Driven IFS and Financial Cartoons

Background

Though there are others, here we describe two methods for converting a time series {x1, x2, ... , xn} into a symbol string {i1, i2, ... , in}.

One method is called equal size bins, the other equal weight bins. More methods will be presented in the sample.

For equal size bins, begin by finding M = max{x1, ... , xn} and m = min{x1, ... , xn}.

Then the range R of {x1, ... , xn} i

R = M - m

and the bin boundaries are

B3 = m + (3/4)R, B2 = m + (1/2)R, and B1 = m + (1/4)R.

Then for each xk of the time series, the corresponding symbol ik is given by

ik = 4 if B3 <= xk <= M ik = 3 if B2 <= xk < B3 ik = 2 if B1 <= xk < B2 ik = 1 if m <= xk < B1

We call the intervals

[B3, M] is bin 4, [B2, B3) is bin 3, [B1, B2) is bin 2, and [m, B1) is bin 1.

For equal weight bins, select the bin boundaries B1, B2, and B3 so that each bin contains one-quarter of the xk.

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