ForEx Analysis

"One way to look at the economy, the standard way in fact, is to view it in physical terms as a collection of activities, technologies, and needs, all interacting through a market system peopled by decision-making agents such as firms, banks, consumers and investors. A very different way ... would be to view the economy in psychological terms: as a collection of beliefs, anticipations, expectations and interpretations; with decision-making and strategizing and action-taking predicated upon these beliefs and expectations." W. Brian Arthur (Citibank Professor, Santé Fe Institute and Morrison Professor of Economics and Population studies, Stanford University) in his introduction to "Complexity in Economic and Financial Markets."

In 1996 I experimented with Foreign Exchange data where these graphs were produced (see below). At the time this was a fluke and without a rigorous mathematical explanation. At that time I had no clear set of metrics to methodically explore these complex algorithms - just a hunch that the crowd was reacting to the financial environment in the same way that crowds react to physical environment.

News of this development featured in an article in the Economist (13th April 1996), on the front page of the Sunday Times in (7th July 1996), and featured in a TV Broadcastlater that same year (August 1996).

Recent developments (June 2008) have led to a clearer understanding of the strange attractors and phase projections for this crowd dynamic.

The basic structure of the phase diagrams and the projection system is shown in the diagram below

Below are a sample of the projections (red) against the actual - these are six months worth of data for 1992, 1993, 1994 (a, b and c), 1995 and 1996.

Clarity

Each of these projections were produce 3 months ahead of the dollar/yen prices.

I've been asked many times over the year "How can this be the case?"

I'm using spot data only but passing through a coupled nonlinear oscillator which is, in effect, extracting the strange attractors out of the data. Projecting that forward using multiple projections and then a superposition algorithm that shows the underlying flocking dynamic of the traders activity.

This isn't simple stuff and involves three processes, a filter, a coupled nonlinear oscillator and finally a superposition algorithm, however the complete algorithm is only a dozen or so lines of code.

yen-92-P

1992 - 9 months of Dollar/Yen predicted 3 months ahead (red) and shown against the actual price movements (black)

yen-93-P

1993 - 9 months of Dollar/Yen predicted 3 months ahead (red) and shown against the actual price movements (black)

yen-94b-P

1994 - 9 months of Dollar/Yen predicted 3 months ahead (red) and shown against the actual price movements (black)

yen-95-P

1995 - 9 months of Dollar/Yen predicted 3 months ahead (red) and shown against the actual price movements (black)

yen-96-P

1996 - 9 months of Dollar/Yen predicted 3 months ahead (red) and shown against the actual price movements (black)

A paper (A New Test for Chaos - July 2002) provided a further clue to the phase locked behaviour of the dynamical system and the future price of the foreign exchange spot prices. An article on Strange Nonchaotic Attractors and the KAM Standard Map papers also provide further insight. However it was re-formulating the algorithms and classifying each element (symplectic integrators) that provided the final pieces of the jigsaw.

The top trace is a display of the tick data (tick-by-tick). The bottom trace is the XenoFractal projection

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