Bootstrap based multi-step ahead joint forecast densities for financial interval-valued time series

Abstract

This study presents two interval-valued time series approaches to construct multivariate multi-step ahead joint forecast regions based on two bootstrap algorithms. The first approach is based on fitting a dynamic bivariate system via a VAR process for minimum and maximum of the interval while the second approach applies for mid-points and half-ranges of interval-valued time series. As a novel perspective, we adopt two bootstrap techniques into the proposed interval-valued time series approaches to obtain joint forecast regions of the lower/upper bounds of the intervals. The forecasting performances of the proposed approaches are evaluated by extensive Monte Carlo simulations and two real-world examples: (i) monthly S&P 500 stock indices; (ii) monthly USD/SEK exchange rates. Our results demonstrate that the proposed approaches are capable of producing valid multivariate forecast regions for interval-valued time series.