A hybrid ETS–ANN model for time series forecasting

Abstract

Over the past few decades, a large literature has evolved to forecast time series using various linear, nonlinear and hybrid linear–nonlinear models. Recently, hybrid models by suitably combining linear models like autoregressive integrated moving average (ARIMA) with nonlinear models like artificial neural network (ANN) have become popular due to superior performance than individual models. These models assume the time series to be a sum of a linear and a nonlinear component. However, a real world time series may be purely linear or purely nonlinear or often contains a combination of linear and nonlinear patterns. Motivated by this need, a new hybrid methodology is developed by combining linear and nonlinear exponential smoothing models from innovation state space (ETS) with ANN. The proposed hybrid ETS–ANN model glorifies the chances of capturing different combination of linear and/or nonlinear patterns in time series. This is because both ETS and ANN models have linear as well as nonlinear modeling capability. However, ANN cannot handle linear patterns equally well as nonlinear patterns. Therefore, in the proposed method, first ETS is applied to the given time series and predictions are obtained. This enhances the chances of capturing existing linear patterns (if any) well using linear ETS models. Then residual error sequence is calculated by subtracting the ETS-predictions from the original series. The residual error sequence obtained is modeled by ANN. Then final prediction is obtained by combining the ETS-predictions with ANN-predictions. Sixteen time series datasets are used for comparative performance analysis of the proposed methodology with ARIMA, ETS, multilayer perceptron(MLP) and some existing hybrid ARIMA–ANN models. Experimental results show that the proposed hybrid model shows statistically promising result for the datasets used.