Dynamically Measuring Statistical Dependencies in Multivariate Financial Time Series Using Independent Component Analysis

Table 1

Example showing comparison of average computation time (in seconds) of mutual information and information coupling, when these measures are used to analyse bivariate data sets containing different number of samples (𝑛_𝑠). The approach used to estimate mutual information is based on a Parzen window based algorithm, as described in [45]. The computational cost of this algorithm is dependent on the window-size (ℎ). The values of ℎ used for the simulations are ℎ=20 for 𝑛_𝑠=10², and ℎ=100 for all other simulations. Results are obtained using a 2.66 GHz processor as an average of 100 simulations.

Computation time (sec)	𝑛𝑠=10^2	𝑛𝑠=10^3	𝑛𝑠=10^4	𝑛𝑠=10^5
Mutual information	0.0214	2.8289	17.0101	119.5088
Information coupling	0.0073	0.0213	0.0561	0.5543