Original Blog Entry: Hurst and Lyapunov exponents

edge — Tue, 16 Jun 2009 02:19:18 GMT

Planning to start estimating these exponents using various data points in lottery time series (starting with mega lottery).

Hurst exponent (H) determines the rate of chaos

Lyapunov exponent (L) determines the rate of predictability

In addition Hurst exponent can distinguish fractal from random time series, or find the long memory cycles.

Will codify both exponents as C++ classes that are generic enough to analyze any data points in lottery time series (ie frequency/number transitions but also others)

If a Hurst exponents is evaluated to a fractal dimension in a lottery time series (key in all this endavour) we will be able to find an attractor and via Lyapunov exponent and multi-fractal and L-variable fractal analysis (the superfractal) try to approximate (an eventually predict) its chaotic orbits

For a nice and short explanation on both exponents see ref.1

References:

1. Energy Time Series and Chaos: http://www.iqnet.cz/dostal/CHA2.htm

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