Short comment on some analyses of this financial crisis

There have been numerous analyses of the current (or “past”) credit crunch, comparing or contrasting it with the 1930 crash. The approach was often putting the DOW JONES time series on top of that of 1930 and discuss the similarities or dissimilarities between the two.

The problem with this approach was - I am shocked that nobody pointed it out - that the fundamental time scales have been changed. The time taken to disseminate market information has been shortened significantly, while other time scales (e.g. intervals between earnings reports, time taken to finalize an M&A deal) have been changed by a more moderate degree, although it is almost certain that all time scales have been shortened. It is hard to fathom which time scales here play a major role in today’s world of finance, but it is understandable that things ought to happen faster now - thus the comparison of stock indexes can not be apple-to-apple.

There is more to the problem. The behavior of dynamic systems is heavily affected by the lineup of its spectrum of modes, and a momentary resonance can lead to a quick breakdown of a recently stable system (to be fair - mathematically it has always been inherently chaotic). The question is, could the evolution of different time scales be the ultimate reason of a breakdown of the financial system?

MORE ON TIME SCALE ANALYSIS

In near-integrable systems, or near-integrable areas, the stability of the system depends heavily on the absence of resonances. In finance, we have this imperfect system in which resonances are multi-dimensional and impossible to capture accurately. However we may indirectly verify this claim by examing the ratio of key time scales - every time they are aligned with small-integer ratios chaos is imminent.

Note that there are two kinds of time scales: dissipative (e.g. time to absorb information) and cyclic; imaginary and real.

MORE ON THE CHAOS MODEL

I am tempted to describe the financial world by a series of elements: resources, assets, and consumption. Denomination is a problem. It is also uncertain whether we should describe the state in a classical or quantum manner. If there are N assets, is the financial space R^N or R^N×R^N? I suspect that the valuation method (i.e. value = dividend/(r-g)) also plays a role in the instability.