I’m continuing this week with posts about cycles and, inevitably, need to address one very popular method of extracting cycles from time series data – the Hodrick-Prescott (HP) filter.

Recently, I’ve been exploring inventory cycles, hoping to post something coherent.

I think I hit paydirt, as they say in gold mining circles.

Here is the cycle component extracted from consumer durable inventories (not seasonally adjusted) from the Census manufacturing with a Hodrick-Prescott filter. I use a Matlab implementation here called hpfilter.

In terms of mechanics, the HP filter extracts the trend and cyclical component from a time series by minimizing an expression, as described by Wikipedia –

What’s particularly interesting to me is that the peak of the two cycles in the diagram are spot-on the points at which the business cycle goes into recession – in 2001 and 2008.

Not only that, but the current consumer durable inventory cycle is credibly peaking right now and, based on these patterns, should go into a downward movement soon.

Of course, amplitudes of these cycles are a little iffy.

But the existence of a consumer durable cycle configured along these lines is consistent with the literature on inventory cycles, which emphasizes stockout-avoidance and relatively long pro-cyclical swings in inventories.