Seasonal decomposition and combination model for short-term forecasting of subway ridership

The subway ridership is related with the social activities, such as, commuting, festival, holiday, and so on, which makes the time series of subway ridership presents seasonal characteristic. This characteristic inspires us to decompose the time series into a seasonal component and an epoch component, and employ a combination forecasting method to estimate the future ridership. We first transform the raw ridership into a time series matrix, then decompose the ridership into a seasonal component and an epoch component, and at last combine the individual forecasting results of the seasonal component and the epoch component to make forecast. Contributions of this paper include formulating the combination forecasting problem as an optimization problem, proposing an In-Sample Algorithm (ISA) and an Out-of-Sample Algorithm (OSA), and conducting extensive experiments based on the individual forecasting model named Auto Regressive Integrated Moving Average (ARIMA) model and the data provided by Chongqing Rail Transit. We prove that the decomposition and combination forecasting model possesses smallest variance than individual forecasting models from the theory aspect. The experiments further demonstrate that the ISA algorithm can effectively fit original ridership time series and the OSA algorithm can make better forecasting performance than individual forecasting models. Most importantly, the ISA algorithm and the OSA algorithm both possess advantages of smaller forecasting error deviation and smaller absolute forecasting errors.