Specification tests for non-Gaussian structural vector autoregressions

We propose specification tests for independent component analysis and structural vector autoregressions that assess the cross-sectional independence of non-Gaussian shocks by comparing their joint cumulative distribution with the product of their marginals at both discrete and continuous grids of argument values, the latter yielding a consistent test. We explicitly consider the sampling variability from computing the shocks using consistent estimators. We study the finite sample size of resampled versions of our tests in simulation exercises and show their non-negligible power against a variety of empirically plausible alternatives. Finally, we apply them to a dynamic model for three popular volatility indices.