  We develop a generalization of correlated trend-cycle decompositions that
avoids prior assumptions about the long-run dynamic characteristics by
modelling the permanent component as a fractionally integrated process and
incorporating a fractional lag operator into the autoregressive polynomial of
the cyclical component. The model allows for an endogenous estimation of the
integration order jointly with the other model parameters and, therefore, no
prior specification tests with respect to persistence are required. We relate
the model to the Beveridge-Nelson decomposition and derive a modified Kalman
filter estimator for the fractional components. Identification, consistency,
and asymptotic normality of the maximum likelihood estimator are shown. For US
macroeconomic data we demonstrate that, unlike $I(1)$ correlated unobserved
components models, the new model estimates a smooth trend together with a cycle
hitting all NBER recessions. While $I(1)$ unobserved components models yield an
upward-biased signal-to-noise ratio whenever the integration order of the
data-generating mechanism is greater than one, the fractionally integrated
model attributes less variation to the long-run shocks due to the fractional
trend specification and a higher variation to the cycle shocks due to the
fractional lag operator, leading to more persistent cycles and smooth trend
estimates that reflect macroeconomic common sense.
