We 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.

中文翻译：

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扩散过程中经偏差校正的估计量的样本外性能

我们调查了最近在Ornstein–Uhlenbeck过程的文献中出现的六个偏差校正估计量的样本外预测性能：朴素估计量，Tang and Chen估计量，Bao等。估计器，自举估计器，Wang等。估计器，以及基于Euler方法的自举估计器，以及基准最小二乘（LS）估计器。我们的蒙特卡洛模拟表明，除Bao等人外，偏差校正后的估计量。估计器产生的样本外预测性能比LS估计器差得多，因为当真实值接近零时，这些其他估计器倾向于生成均值回归参数的负估计。但是，如果我们将所有这些估算器（包括LS估算器）的下限设置为零，只要真实均值回归参数不是很大，所有经过偏差校正的估计量都会改善LS估计量的样本外预测性能。这些主要结果也适用于Cox–Ingersoll–Ross工艺。我们的实际数据应用证实了这些总体发现。