COMPARISON OF DETERMINISTIC AND STOCHASTIC PREDICTORS IN NONLINEAR-SYSTEMS WHEN THE DISTURBANCES ARE SMALL

This paper compares the deterministic and stochastic predictors of non linear 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 bia sed, there are some Monte Carlo experiments that suggest the magnitude of this bias is rather insignificant. Here, we offer a possible expla nation of the smallness of the deterministic bias. It is shown that wh en the error terms have small standard deviation, the deterministic pr edictor turns out to be asymptotically unbiased. The results are based on deriving asymptotic expansions for alternative predictors. The asy mptotic expansions carried out here are similar to the large-sample as ymptotic 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 conta ining the Box-Cox transformation.