Random Fractals and the Stock Market

Surrogates of the Stock Market - Trading Time Example 1

Trading Time Generator

To find the trading time generator, first we solve

1 = |dY1|D + |dY2|D + |dY3|D = 0.5D + 0.25D + 0.75D.

The Mathematica command is

FindRoot[0.5^D + 0.25^D + 0.75^D == 1,{D,1}]

The approximate solution is D = 1.73051.

With this value of D we find the trading time generators dT1, dT2, and dT3:

dT1 = |dY1|D = |.5|1.73051 = 0.301345, dT2 = |dY2|D = |.25|1.73051 = 0.0908091, and dT3 = |dY3|D = |.75|1.73051 = 0.607844.

Here is the trading time-clock time generator.

Return to Example 1.