Random Fractals and the Stock Market

Surrogates of the Stock Market - Trading Time Example 2

Price and Clock Time Increments

The generator has turning points (0.2, 0.7) and (0.6, 0.4), so the price and clock time increments

dY1 = 0.7 - 0 = 0.7, dt1 = 0.2 - 0 = 0.2 dY2 = 0.4 - 0.7 = -0.3, dt2 = 0.6 - 0.2 = 0.4 dY3 = 1 - 0.4 = 0.6, dt3 = 1 - 0.6 = 0.4.

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

H1 = Log(0.7)/Log(0.2) = 0.221615, H2 = Log(0.3)/Log(0.4) = 1.31396, and H3 = Log(0.6)/Log(0.4) = 0.557493.

Return to Example 2.