A Review on Two Interval-Valued Time Series Models

Interval-valued data as one important class of symbolic data include observations defined by two lower and upper limit points. In this paper, two approaches are presented to forecast the interval-valued time series which are expressed based on the linear auto-regressive integrated moving average models and a nonlinear artificial neural network model. In each case, two models are fitted on the mid-point and the range of the interval-valued time series in the learning sets. Forecasting the lower and upper bounds of the intervals is accomplished by combining the forecasts of the midpoint and the range of the intervals. Applicability of artificial neural network model as the alternative forecasting model for interval-valued time series is investigated based on the mean squared error in the framework of a Monte Carlo experiment.