A new approach to testing Gaussianity with the characteristic function

The use of an alternative to the kernel characteristic function estimator and empirical characteristic function based Gaussianity tests, has been proposed. It uses a smoothed difference function found by applying a smoothing kernel to the difference between the empirical characteristic function and the characteristic function under H₀ . After an investigation into the choice of test statistics, an omnibus test is proposed that is powerful against a wide range of alternatives. Different test statistics are proposed to increase power against symmetric and/or asymmetric alternatives. Simulations are performed, confirming the increased power due to the smoothed difference function, as well as the rationale behind the choice of test statistics