Statistical Distributions, Detrending, HP Filter, Bandpass Filter, Normality, Fat Tails, Time Series, Exponential-Power Density, Business Cycles Dynamics.

C1, E3

We study the impact of alternative detrending techniques on the distributional properties of U.S. output time series. We detrend GDP and industrial production time series employing first-differencing, Hodrick-Prescott and bandpass filters. We show that the resulting distributions can be approximated by symmetric Exponential-Power densities, with tails fatter than those of a Gaussian. We also employ frequency-band decomposition procedures finding that fat tails occur more likely at high and medium business-cycle frequencies. These results confirm the robustness of the fat-tail property of detrended output time-series distributions and suggest that business-cycle models should take into account this empirical regularity.