Time series decomposition and measurement of business cycles, trends and growth cycles

A study of business cycles does not require trend estimation and elimination, but a study of growth cycles does. Major cyclical slowdowns and speedups deserve to be analyzed, but the needed time series decomposition presents difficult problems, mainly because trends and cycles influence each other. We compare cyclical movements in levels, deviations from trend, and smoothed growth rates for both the quarterly real GDP and the monthly U.S. Coincident Index—using the phase average trend (PAT). Then we compare alternative trend estimates, deterministic and stochastic, linear and nonlinear, and the corresponding series of deviations from these trends. We discuss how the resulting estimates differ for U.S. growth cycles in the post-World War II period. The results of PAT show great similarity to the results obtained with the Hodrick–Prescott, local linear trend, band-pass filtering methods.