In this box you will work with the HP-filter. This is a procedure to decompose economic variables into a trend and a cycle. The HP-filter allows for a flexible time-varying trend, in contrast to imposing a constant trend over long periods of time —say, decades. Since long-term trends change (eventually), this provides a better measure of the cycles i.e. deviations from trend.

The purpose of the box is to calculate the co-movement and volatility of consumption and investment relative to GDP, all measured in real terms. For this exercise you will use table 1.1.6 from BEA.gov once again; starting in 1960:Q1 to the latest available year at a quarterly frequency. The smoothing parameter λ (lambda) for quarterly data is 1,600.