Testing for linearity of noisy stationary signals

Existing approaches (Subba Rao-Gabr, 1980 and Hinich, 1982) to nonlinear signal detection via testing for linearity of a stationary non-Gaussian time series may fail if the data are contaminated with noise. These tests are based upon the skewness function (or bicoherence) of the time series which is a constant for linear processes in the absence of any measurement noise. In this paper a modification to the Subba Rao-Gabr approach is proposed by defining a scaled skewness function based upon the data bispectrum and a bispectrum-based power spectrum estimate. Under the null hypothesis, the modified skewness function of the noisy data is a constant. It is shown that this modified skewness function satisfies all the desired properties to qualify as a test statistic for the Subba Rao-Gabr test. On the other hand modifications to the Hinich test are not obvious. Computer simulation results are presented in support of the proposed approach