A simple approach to standardized-residuals-based higher-moment tests

► We propose a simple approach to higher-moment tests for distribution, symmetry, or independence hypothesis. ► Our approach purges the estimation effect using the first and second moments of the standardized residuals. ► Our tests are simple and invariant to various conditional mean-and-variance models. ► Examples include skewness-kurtosis tests, characteristic-function-based tests, and Value-at-Risk tests. ► Simulation and empirical example show the validity of our approach.