Instability in smooth and quantized models

Things that are unsustainable will not be sustained. Who said that?

In smooth world the time series oscillates in ever larger amplitudes. In quantized world transactions get larger and more frequent. On the yield curve we get an inversion. In the real economy some warehouses almost go empty. Then it breaks, mainly by shortening the supply lines in the real economy.

In the smooth world, there is a bell curve underlying support of the observed yield curve, this bell curve peaks at a stationary point, in distribution, where inventory is growing. That bell curve can shift, spread, and narrow. It defines the drunkards walk in economics. In smooth world, a Guassian walk in time converts into a gaussian spread on the yield. But we only see an obscured view of the smooth distribution, the complete curve. The tendency of this bell curve is to move toward zero, a balance between growth and decay. It takes energy to keep this bell curve shifted left on the yield axis.

In the quantized world there are sparse solutions, a finite set of points along the X axis where the short end of yield meets the noise, call that the bandwidth in the smooth world. In the quantized world we have quantized values of quants. In the real economy it shows up as a limited set of cargo sizes available.