Random Fractals and the Stock Market

Surrogates of the Stock Market - Trading Time Example 2

Trading Time Generator

To find the trading time generator, first we solve
1 = |dY1|D + |dY2|D + |dY3|D = 0.7D + 0.3D + 0.6D.
The Mathematica command is
FindRoot[0.7^D + 0.3^D + 0.6^D == 1,{D,1}]
The approximate solution is D = 1.87638.
With this value of D we find the trading time generators dT1, dT2, and dT3:
dT1 = |dY1|D = 0.71.87638 = 0.512090
dT2 = |dY2|D = 0.31.87638 = 0.104443
dT3 = |dY3|D = 0.61.87638 = 0.383467
Here is the trading time-clock time generator. The turning points of the generator are
(dt1, dT1) = (0.2, 0.512909) and
(dt1, dT1) + (dt2, dT2) = (0.6, 0.616533)

Return to Example 2.