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

We examine the orthogonality assumption of seasonal and nonseasonal components for official quarterly unemployment figures in Germany and the United States. 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. we find that the unadjusted data can be described by periodic autoregressive models with a unit root. In simulations we replicate the empirical findings for the German data, where we use these simple models to generate artificial samples. Multiplicative seasonal adjustment leads to large periodic correlations. Additive adjustment leads to smaller ones.