Asymmetric cycles in unobserved components models

A class of structural time series models with an asymmetric cyclical component is presented and used in order to test for asymmetry in economic time series. The asymmetric cycle is defined as a sine-cosine wave where the frequency of the cycle depends on past observations of the stochastic process being modelled. Due to the conditional Gaussianity of the model, Kalman filtering techniques can be used in the estimation of the parameters, and a standard test for equality of cyclical frequency can be used as a symmetry test. Applying the test to US economic time series reveals strong cyclical asymmetries in unemployment and industrial production, and no significant deviation from symmetry in GDP. The test is also applied to industrial production data in EU countries, with mixed results.