  This paper proposes to model chaos in the ATM cash withdrawal time series of
a big Indian bank and forecast the withdrawals using deep learning methods. It
also considers the importance of day-of-the-week and includes it as a dummy
exogenous variable. We first modelled the chaos present in the withdrawal time
series by reconstructing the state space of each series using the lag, and
embedding dimension found using an auto-correlation function and Cao's method.
This process converts the uni-variate time series into multi variate time
series. The "day-of-the-week" is converted into seven features with the help of
one-hot encoding. Then these seven features are augmented to the multivariate
time series. For forecasting the future cash withdrawals, using algorithms
namely ARIMA, random forest (RF), support vector regressor (SVR), multi-layer
perceptron (MLP), group method of data handling (GMDH), general regression
neural network (GRNN), long short term memory neural network and 1-dimensional
convolutional neural network. We considered a daily cash withdrawals data set
from an Indian commercial bank. After modelling chaos and adding exogenous
features to the data set, we observed improvements in the forecasting for all
models. Even though the random forest (RF) yielded better Symmetric Mean
Absolute Percentage Error (SMAPE) value, deep learning algorithms, namely LSTM
and 1D CNN, showed similar performance compared to RF, based on t-test.
