructs a stochastic projection and factoring method by casting long-term traffic volume counts into an integrated and rigorous framework of a more refined structural time series component model with piecewise stationary renewal processes capturing time-of-day, day-of-week, monthly, and yearly variations. By doing so, the new method roots itself in a solid theoretical foundation and generates two advantages. First, it results in a more accurate point prediction of cumulative traffic by taking into account the time-of-day traffic count variation in the modeling of unobservable future long-term traffic flow at temporary count stations or at a site under investigation as a mixture of piecewise stationary renewal processes with different means and variances. Second, it allows an interval prediction to be estimated by incorporating uncertainty into the modeling and forecasting process.