Random Fractals and the Stock Market

Surrogates of the Stock Market - Trading Time Example 1

Price and Clock Time Increments

The generator has turning points (1/4, 1/2) and (3/4, 1/4), so the price and clock time increments

dY1 = 1/2 - 0 = 1/2, dt1 = 1/4 - 0 = 1/4 dY2 = 1/4 - 1/2 = -1/4, dt2 = 3/4 - 1/4 = 1/2 dY3 = 1 - 1/4 = 3/4, dt3 = 1 - 3/4 = 1/4.

It is easy to see this is not a unifractal generator: compute Hi = Log|dYi|/Log(dti).

We obtain

H1 = Log(1/2)/Log(1/4) = 0.5, H2 = Log(1/4)/Log(1/2) = 2, and H3 = Log(3/4)/Log(1/4) = 0.207519.

Return to Example 1.