Forecasting traffic flow time series with vine–transform ARMA copula models

Traffic–flow forecasting is gaining prominence in urban areas to facilitate urban planning for early warning systems and optimized logistics. Hence, there is a growing need for simple and high–performing statistical models. This study leverages the Vine–Transform AutoRegressive Moving–Average (VT–ARMA) copula model to forecast traffic data, and it emphasizes the evaluation of forecasting performance. Accordingly, we used real–life data on origin–destination signals extracted from mobile phone signals for specific areas in the province of Brescia (Italy). We conducted performance evaluation using the rank–graduation box approach along with a moving window cross–validation strategy, and incorporated rank–graduation accuracy for precision and rank–graduation explainability for component analysis. As a benchmark for comparison, the VARX–DHR and the Facebook Prophet models were used. Our results reveal that the VT–ARMA copula approach performed well in terms of accuracy, which was approximately 0.99 under the best specification. Furthermore, the copula component presented greater explainability than the autoregressive and moving–average components. In addition, residual diagnostics show significantly lower autocorrelation and partial autocorrelation with respect to the original data, and that the residuals are approximately normally distributed. Overall, the method developed in this study could provide valuable insights supporting urban planners and analysts in making informed decisions.