Zero-Centered Bins

While there is no reason to think 0 holds any special importance for the data set

y₁, y₂, ..., y_N,

it may for the first differences

y₂ - y₁, y₃ - y₂, ..., y_N - y_N-1.

For instance, a positive first difference means the data values are increasing, a negative first difference means the data values are decreasing. This has clear significance for financial data.

Take B₂ = 0, and in the absence of other information, take B₁ and B₃ symmetrically spaced about B₂ = 0.

Usually express B₁ and B₃ as a fraction of the range of the differences.

Here is a time series generated by the logistic map, and the driven IFS produced using zero-centered bins.

Return to Coarse-Graining.