The BDS statistic and residual test

The conventional nonparametric tests have been widely used in many fields for the residual analysis of a fitted model on observations. Also, in recent, a new technique called the BDS (Brock-Dechert-Scheinkman) statistic has been shown that it can be used as a powerful tool for the residual analysis, especially, of a nonlinear system. The purpose of this study is to compare the powers of the nonparametric tests and BDS statistic by residual analysis of the fitted models. This study evaluates stochastic models for four monthly rainfalls in Korea through the residual analysis by using the conventional nonparametric and BDS statistics. We use SARIMA and AR Error models for fitting each rainfall and perform the residual analysis by using the test techniques. As a result, we find that the BDS statistic is more reasonable than the conventional nonparametric tests for the residual analysis and AR Error model may be more appropriate than SARIMA model for modeling of monthly rainfalls.