A test of symmetry based on L-moments with an application to the business cycles of the G7 economies

We study the performance of tests of distributional symmetry based on the coefficient of skewness and on L-moments and present a bootstrap implementation of such tests that is suitable in time series applications. We show with Monte Carlo simulations that both tests are correctly sized – provided that their null distribution is approximated with the bootstrap – and that the procedure based on L-moments has more power than that based on the conventional coefficient of skewness. An empirical application analyses the symmetry of business cycles for the G7 countries implementing tests of symmetry as tools to investigate time reversibility.