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 and among coefficients across equations, for a univariate representation of seasonality to be appropriate. Applied to a set of 23 UK macroeconomic variables, our test shows that a multivariate representation of seasonality should be preferred in at least eight cases. This introduces a serious questioning of standard univariate filters to estimate the seasonal component in some economic time series, and suggests the possibility of a more complex but richer way of characterizing relationships among seasonal economic variables.