Exact nonparametric inference for detection of nonlinearity

We propose an exact nonparametric inference scheme for the detection of nonlinearity. The essential fact utilized in our scheme is that, for a linear stochastic process with jointly symmetric innovations, its ordinary least square (OLS) linear prediction error is symmetric about zero. Based on this viewpoint, a class of linear signed rank statistics, e.g. the Wilcoxon signed rank statistic, can be derived with the known null distributions from the prediction error. Thus one of the advantages of our scheme is that, it can provide exact confidence levels for our null hypothesis tests. Furthermore, the exactness is applicable for finite samples. We demonstrate the test power of this statistic through several examples.