SARIMAX with Fourier terms for predicting travel times for on-demand public transport in Sofia

This paper presents a complex prediction of travel times of city transport of Sofia (Bulgaria) using the Seasonal autoregressive integrated moving average with exogenous inputs with Fourier terms for the needs of On-demand public transport scheme proposed by INNOAIR project. The model is tested on a particular use-case data. The procedure to implement a prediction model goes through three phases: model identification, parameter estimation/optimization, and prediction, with their corresponding sub-phases. The input data used have two sources – traffic data for times of arrival for 4 consecutive stops of a bus line in Sofia and weather data. For validation the root-mean-square error measured in seconds for each stop is used, calculated on the forecast for the test set (last week of observations).