High-precision surrogate data based tests for Gaussianity and linearity of discrete time random processes

We have put Hinich's asymptotic tests for Gaussianity and linearity under scrutiny, and we show that these tests suffer from severe statistical problems. We propose the use of carefully designed surrogate data to ensure correct false alarm rate. Using theoretical considerations about estimation of higher order spectra, we propose new high-precision detections statistics for Gaussian and linear signals. Results from synthetic and experimental data demonstrate the applicability of the proposed tests.