# Exploitation of Information as a Trading Characteristic: A Causality-Based Analysis of Simulated and Financial Data

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## Abstract

**:**

## 1. Introduction

## 2. Simulation Experiment Design

_{t}. Lagged information can also be transferred non-propositionally (nonlinear lagged X terms) into X

_{t}, revealing that each variable at time t either over- or under-reacts to the past. Both conditions determine the spreading of information flow and feedback within the system.

#### 2.1. System S1 by Schelter et al. (2006)

**S1t:**S1 with noise terms ${\epsilon}_{i,t},i=1,\dots ,5$ from a t-Student distribution, with df = 2 degrees of freedom. The generated series exhibit leptokurtic behavior that increases with the sample. Among all the variables, X5, participating in more couplings than the rest, seems to be more sensitive to residual irregularity, having the highest kurtosis and varying skewness values.

**S1n:**S1 with noise terms ${\epsilon}_{i,t},i=1,\dots ,5$ from the following GARCH(1,1) model:

**S1b:**S1 with noise terms ${\epsilon}_{i,t},i=1,\dots ,5$ from a beta distribution, with parameters $a=20$, $b=2$. All the variables present abnormal negative skewness.

**S1g:**S1 with noise terms ${\epsilon}_{i,t},i=1,\dots ,5$ from a GARCH(1,1) model, as defined for S1n, where ${w}_{t}$ follows the gamma distribution with parameters $=16$, $b=1/4$. As in S1n, the simulated time series are leptokurtic and asymmetric. X5 has the most important kurtosis and positive asymmetry as well.

**S1f**: S1 with noise terms ${\epsilon}_{i,t},i=1,\dots ,5$ resulting from the following FIGARCH(1,d,1) model:

#### 2.2. Systems S2 by Montalto et al. (2014) and S3

**S2t and S3t:**S2 and S3 with noise terms ${\epsilon}_{i,t},i=1,\dots ,5$ from a t-Student distribution, with df = 2 degrees of freedom. The inclusion of t-student disturbances aggravates the non-normality. More specifically, the kurtosis and skewness of variables X2, X4, and X5 double if compared with their respective behavior in the original system S2. In S3, the amplification gives birth to extreme fat-tail and asymmetric behavior for all variables. It is worth noticing that, even for small sample sizes, the kurtosis approaches the value of 250, while the skewness is about 15. This finding refines the view that the nature of shock matters a lot in the propagation mechanism within a system.

**S2n and S3n:**S2 and S3 with noise terms ${\epsilon}_{i,t},i=1,\dots ,5$ from the corresponding GARCH(1,1) model, as defined for S1n. Although all the variables are skewed and leptokurtic, the kurtosis and skewness of X2, X4, and X5 reach high values. Again, the amplification of irregularity is more pronounced for S3.

**S2b and S3b:**S2 and S3 with noise terms ${\epsilon}_{i,t},i=1,\dots ,5$ from a beta distribution, with parameters $a=20$, $b=2$, producing negative skewness. The simulated results show that the beta distribution of the noise terms is imposed on the mean structure of the system, destroying the excess kurtosis we detected for the nonlinearly connected variables X2, X4, and X5 of S2. On the contrary, in S3 the kurtosis turns into platykurtic values.

**S2g and S3g:**S2 and S3 with noise terms ${\epsilon}_{i,t},i=1,\dots ,5$ from a GARCH(1,1) model, as for S1g. The distributional characteristics of the system variables are similar to those of the system S2n. It is worth mentioning the steadily negative asymmetry of variable X4 in the case that the residuals follow a GARCH-type process. If we compare the strength of non-Gaussianity between S2 and S3, we come to the conclusion that the specific nonlinearity in the skeleton of the third system favors the detection of higher 3rd and 4th moment statistics via interaction.

**S2f and S3f**: S2 and S3 with noise terms ${\epsilon}_{i,t},i=1,\dots ,5$ from a FIGARCH(1,d,1) model, similar to S1. For both systems, clear leptokurtic behavior is detected for X2, X4, and X5, but with a lower intensity. Regarding skewness, we notice a remarkable increase as the sample size rises, with values reaching 5 and 6 (S2 and S3 respectively) for X2, as well as −5 and −6 for X4 (S2 and S3, respectively).

