The linearity of nine long Swedish macroeconomic time series, whose business cycle properties were discussed by Englund, Persson, and Svensson (1992), is tested and rejected for all but two. Non-linear (STAR) models are estimated, and their properties are investigated. Business cycle frequency variation does not seem to be constant over time for all series; it is difficult to find a 'Swedish business cycle'. Pairwise Granger non-causality tests are adapted to the STAR case, and non-causality is tested. The results point at strong temporal interactions and indicate that the functional form (linear or STAR) strongly affects the outcome of these tests.