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:: 'Turbulent' Time Series ::

In 1996 Ghashghaie et al. published a letter in Nature titled 'Turbulent cascades in foreign exchange markets'. This paper discussed their findings of the similarities of financial exchange markets with hydrodynamic turbulence. In particular, they focused on the similar statistical behaviour found between the price fluctuations in market and velocity changes in turbulent flow. This is essentially the non-gaussian statistical behaviour we have already looked at.

Nature 381 (1996) 767

The figures above show, firstly (a), the PDFs of the price returns for time lags of seconds to weeks from top to bottom Once again the approach from a lepokurtic to a gaussian distribution. In figure (b), the same is done for a turbulent flow fluid with price returns analogous to the changes of log fluid velocity of neighbouring points. The separations are spatial rather than temporal, as is the case in the FX data, increasing from top to bottom. We can see the two systems exhibit similar statistical behaviour.

For the FX data this would suggest periods of stable prices followed by sudden extreme fluctuations - a property often referred to as intermittency like that seen in fluid dynamics. In turbulent flow there are periods of smooth laminar flow with irregular bursts of chaotic flow that dissipates energy. In this treatment the flow of information in the market is analogous to the energy flow in the fluid. It is thought that information passed on to the short term investors by those taking a long term position 'cascade' down rather like the large scale energy pumped into fluid flow dissipated on smaller scales.

The main breakdown of the analogy are the anticorrelations in the price fluctuations in fluids and the lack of any significant ones in markets. (Any correlations in the price fluctuations would violate the EMH). In fluid flow energy pumped into the system at large scales (e.g. by a jet engine) is dissipated at smaller scales by some form of hierarchy, thus the general tendency will be for neighbouring points in the fluid restore laminar flow. In that sense, the market is a much more 'open' system.

Written by Alessio Farhadi

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