Out‐of‐sample performance of bias‐corrected estimators for diffusion processes

Abstract

AbstractWe investigated the out‐of‐sample forecasting performance of six bias‐corrected estimators that have recently emerged in the literature for the Ornstein–Uhlenbeck process: the naïve estimator, the Tang and Chen estimator, the Bao et al. estimator, the bootstrap estimator, the Wang et al. estimator, and the bootstrap estimator based on the Euler method, along with the benchmark least squares (LS) estimator. Our Monte Carlo simulations illustrated that the bias‐corrected estimators, except for the Bao et al. estimator, produced much worse out‐of‐sample forecasting performance than the LS estimator because these other estimators have a tendency to generate negative estimations of the mean reversion parameter when the true value is close to zero. However, if we set a zero lower bound to all of these estimators, including the LS estimator, all the bias‐corrected estimators improved the out‐of‐sample forecasting performance of the LS estimator as long as the true mean reversion parameter was not very large. These main results also hold for the Cox–Ingersoll–Ross process. Our real data applications confirmed these overall findings.