## 3. Connectivity Measures and Performance Metrics

## 4. Simulated Series Results

## 5. Application to Real Financial Data

## 6. Implications

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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S2 | Statistics | X1 | X2 | X3 | X4 | X5 |
---|---|---|---|---|---|---|

n = 512 | Kurtosis | 2.8503 | 10.5592 | 2.9148 | 10.4099 | 8.3788 |

Skewness | −0.0035 | 2.3476 | −0.0056 | −2.3153 | 1.88 | |

n = 1024 | Kurtosis | 2.9718 | 12.4619 | 2.9718 | 12.2474 | 9.8692 |

Skewness | −0.0041 | 2.5871 | 0.0052 | −2.542 | 2.0923 | |

n = 2048 | Kurtosis | 3.0084 | 13.2875 | 3.0187 | 13.0753 | 10.514 |

Skewness | 0.0069 | 2.6586 | −0.0049 | −2.6187 | 2.1609 | |

n = 4096 | Kurtosis | 2.996 | 13.3986 | 2.99 | 13.1881 | 10.72 |

Skewness | −0.001 | 2.6717 | −0.0006 | −2.6317 | 2.191 | |

S3 | ||||||

n = 512 | Kurtosis | 2.9718 | 6.1201 | 3.0166 | 5.2279 | 3.1684 |

Skewness | 0.0004 | 1.1213 | 0.0169 | −0.8763 | 0.1126 | |

n = 1024 | Kurtosis | 2.9317 | 6.2288 | 2.9997 | 5.2341 | 3.1281 |

Skewness | −0.0022 | 1.1212 | 0.0044 | −0.8709 | 0.1167 | |

n = 2048 | Kurtosis | 2.9323 | 6.0725 | 2.9903 | 5.2023 | 3.1374 |

Skewness | 0.0021 | 1.0896 | −0.0029 | −0.8581 | 0.1115 | |

n = 4096 | Kurtosis | 2.9317 | 6.2288 | 2.9997 | 5.2341 | 3.1281 |

Skewness | −0.0022 | 1.1212 | 0.0044 | −0.8709 | 0.1167 |

**Table 2.**Outcomes from the binary classification metrics for all the S1 series. RC, PM, and PT stand for the RCGCI, PMIME, and PTENUE measures, respectively.

S1 | Sensitivity | Specificity | MCC | ||||||
---|---|---|---|---|---|---|---|---|---|

