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

Figure 2

(a) Temporal variation of information coupling, 𝜂(𝑡), plotted as a function of time. Step changes in coupling are visible after every 8000 time steps; that is, 𝜌_TC=0.2 when 𝑡=1 : 8000, 𝜌_TC=0.4 when 𝑡=8001 : 16000, 𝜌_TC=0.6 when 𝑡=16001 : 24000, and 𝜌_TC=0.8 when 𝑡=24001 : 32000. Also plotted are the median, [𝜂(𝑡)]_median, and the 5% and 95% confidence interval contours, [𝜂(𝑡)]^95%_5%. (b) Normalised empirical pdf plots for information coupling (𝜂), linear correlation (𝜌), and rank correlation (𝜌_𝑅). The vertical lines represent the true correlation (𝜌_TC) values. The relative accuracy of the information coupling measure is evident from these results.

(a)

(b)