Prediction regions for interval‐valued time series (replication data)

After fitting a possibly non-Gaussian bivariate vector autoregression (VAR) model to the center/log-range system, we transform prediction regions (analytical and bootstrap) for this system into regions for center/range and upper/lower bounds systems. Monte Carlo simulations show that bootstrap methods are preferred according to several new metrics.

For daily S&P 500 low/high returns, we build joint conditional prediction regions of the return level and volatility. We illustrate the usefulness of obtaining bootstrap forecasts regions for low/high returns by developing a trading strategy and showing its profitability when compared to using point forecasts.