Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series

Abstract

This paper develops a set of approximate band-pass filters designed for use in a wide range of economic applications. In particular, we design and implement a specific band-pass filter which isolates business-cycle fluctuations in macroeconomic time series. This filter was designed to isolate fluctuations in the data which persist for periods of two through eight years. This filter also 'detrends' the data, in the sense that it will render stationary time series that are integrated of order two or less, or that contain deterministic time trends. We apply our filter to several of the key macroeconomic time series, and describe the picture of the U.S. postwar business cycle that emerges from our analysis. We also provide detailed comparisons with several alternative detrending methods.