Permanent components in seasonal variables

We propose considering a seasonal time series as the realization of a s-variate stochastic process, s being the seasonal periodo In this paper we propose a test statistic for the hypothesis of a univariate versus a multivariate representation of seasonality. We find evidence against the more standard univariate representation for some key variables of the U.S. economy. When a VAR representation is chosen for each of these variables and its residuals are properly orthogonalized, forecasting perfomance is improved, relative to univariate ARIMA models. Also, a Permanent-Transitory decomposition of each variable reveals that permanent components exhibit important seasonal fluctuations. This supports the view that seasonality should be considered as an integral part of agents' decision-making