The validity of trend-cycle decomposition using unobserved component model: Monte Carlo evidence

The validity of trend-cycle decomposition using the unobserved component model is examined via Monte Carlo simulations. It is shown that the nearer to the unit-root process the assumed cycle component and/or the larger the assumed innovation covariance, the more frequent the occurrence of the boundary estimate for the innovation covariance, that the nearer to the unit-root process the assumed cycle component in the case of applying the model with zero restriction on the innovation covariance, the more frequent the occurrence of a linear time trend in the trend estimation, and that a linear time trend cannot be obtained from the model without zero restriction.