Moment tests of independent components

We propose simple specification tests for independent component analysis and structural vector autoregressions with non-Gaussian shocks that check the normality of a single shock and the potential cross-sectional dependence among several of them. Our tests compare the integer (product) moments of the shocks in the sample with their population counterparts. Importantly, we explicitly consider the sampling variability resulting from using shocks computed with consistent parameter estimators. We study the finite sample size of our tests in several simulation exercises and discuss some bootstrap procedures. We also show that our tests have non-negligible power against a variety of empirically plausible alternatives.

Automated summary

The study proposes simple specification tests for independent component analysis and structural vector autoregressions with non-Gaussian shocks to check the normality of shocks and potential cross-sectional dependence. The tests compare integer moments of shocks in the sample with their population counterparts while considering sampling variability. The tests show non-negligible power against empirically plausible alternatives.