A0576
Title: The fractional unobserved components model
Authors: Tobias Hartl - University of Regensburg (Germany) [presenting]
Abstract: A data-driven solution to the specification of long-run dynamics in trend-cycle decompositions is provided. A novel state-space model of form $y = x + c$ is introduced, allowing the unobserved trend to be fractionally integrated of order d, whereas c represents an unobserved stationary cyclical component. As d can take any value on the positive real line, the model allows for intermediate solutions between integer-integrated specifications and thus for richer long-run dynamics. Trend and cycle can be estimated via the Kalman filter, for which a closed-form solution is provided. The integration order d is treated as unknown and is estimated jointly with the other model parameters via the conditional sum-of-squares estimator. The asymptotic theory is derived for parameter estimation under relatively mild assumptions, showing the conditional sum-of-squares estimator to be consistent and asymptotically normally distributed. While the proofs are carried out for a prototypical model, the asymptotic theory carries over to generalizations allowing for deterministic terms and correlated innovations, but also to quasi-maximum likelihood estimation. An application to annual US carbon emissions reveals a smooth trend component starting to exhibit an inverted U-shape, together with cyclical emissions that are closely coupled to the business cycle.
