Do Keynesians understand the Yield Curve?

My hordes of readers know that I come from a signal processing background, adaptive linear filters and minimum variance equilibrium. So, coming to economics I had to ultimately see the real Yield Curve as a measured output of the system. The Yield Curve is really a partial Fourier Transform with the negative terms hidden.

What does this mean for the investor? Well, the first point is that the investor is watching two things, the planned growth of an investment, the upper left quardant of Fourier and the risk of reversal, the negative right side terms. The investor is publicly told about proposed positive growth, and analysts fill in the potential for reversal in the investment. But we only publish measured positive growth.

The yield curve, in frequency space is a Normal distribution of frequencies, a bell shape. The result derives from the minimum phase condit6ion which says that at equilibrium inventory levels are minimum. The investor sees the published right side of this distribution and has to individually estimate the negative terms on his/her own. That is the key to investing, and good investors do it automatically with out realizing they are performing a Fourier Transform.

Looking at Yield from frequency space rather than term space is instructive. The shortest possible term is overnight, and that has a frequency of 365. The update frequency of the central bank is 4, equivalent to 3 months. The signal between 365 and 4 is generally noise. So in frequency space the string is truly long.

Now Kling says that we are mostly in a liquidity trap, Krugman says a liquidity trap is unusual. The realdefinition is that the economy is never in a liquidity trap, it always measures the Yield Curve, either the bankers yield curve or the shoelace yield curve, it is always measured.

So what to they mean by liquidity trap? They mean that the point at which the shortest term on the bankers Yield meets the noise floor on the X axis. That point represents the bandwidth of the Central Banker, and that bandwidth is generally about three months, allowing the central bank to track economic movements on scales longer than six months (bandwidth is 1/2 the sample rate). That point, where the noise floor and the shortest term meet always exists if the economy exists. We are never in a liquidity trap, there is always a bandwidth point at which the central bank is effective.

What does this mean for the Taylor rule? The Taylor rule is likely the best norm for meeting Congressional dictate, but is will be cyclic. The only equilibriating response is for the Fed to select the sample rate it needs by noting where the short term meets the noise floor. Then in frequency space, make that term interest rate fill in the nominal Bell Shape we need from the yield curve, and ignore Congress in the process.