Thursday, December 8, 2011

Confidence Bands for the Hodrick-Prescott Filter

Signal extraction is a common pastime in empirical economics. When we fit a regression model we're extracting a signal about the dependent variable from the data, and separating it from the "noise". When we use the Hodrick-Prescott (HP) filter to extract the trend from a time-series, we're also engaging in signal extraction. In the case of a regression model we wouldn't dream of reporting estimated coefficients without their standard errors; or predictions without confidence bands. Why is it, then, that the trend that's extracted using the HP filter is always reported without any indication of the associated uncertainty?