Prediction Regions for Interval-valued Time Series

We approximate probabilistic forecasts for interval-valued time series by offering alternative approaches to construct bivariate prediction regions of the interval center and range (or lower/upper bounds). We estimate a bivariate system of the center/log-range, which may not be normally distributed. Implementing analytical or bootstrap methods, we directly transform prediction regions for center/log-range into those for center/range and upper/lower bounds systems. We propose new metrics to evaluate the regions performance. Monte Carlo simulations show bootstrap methods being preferred even in Gaussian systems. For daily SP500 low/high return intervals, we build joint conditional prediction regions of the return level and return volatility.