Model averaging for interval-valued data

In recent years, model averaging, by which estimates are obtained based on not one single model but a weighted ensemble of models, has received growing attention as an alternative to model selection. To-date, methods for model averaging have been developed almost exclusively for point-valued data, despite the fact that interval-valued data are commonplace in many applications and the substantial body of literature on estimation and inference methods for interval-valued data. This paper focuses on the special case of interval time series data, and assumes that the mid-point and log-range of the interval values are modelled by a two-equation vector autoregressive with exogenous covariates (VARX) model. We develop a methodology for combining models of varying lag orders based on a weight choice criterion that minimises an unbiased estimator of the squared error risk of the model average estimator. We prove that this method yields predictors of mid-points and ranges with an optimal asymptotic property. In addition, we develop a method for correcting the range forecasts, taking into account the forecast error variance. An extensive simulation experiment examines the performance of the proposed model averaging method in finite samples. We apply the method to an interval-valued data series on crude oil future prices.