HOS or SOS for parametric modeling?

Parametric models obtained via second-order statistics (SOS) are appropriate when the available stationary data are linear, Gaussian, and time-reversible. On the other hand, evidence of nonlinearity, non-Gaussianity, or time-irreversibility favors the use of higher-order statistics (HOS). To quantify normality and time-reversibility, and thus resolve the title question, consistent, time-domain statistical tests are developed and analyzed in a Neyman-Pearson framework. The novel test statistics are computationally attractive and streamlined towards parametric modeling because they employ the minimal HOS lags which uniquely characterize autoregressive moving-average processes. Simulations illustrate the performance of the proposed tests.