Forecasting with a combined model of ETS and ARIMA

Abstract

This paper considers a combined model of exponential smoothing (ETS) and autoregressive integrated moving average (ARIMA) models that are commonly used to forecast time series data.The combined model is constructed through an innovational state space model based on the level variable instead of the differenced variable, and the identifiability of the model is investigated.We consider the maximum likelihood estimation for the model parameters and suggest the model selection steps.The forecasting performance of the model is evaluated by two real time series data.We consider the three competing models; ETS, ARIMA and the trigonometric Box-Cox autoregressive and moving average trend seasonal (TBATS) models, and compare and evaluate their root mean squared errors and mean absolute percentage errors for accuracy.The results show that the combined model outperforms the competing models.