Driven IFS and Data Analysis

Traditional and Driven IFS Correlations

As a simple measure of the differences between the driven IFS of stocks X and Y, Kalla and Sobhan proposed counting the number of points N(X,Y) in different bins between X and Y. That is,

N(X,Y) = |n11(X) - n11(Y)| + |n12(X) - n12(Y)| + ... + |n44(X) - n44(Y)|

and then normalizing this count; that is, define

ρ~ = ((total number of points in X) - N(X,Y)) / (total number of points in X)

Here is how Kalla and Sobhan justify ρ~ as a measure of the similarity of the driven IFS.

Suppose the total number of points is 250. If n11(X) = 250 and n22(Y) = 250, then N(X,Y) = 500 and ρ~ = (250 - 500)/250 = -1. This is reasonable, because there is no similarity at all between the two driven IFS.

On the other hand, if both X and Y have the same number of points in each bin, then N(X,Y) = 0 and ρ~ = (250 - 0)/250 = +1. Again, this is sensible because at the level of length 2 addresses, the driven IFS are identical.

Here are the ρ~ values for these stocks.

Using ρ~, the highest correlation is between Coca-Cola and Microsoft, as suggested by the driven IFS plots.

The highest ρ value was between Nokia and Microsoft, yet their ρ~ is the fourth lowest.

Motivated by these and similar observations, Kalla and Sobhan computed the correlation between rho and ρ~, obtaining a small negative value.

Retrun to Address correlation.