Data Analysis by Driven IFS

Background - Converting time series to symbol strings

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

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{x_i: i = 1, ... , n} and

m = min{x_i: i = 1, ... , n}.

Then the range of the x_i is R = M - m and

the bin boundaries are

B₁ = m + (1/4)R,

B₂ = m + (1/2)R, and

B₃ = m + (3/4)R.

Then for each x_k of the time series, the corresponding symbol i_k is given by

i_k = 4 if B₃ <= x_k <= M

i_k = 3 if B₂ <= x_k < B₃

i_k = 2 if B₁ <= x_k < B₂

i_k = 1 if m <= x_k < B₁

We call the intervals [m, B₁), [B₁, B₂), [B₂, B₃), and [B₃, M] bin 1, bin 2, bin 3, and bin 4, respectively.

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

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