Modeling Cyclical Behavior with Differential-Difference Equations in an Unobserved Components Framework

This paper considers a continuous time unobserved components model in which the cyclical component follows a differential-difference equation whereas the trend and seasonal components follow more standard differential equations. Estimation of the parameters of the model with either a stock or a flow variable is analyzed using a frequency domain Gaussian estimator whose asymptotic properties are derived paying particular attention to the role of a truncation parameter that arises in the practical computation of the spectral density function. The results of a simulation exercise, which assesses the finite sample performance of the estimator, are also provided.