RC | PM | PT | RC | PM | PT | RC | PM | PT | |

n = 512 | 100 | 99.86 | 99.14 | 93.62 | 88.77 | 97.69 | 92.06 | 86.18 | 96.34 |

n = 1024 | 100 | 100 | 100 | 95.77 | 87 | 97.31 | 94.57 | 84.53 | 96.57 |

n = 2048 | 100 | 100 | 100 | 96.15 | 87.54 | 98 | 95.11 | 85.04 | 97.39 |

n = 4096 | 100 | 100 | 100 | 97.15 | 87.38 | 97.15 | 96.36 | 85.04 | 96.32 |

overall | 100 | 99.97 | 99.79 | 95.67 | 87.67 | 97.54 | 94.53 | 85.2 | 96.66 |

S1t | |||||||||

n = 512 | 100 | 100 | 99.86 | 95.92 | 87.15 | 96.77 | 94.83 | 84.71 | 95.79 |

n = 1024 | 100 | 100 | 100 | 97.46 | 89.54 | 97.46 | 96.71 | 87.40 | 96.76 |

n = 2048 | 100 | 100 | 100 | 97.15 | 90.15 | 98.38 | 96.31 | 87.99 | 97.87 |

n = 4096 | 100 | 100 | 100 | 97.08 | 87.92 | 98 | 96.22 | 85.48 | 97.38 |

overall | 100 | 100 | 99.97 | 96.90 | 88.69 | 97.65 | 96.02 | 86.4 | 96.95 |

S1n | |||||||||

n = 512 | 98.71 | 99 | 99 | 90.38 | 90.92 | 97.92 | 87.20 | 88.01 | 96.49 |

n = 1024 | 99.71 | 99.86 | 100 | 90.69 | 92.62 | 98.15 | 88.52 | 90.78 | 97.62 |

n = 2048 | 99.86 | 100 | 100 | 91.46 | 90.46 | 98.46 | 89.41 | 88.33 | 98 |

n = 4096 | 100 | 100 | 100 | 89.62 | 94.38 | 99 | 87.49 | 93 | 98.7 |

overall | 99.57 | 99.72 | 99.75 | 90.54 | 92.1 | 98.38 | 88.16 | 90.03 | 97.70 |

S1b | |||||||||

n = 512 | 100 | 100 | 100 | 95.92 | 87.15 | 96.77 | 94.83 | 84.71 | 95.79 |

n = 1024 | 100 | 100 | 100 | 97.46 | 89.54 | 97.46 | 96.71 | 87.40 | 96.76 |

n = 2048 | 100 | 100 | 100 | 97.15 | 90.15 | 98.38 | 96.31 | 87.99 | 97.87 |

n = 4096 | 100 | 100 | 100 | 97.08 | 87.92 | 98 | 96.22 | 85.48 | 97.38 |

overall | 100 | 100 | 100 | 96.90 | 88.69 | 97.65 | 96.02 | 86.4 | 96.95 |

S1g | |||||||||

n = 512 | 99.14 | 99.43 | 99.71 | 90.85 | 90.77 | 98.23 | 88.08 | 88.21 | 97.48 |

n = 1024 | 99.57 | 100 | 100 | 91.54 | 91.54 | 98.38 | 89.24 | 89.56 | 97.89 |

n = 2048 | 100 | 100 | 100 | 92.23 | 92.54 | 98.15 | 90.28 | 90.69 | 97.61 |

n = 4096 | 100 | 100 | 100 | 90.77 | 93.69 | 99.31 | 88.77 | 92.13 | 99.41 |

overall | 99.68 | 99.86 | 99.93 | 91.35 | 92.14 | 98.52 | 89.09 | 90.15 | 98.1 |

S1f | |||||||||

n = 512 | 96.43 | 92.43 | 88.86 | 92.85 | 84.46 | 94.92 | 87.95 | 75.09 | 84.69 |

n = 1024 | 99.14 | 92.29 | 94.92 | 93.77 | 87.23 | 95.31 | 91.49 | 81.63 | 89.81 |

n = 2048 | 99.71 | 98.86 | 98 | 94.46 | 85.62 | 96.54 | 92.88 | 81.98 | 94.06 |

n = 4096 | 100 | 99.86 | 99.43 | 93.85 | 87.23 | 96.08 | 92.25 | 84.65 | 94.54 |

overall | 98.82 | 95.86 | 95.30 | 93.73 | 86.14 | 95.71 | 91.14 | 80.84 | 90.78 |

**Table 3.**Outcomes from the binary classification metrics for all S2 series. RC, PM, and PT stand for the RCGCI, PMIME, and PTENUE measures, respectively.

S2 | Sensitivity | Specificity | MCC | ||||||
---|---|---|---|---|---|---|---|---|---|

