Friday, August 7, 2015

The H-P Filter and Unit Roots

The Hodrick-Prescott (H-P) filter is widely used for trend removal in economic time-series, and as a basis for business cycle analysis, etc. I've posted about the H-P filter before (e.g., here).

There's a widespread belief that application of the H-P filter will not only isolate the deterministic trend in a series, but it will also remove stochastic trends - i.e., unit roots. For instance, you'll often hear that if the H-P filter is applied to quarterly data, the filtered series will be stationary, even if the original series is integrated of order up to 4.

Is this really the case?

Let's take a look at two classic papers relating to this topic, and a very recent one that provides a bit of an upset.