  We design a novel, nonlinear single-source-of-error model for analysis of
multiple business cycles. The model's specification is intended to capture key
empirical characteristics of business cycle data by allowing for simultaneous
cycles of different types and lengths, as well as time-variable amplitude and
phase shift. The model is shown to feature relevant theoretical properties,
including stationarity and pseudo-cyclical autocovariance function, and enables
a decomposition of overall cyclic fluctuations into separate frequency-specific
components. We develop a Bayesian framework for estimation and inference in the
model, along with an MCMC procedure for posterior sampling, combining the Gibbs
sampler and the Metropolis-Hastings algorithm, suitably adapted to address
encountered numerical issues. Empirical results obtained from the model applied
to the Polish GDP growth rates imply co-existence of two types of economic
fluctuations: the investment and inventory cycles, and support the stochastic
variability of the amplitude and phase shift, also capturing some business
cycle asymmetries. Finally, the Bayesian framework enables a fully
probabilistic inference on the business cycle clocks and dating, which seems
the most relevant approach in view of economic uncertainties.
