Seventh Homework Set Answers

1. (a) From the picture of the generator, we compute

dY1 = 0.5, dY2 = -0.25, dY3 = 0.25, dY4 = 0.5

dt1 = dt2 = dt3 = dt4 = 0.25

(b) All the dti are equal, not all the dYi are equal, so not all the Hi = log(|dYi|)/log(dti) are equal. Consequently, this generator is multifractal.

(c) To find the Trading time generators, first solve the equation

|dY1|D + |dY2|D + |dY3|D + |dY4|D = 1

Here this becomes

.5D + .25D + .25D + .5D = 1

The solution is D = 1.45

Then the Trading time generators are dTi = |dYi|D. That is,

dT1 = dT4 = .51.45 = 0.366   and   dT2 = dT3 = .251.45 = 0.134

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