Multiple ARIMA subsequences aggregate time series model to forecast cash in ATM

This paper proposes a new forecasting model for the amount of cash in ATM, called a multiple ARIMA subsequences aggregate time series model or MASA model. To assess the MASA model, the time series data is split into in-sample for building and out-sample data for evaluating. To build the MASA model, the aggregate in-sample data is subdivided into training time series data and validating time series data. The aggregate technique by its period is used to reduce a sway in the time series. A fixed number of subsequence patterns are generated and fitted using ARIMA models and then validated using the symmetric mean absolute percentage error or SMAPE to identify the best fitted model. The step of forecasting a future value in the aggregate group using the MASA model needs to identify the subsequence with the best fitted ARIMA model. The disaggregate process will distribute this group value into future values using a ratio from the past. The MASA model is compared using SMAPE with the SARIMA model and ETS exponential smoothing model. The results exhibit the better SMAPE than the SARIMA model and ETS exponential smoothing model.