On periodic correlations between estimated seasonal and nonseasonal components for US and German unemployment

The orthogonality assumption of seasonal and nonseasonal components for official quarterly unemployment figures in Germany and the US is examined. Although nonperiodic correlations do not seem to reject the orthogonality assumption, a periodic analysis based on correlation functions that vary with the seasons indicates the violation of orthogonality. The unadjusted data can be described by periodic autoregressive models with a unit root. In simulations, the empirical findings for the German data are replicated, where simple models are used to generate artificial samples. Multivariate seasonal adjustment leads to large periodic correlations. Additive adjustment leads to smaller ones.