Causality in Time Series - ClopiNet

Popescuβ > 0 y C,i =x N,i =⎡K∑︁k=1⎢⎣⎡K∑︁k=1⎢⎣a 11 0 0a 12 a 22 0 y⎤⎥⎦ C,i−k + w C,i (39)0 0 a 33 C,ka 11 0 00 a 22 0 x⎤⎥⎦ N,i−k + w N,i0 0 a 22 N,ky N,i = Bx N,i (40)x D,i =⎡K∑︁k=1⎢⎣a 11 0 a 130 a 22 a 23 x⎤⎥⎦ D,i−k + w D,i0 0 a 22 D,ky MC = (1 − |β|)y N + |β|y C‖y N ‖ F‖y C ‖ F(41)y DC = (1 − χ )y MC + χ y D‖y MC ‖ F‖y D ‖ F(42)The Table 3, similar to the tables in the preceding section, shows results for allusual methods, except for PSIpartial which is PSI calculated on the partial coherenceas defined above and calculated from Welch (cross-spectral) estimators in the case ofmixed noise and a common driver.Table 3: TRIPLES: Commonly driven, additive mixed colored noiseMax. Accuracy TP , FP< 0.10100 500 1000 5000 100 500 1000 5000Ψ p 0.53 0.61 0.71 0.75 0.12 0.31 0.49 0.56Ψ 0.54 0.60 0.70 0.72 0.10 0.25 0.40 0.52CSI 0.51 0.60 0.69 0.76 0.09 0.27 0.38 0.45PDC 0.55 0.54 0.60 0.58 0.13 0.12 0.16 0.13DTF 0.51 0.56 0.59 0.61 0.12 0.09 0.09 0.11Notice that the TP rates are lower for all methods with respect to Table 2 whichrepresents the mixed noise situation without any common driver.10. DiscussionIn a recent talk, Emanuel Parzen (Parzen, 2004) proposed, both in hindsight and forfuture consideration, that aim of statistics consist in an ‘answer machine’, i.e. a moreintelligent, automatic and comprehensive version of Fisher’s almanac, which currentlyconsists in a plenitude of chapters and sections related to different types of hypotheses62