Forecast performance and bubble analysis in noncausal MAR(1, 1) processes

Abstract

AbstractThis paper examines the performance of nonlinear short‐term forecasts of noncausal processes from closed‐form functional predictive density estimators. The processes considered have mixed causal–noncausal MAR(1, 1) dynamics and non‐Gaussian distributions with either finite or infinite variance. The quality of point forecasts is affected by spikes and bubbles in the trajectories of these processes, which also characterize many financial and economic time series. This is due to deformations of estimated predictive densities from multimodality during explosive episodes. We show that two‐step‐ahead predictive densities of future trajectories based on the MAR(1, 1) Cauchy process can be used as a new graphical tool for early detection of bubble outsets and bursts. The method is applied to the Bitcoin/US dollar exchange rates and commodity futures.