A Steady State Approach to Trend / Cycle Decomposition

This paper presents a new approach to trend/cycle decomposition. The trend of an integrated time series is measured as the conditional expectation of the steady-state level of the series, where steady state is determined by simulation from an appropriate forecasting model. By explicitly linking the trend component to the concept of steady state, our method can produce different results from the long-horizon forecast decomposition introduced by Beveridge and Nelson (1981) and extended to nonlinear forecasting models by Clarida and Taylor (2003). We demonstrate the advantages of the steady-state approach by considering the trend/cycle decomposition of integrated time series generated from regime-switching processes. We then apply our approach to estimate the trend and cycle of U.S. real GDP. Our findings portray a very different picture of the business cycle than implied by standard linear forecasting models