Warp statistics and financial returns

ABSTRACT

We introduce a new approach to financial returns and data analysis based on an infinite family of statistics called warp statistics. These statistics provide evidence that certain distributions such as the stable distributions are not good models for the financial returns from various securities or indexes like the S&P 500 and the Dow Jones. As statistics for general random variables, these numbers often appear to converge in simulations and we give several examples where the reciprocal of the first warp statistic appear to converge to the Hausdorff dimension. For any normal random variable, simulations suggest that the first and second warp statistics are $4/\pi$ and $-1$ which provides new goodness of fit tests for normality. We give explicit formulas for the first and second warp statistics that are easily evaluated by a computer which makes this theory particularly suitable for applications.

KEYWORDS:

• Financial mathematics
• stochastic process
• Hausdorff dimension
• spatial statistics
• fractal analysis
• warp statistics
• tangible process

1991 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 91G70
• Secondary: 28A78

Disclosure statement

No potential conflict of interest was reported by the authors.