Scaling, correlations, and cascades in finance and turbulence

✍ Scribed by Joseph L. McCauley

• Book ID: 104340963
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 137 KB
• Volume: 329
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/s0378-4371(03)00590-9

✦ Synopsis

The question of information cascades in ÿnance appears in the literature. We use the dynamics of Kolmogorov's 1962 (K62) turbulence model, an example of multia ne scaling, to illustrate how evidence for di usion from large to small length scales, or correspondingly an information cascade from large to small times in ÿnance, could be inferred from a certain multia ne scaling exponent. As an alternative to the derivations given by Kolmogorov, Onsager, and Heisenberg, we also show how to derive the K41 model from 'time' reversible dynamics. We then discuss and compare ÿve di erent analyses of ÿnance data by econophysicists, including one where the information cascade was suggested. We explain why there is as yet no compelling evidence for an information cascade in ÿnance. We point out the di erent ÿnance data analyses are largely in disagreement with each other, and suggest the use of a stronger condition in data analysis in order to resolve the di erences. We observe that errors are incurred for large returns by using price di erences instead of the logarithmic return, which is a dimensionless, additive variable.