A general test for univariate seasonality

We propose a general test for univariate seasonality. Starting from a multivariate model for the seasons. some constraints must hold both, on the covariance matrix of the innovations, as well as among coefficients across equations, for a univariate representation of seasonality to be appropriate. Appied to a set of 23 U.K. macroeconomic variables, our test shows that a multivariate representation of seasonality should be preferred in at least 8 cases.