ATM cash demand forecasting in an Indian bank with chaos and hybrid deep learning networks

Abstract

This paper proposes to model chaos in the automated teller machine (ATM) cash withdrawal time series of a large Indian commercial bank and forecast the withdrawals using deep learning (DL) and hybrid DL methods. It also considers the influence of “day-of-the-week” on the results. We first modelled the chaos present in the withdrawal time series by reconstructing the state space of each series using the optimal lag and embedding dimension. This process converts the original univariate time series into a multi variate time series. The “day-of-the-week” dummy variable is converted into seven variables using one-hot encoding and augmented to the multivariate or univariate time series depending on whether chaos was present or absent. For forecasting the future cash withdrawals, we employed (i) statistical technique namely autoregressive integrated moving average (ARIMA), (ii) machine learning techniques such as random forest (RF), support vector regression (SVR), multi-layer perceptron (MLP), group method of data handling (GMDH), and general regression neural network (GRNN), and (iii) DL techniques such as long short term memory (LSTM) neural network, Gated Recurrent Unit (GRU) and 1-dimensional convolutional neural network (1D-CNN). We also explored hybrid DL techniques such as 1D-CNN + LSTM and 1D-CNN + GRU. We observed improvements in the forecasts for all techniques when “day-of-the-week” variable was included. It is observed that chaos was present in 28 ATMs, whereas in the remaining 22 ATMs chaos was absent. In both the cases, LSTM yielded the best Symmetric Mean Absolute Percentage Error (SMAPE) on the test data. However, LSTM showed statistically different performance than the 1D-CNN + LSTM in chaos category but equal performance with 1D-CNN in non– category yet statistically significant than 1D-CNN.