Predicting the seasonality of passengers in railway transport based on time series for proper railway development

Planning the frequency of rail services is closely related to forecasting the number of passengers and is part of the comprehensive analysis of railway systems. Most of the research presented in the literature focuses only on selected areas of this system (e.g. urban agglomerations, urban underground transport, transfer nodes), without presenting a comprehensive evaluation that would provide full knowledge and diagnostics of this mode of transport (i.e. railway transport). Therefore, this article presents methods for modelling passenger flow in rail traffic at a national level (using the example of Poland). Time series models were used to forecast the number of passengers in rail transport. The error, trend, and seasonality (ETS) exponential smoothing model and the model belonging to the ARMA class were used. An adequate model was selected, allowing future values to be forecast. The autoregressive integrated moving average (ARIMA) model follows the tested series better than the ETS model and is characterised by the lowest values of forecast errors in relation to the test set. The forecast based on the ARIMA model is characterised by a better detection of the trends and seasonality of the series. The results of the present study are considered to form the basis for solving potential rail traffic problems, which depend on the volume of passenger traffic, at the central level. The methods presented can also be implemented in other systems with similar characteristics, which affects the usability of the presented solutions.