Modeling Interval Time Series with Space-Time Processes

Abstract

We consider interval-valued time series, that is, series resulting from collecting real intervals as an ordered sequence through time. Since the lower and upper bounds of the observed intervals at each time point are in fact values of the same variable, they are naturally related. We propose modeling interval time series with space-time autoregressive models and, based on the process appropriate for the interval bounds, we derive the model for the intervals' center and radius. A simulation study and an application with data of daily wind speed at different meteorological stations in Ireland illustrate that the proposed approach is appropriate and useful.