Summary
International Symposium on Nonlinear Theory and its Applications
2005
Session Number:3-1-4
Session:
Number:3-1-4-5
Nonparametric Rank Test for Nonlinearity Detection
Xiaodong Luo, Jie Zhang, Michael Small,
pp.642-645
Publication Date:2005/10/18
Online ISSN:2188-5079
Summary:
In this report we propose a rank test scheme to detect the potential nonlinearity in a scalar time series. Our scheme is based on the fact that, for a stationary linear stochastic process with jointly symmetric innovations, it proves that its ordinary least square (OLS) prediction error of linear autoregressive (AR) predictors are symmetric about zero. With this knowledge, a discriminating statistic, namely the Wilcoxon signed rank statistic, can be derived from the prediction error. The advantage of this statistic is that it has a known null distribution, thus we can perform statistical inference of the underlying system with exact confidence level. In addition, the exactness of the null distribution of the rank statistic does not depend on the sample size, which is usually not possessed by many other discriminating statistics such as the correlation dimension. To illustrate the discriminating power of the test scheme, we examine several examples through our methods.