I have been in the process of constructing randomly generated unemployment time series based on the dynamic equilibrium model (partially inspired by writing my qualitative analysis post). I'm still in the process of working out the parameters (or rather, the distributions the parameters are drawn from). However, the work in progress looks neat on its own.
Here's what I mean by a randomly generated time series: effectively a series of Gaussian shocks with random centers, amplitudes, and widths.
Here is the actual unemployment rate time series (red) alongside a randomly generated path (blue):
In constructing the model (still in progress), I came across some interesting mistakes. For example, if you (accidentally) use a Poisson distribution to yield integer recession transitions:
If you run it for 500 paths you get this:
And here is what happens if you use quarters:
It would be fascinating if there was some resonance with the annual cycle ... Again, this is a work in progress. I will keep you updated.