  A new model for general cyclical long memory is introduced, by means of
random modulation of certain bivariate long memory time series. This
construction essentially decouples the two key features of cyclical long
memory: quasi-periodicity and long-term persistence. It further allows for a
general cyclical phase in cyclical long memory time series. Several choices for
suitable bivariate long memory series are discussed, including a parametric
fractionally integrated vector ARMA model. The parametric models introduced in
this work have explicit autocovariance functions that can be used readily in
simulation, estimation, and other tasks.
