Forecasting models for interval-valued time series

This paper presents approaches to interval-valued time series forecasting. The first and second approaches are based on the autoregressive (AR) and autoregressive integrated moving average (ARIMA) models, respectively. The third approach is based on an artificial neural network (ANN) model and the last is based on a hybrid methodology that combines both ARIMA and ANN models. Each approach fits, respectively, two models on the mid-point and range of the interval values assumed by the interval-valued time series in the learning set. The forecasting of the lower and upper bounds of the interval value of the time series is accomplished through a combination of forecasts from the mid-point and range of the interval values. The evaluation of the models presented is based on the estimation of the average behavior of the mean absolute error and mean squared error in the framework of a Monte Carlo experiment. The results demonstrate that the approaches are useful in forecasting alternatives for interval-valued time series and indicate that the hybrid model is an effective way to improve the forecasting accuracy achieved by any one of the models separately. (C) 2008 Elsevier B.V. All rights reserved.