Comparison of Deterministic and Stochastic Predictors in Nonlinear Systems When the Disturbances Are Small
研究了当扰动项标准差很小时，非线性模型中确定性预测器的渐近无偏性，解释了蒙特卡洛实验中其偏差很小的原因，并推导了包含Box-Cox变换模型的渐近偏差和均方预测误差。
This paper compares the deterministic and stochastic predictors of nonlinear models when the disturbances are small. Large-sample properties of these predictors have been analyzed extensively in the econometric literature. While the deterministic predictors are asymptotically biased, there are some Monte Carlo experiments that suggest the magnitude of this bias is rather insignificant. Here, we offer a possible explanation of the smallness of the deterministic bias. It is shown that when the error terms have small standard deviation, the deterministic predictor turns out to be asymptotically unbiased. The results are based on deriving asymptotic expansions for alternative predictors. The asymptotic expansions carried out here are similar to the large-sample asymptotic expansions; however, the expansions here are in terms of the standard deviation of the disturbance terms. The results are then used to obtain the asymptotic bias and asymptotic mean squared prediction errors of the deterministic and stochastic predictors of a model containing the Box-Cox transformation.