Seventh Homework Set Answers

12. (a) All the clock time increments are dti = 0.2, and the price increments are
dY1 = 0.7, dY2 = -0.3, dY3 = 0.3, dY4 = -0.1, dY5 = 0.4
because some of the |dYi| are different and all the dti are equal, not all of the Log|dYi|/Log(dti) are equal and so the cartoon is multifractal.
(b) First, find the exponent D satisfying
|dY1|D + |dY2|D + |dY3|D + |dY4|D + |dY5|D = 1
Substituting in the values of dYi gives
0.7D + 0.3D + 0.3D + 0.1D + 0.4D = 1
Solving numerically gives D ≈ 1.747
Then the trading time generators are given by dTi = |dYi|D. This gives
dT1 ≈ 0.536, dT2 = dT3 ≈ 0.122, dT4 ≈ 0.018, dT4 ≈ 0.202

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