Cross-Correlation Analysis and Multivariate Prediction of Spatial Time Series of Freeway Traffic Speeds

Short-term traffic prediction on freeways is one of the critical components of the advanced traveler information system (ATIS). The traditional methods of prediction have used univariate ARIMA time-series models based on the autocorrelation function of the time series of traffic variables at a location. However, the effect of upstream and downstream location information has been largely neglected or underused in the case of freeway traffic prediction. The purpose of this study is to demonstrate the effect of upstream as well as downstream locations on the traffic at a specific location. To achieve this goal, a section of five stations extending over 2.5 mi on I-4 in the downtown region of Orlando, Florida, was selected. The speeds from a station at the center of this location were then checked for cross-correlations with stations upstream and downstream. The cross-correlation function is analogous to the autocorrelation function extended to two variables. It indicates whether the past values of an input series influence the future values of a response series. It was found in this study that the past values of upstream as well as downstream stations influence the future values at a station and therefore can be used for prediction. A vector autoregressive model was found appropriate and better than the traditional ARIMA model for prediction at these stations.