Time Series Regression Forecasting of London Santander Cycles Demand: Nested Modelling with Unequal Weight Rolling Lags and Weekly Lag Correction

Against the background of fast-growing urban shared bike services, supply-demand imbalance has become a key operational challenge. Without reliable demand forecasting, operators face recurring vehicle surplus or shortage, raising logistics costs and harming user experience. This paper constructs time series regression forecasting models using daily Santander Cycles rental data from London spanning 2015 to 2017. We first build the baseline M13 model with an unequal-weight rolling lag term to capture short-term demand continuity. Nested models M1 and M4 are then developed by sequentially adding weekend, holiday, meteorological, and monthly seasonal covariates. To mitigate residual weekly autocorrelation, an extended M4 L7 model is created by introducing the lag7_cnt weekly lag variable. Model performance is assessed via static out-of-sample tests and 365-day rolling window recursive forecasting. Results show that M13 performs optimally for rolling-window high-frequency operational prediction, while M3 delivers the best static forecasting performance for long-term planning. M4 L7 effectively reduces medium- and long-term residual autocorrelation and balances explanatory power and prediction accuracy. This study provides scenario-specific model selection references for different bike-sharing operators.