The books dollar-Deutschemark tests report multifractal scaling over a bounded interval of observation scales, with short-horizon microstructure and long-horizon attenuation of wildness producing crossovers.

groundsUntitled source

More importantly, the multifractal model successfully predicts what the data show, that at short time frames prices vary wildly, and at longer time frames they start to settle down. Putting the model to work. but enough of theory. How do you use these ideas as a real-world financial tool? First, the equations need to feed into a computer model. The model must work two ways, forward and backward. Forward means that we should be able to construct artificial price charts from the fractal seeds, just as we did with the cartoons. Backward means that we should be able to take raw price data, analyze it on our computers, and estimate the key parameters that the multifractal model requires. Then, using those values, we should be able to tell the computer to reconstitute the market, to generate an artificial price series that differs from the real one, but follows the same statistical pattern.

groundsUntitled source

In the late 1990s, the first tests of the model's applicability were conducted in the doctoral dissertations of two of my Yale students, Laurent Calvet and Adlai Fisher, now teaching at, respectively, Harvard University and the University of British Columbia. We focused on the global market for Dollar-Deutsch-Mark exchange. It, like cotton, has special appeal to an economist. Its volume is huge, its significance to the global economy is great, and its records are long, copious, reliable, and easily available. We used the real data of Real Marketplace, tick-by-tick records, from thousands of trading screens across the world, of the live quotes posted by banks and other major currency traders. These data, gathered and stored by a Zurich consulting firm, Olson & Associates, focused on a one-year period from autumn 1992 to autumn 1993. 1,472,241 prices in all. For easier comparison with other economic research, we also looked at a conventional data set.