Since the extensive work by Burns and Mitchell, many economists have i
nterpreted economic fluctuations in terms of business-cycle phases. Gi
ven this, we argue that, in addition usual model-selection criteria cu
rrently used in the profession, the adequacy of a univariate macroecon
omic time series model should be based on its ability to replicate two
important business-cycle features of the U.S. data-duration and ampli
tude. We propose several checks for whether univariate statistical mod
els generate business-cycle features observed in U.S. gross domestic p
roduct (GDP) and find that many popular nonlinear models for the log o
f real GDP are no better at replicating the duration and amplitude fea
tures of the data than a simple ARIMA(1, 1. 0).