Chaotic time series analysis with neural networks to forecast cash demand in ATMs

In this paper, we employed both traditional and chaotic approaches for time series forecasting. It concerns the forecasting of cash withdrawal amounts at automated teller machines (ATMs) for which the NN5 forecasting competitions data was used. The data consists of 111 time series representing daily withdrawal amounts. In the first method (traditional, non-chaotic) missing values of the time series are imputed and data is deseasonalized with a time lag of seven days as a preprocessing step. Then, techniques namely Auto Regressive Integrated Moving Average (ARIMA), Multi Layer Perceptron (MLP), Wavelet Neural Network (WNN) and General Regression Neural Network (GRNN) are applied in the forecasting phase. In the second method (non-traditional, chaotic), we reconstructed the phase space using the chaotic parameters, viz., embedding dimension and delay time using TISEAN tool, while forecasting of the resulting time series is taken care of by GRNN, MLP and Group Method of Data Handling (GMDH). With the optimal embedding dimension and delay time of 2 and 3 respectively, GRNN yielded a SMAPE value of 14.71%. This result convincingly outperformed the results of Andrawis et al. [4], the winner of the competition, as well as Venkatesh et al [9].