To gain insights in the current status of the economy, macroeconomic time series are often decomposed into trend, cycle and irregular components. This can be done by nonparametric band-pass filtering methods in the frequency domain or by model-based decompositions based on autoregressive moving average models or unobserved components time series models. In this paper we consider the latter and extend the model to allow for asymmetric cycles. In theoretical and empirical studies, the asymmetry of cyclical behavior is often discussed and considered for series such as unemployment and gross domestic product (GDP). The number of attempts to model asymmetric cycles is limited and it is regarded as intricate and nonstandard. In this paper we show that a limited modification of the standard cycle component leads to a flexible device for asymmetric cycles. The presence of asymmetry can be tested using classical likelihood based test statistics. The trend-cycle de! composition model is applied to three key U.S. macroeconomic time series. It is found that cyclical asymmetry is a prominent salient feature in the U.S. economy.
Asymmetric business cycles Unobserved Components Nonlinear state space models Monte Carlo likelihood Importance sampling