Vangala Sarveswararao

Vangala Sarveswararao, Vadlamani Ravi, Sheik Tanveer Ul Huq

In a first-of-its-kind study, this paper proposes the formulation of constructing prediction intervals (PIs) in a time series as a bi-objective optimization problem and solves it with the help of Nondominated Sorting Genetic Algorithm (NSGA-II). We also proposed modeling the chaos present in the time series as a preprocessor in order to model the deterministic uncertainty present in the time series. Even though the proposed models are general in purpose, they are used here for quantifying the uncertainty in macroeconomic time series forecasting. Ideal PIs should be as narrow as possible while capturing most of the data points. Based on these two objectives, we formulated a bi-objective optimization problem to generate PIs in 2-stages, wherein reconstructing the phase space using Chaos theory (stage-1) is followed by generating optimal point prediction using NSGA-II and these point predictions are in turn used to obtain PIs (stage-2). We also proposed a 3-stage hybrid, wherein the 3rd stage invokes NSGA-II too in order to solve the problem of constructing PIs from the point prediction obtained in 2nd stage. The proposed models when applied to the macroeconomic time series, yielded better results in terms of both prediction interval coverage probability (PICP) and prediction interval average width (PIAW) compared to the state-of-the-art Lower Upper Bound Estimation Method (LUBE) with Gradient Descent (GD). The 3-stage model yielded better PICP compared to the 2-stage model but showed similar performance in PIAW with added computation cost of running NSGA-II second time.

Sarveswararao Vangala, Ravi Vadlamani

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.