Various methods are available to extract the “business cycle component” of a given time series variable. These methods may be derived as solutions to frequency extraction or signal extraction problems and differ in both their handling of trends and noise and their assumptions about the ideal...

The econometrics literature contains a variety of two-sided tests for unknown breakpoints in time-series models with one or more parameters. This paper derives an analogous one-sided test that takes into account the direction of the change for a single parameter. In particular, we propose a sup...