Testing for linearity of noisy stationary signals

Existing approaches 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 and Gabr (1980) 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 and Gabr test. On the other hand modifications to the Hinich (1982) test are not obvious. Computer simulation results are presented in support of the proposed approach