RC | PM | PT | RC | PM | PT | RC | PM | PT | |

n = 512 | 54.4 | 82.2 | 81.4 | 84.73 | 89.8 | 93.6 | 38.98 | 70.42 | 76.02 |

n = 1024 | 59.6 | 90.4 | 86.8 | 82.87 | 88.73 | 90.6 | 41.16 | 75.29 | 74.96 |

n = 2048 | 67.4 | 99.8 | 99.4 | 82.2 | 85.6 | 85.2 | 46.9 | 78.3 | 76.88 |

n = 4096 | 66 | 100 | 100 | 79.8 | 84.07 | 85.27 | 42.76 | 76.36 | 77.35 |

overall | 61.85 | 93.1 | 91.9 | 82.4 | 87.05 | 88.67 | 42.45 | 75.09 | 76.30 |

S2t | |||||||||

n = 512 | 73.2 | 86.2 | 84.4 | 78 | 88.53 | 93.4 | 47.26 | 71.05 | 77.17 |

n = 1024 | 80.2 | 88.2 | 90.4 | 73.4 | 87.6 | 92 | 48.06 | 71.42 | 79.23 |

n = 2048 | 84.2 | 88.8 | 93 | 72.93 | 88.4 | 91.73 | 51.01 | 72.72 | 80.7 |

n = 4096 | 90 | 90 | 96.8 | 69.93 | 89.27 | 91.47 | 52.59 | 74.85 | 83.21 |

overall | 81.9 | 88.3 | 91.15 | 73.5 | 88.45 | 92.15 | 49.73 | 72.51 | 80.08 |

S2n | |||||||||

n = 512 | 72.8 | 94.2 | 93 | 76.47 | 88.47 | 95.53 | 45.58 | 77.68 | 87.41 |

n = 1024 | 80.4 | 98.2 | 97.8 | 74.67 | 90.8 | 95.67 | 49.92 | 84.04 | 91 |

n = 2048 | 83.4 | 99.6 | 99.6 | 69 | 90.87 | 95.2 | 46.85 | 84.98 | 91.64 |

n = 4096 | 88.6 | 100 | 100 | 64.67 | 90.2 | 94.67 | 47.13 | 84.22 | 91.03 |

overall | 81.3 | 98 | 97.6 | 71.2 | 90.09 | 95.27 | 47.37 | 82.73 | 90.27 |

S2b | |||||||||

n = 512 | 95.2 | 95.2 | 95.8 | 90.6 | 94.6 | 98.33 | 81.67 | 87.45 | 94.23 |

n = 1024 | 99.6 | 100 | 100 | 93.27 | 96.6 | 98.47 | 88.75 | 94.33 | 97.35 |

n = 2048 | 100 | 100 | 100 | 90.4 | 95.07 | 98.53 | 84.5 | 91.72 | 97.43 |

n = 4096 | 100 | 100 | 100 | 87.2 | 94.33 | 97.93 | 80.16 | 90.58 | 96.41 |

overall | 98.7 | 98.8 | 98.95 | 90.37 | 95.15 | 98.32 | 83.77 | 91.02 | 96.36 |

S2g | |||||||||

n = 512 | 74.6 | 95.6 | 92.2 | 75.4 | 89.13 | 96 | 45.78 | 79.46 | 87.64 |

n = 1024 | 77.2 | 99.6 | 97.8 | 74.8 | 89.87 | 94.13 | 47.29 | 83.75 | 88.75 |

n = 2048 | 84.4 | 99.6 | 99.8 | 70.07 | 89.13 | 94.73 | 48.7 | 82.58 | 90.9 |

n = 4096 | 87 | 100 | 100 | 66.13 | 89.13 | 94.2 | 47.08 | 82.63 | 90.29 |

overall | 80.8 | 98.7 | 97.45 | 71.6 | 89.32 | 94.77 | 47.21 | 82.11 | 89.4 |

S2f | |||||||||

n = 512 | 60.20 | 87.2 | 85.6 | 84 | 88.47 | 92.6 | 43.58 | 71.96 | 76.79 |

n = 1024 | 59.80 | 91.4 | 92.2 | 82.67 | 86.8 | 91.53 | 41.29 | 73.17 | 80.34 |

n = 2048 | 64.80 | 95.2 | 95.4 | 80.27 | 87 | 89.67 | 42.94 | 76.24 | 79.88 |

n = 4096 | 70.80 | 96 | 98.2 | 78.93 | 86.6 | 89.13 | 46.02 | 76.14 | 81.52 |

overall | 63.9 | 92.45 | 92.85 | 81.47 | 87.22 | 90.73 | 43.46 | 74.38 | 79.63 |

**Table 4.**Outcomes from the binary classification metrics for all S3 series. RC, PM, and PT stand for the RCGCI, PMIME, and PTENUE measures, respectively.

S3 | Sensitivity | Specificity | MCC | ||||||
---|---|---|---|---|---|---|---|---|---|

RC | PM | PT | RC | PM | PT | RC | PM | PT | |

n = 512 | 65.4 | 100 | 99.8 | 93.07 | 80.33 | 94.47 | 62.88 | 72.74 | 90.89 |

n = 1024 | 63.8 | 100 | 100 | 92.87 | 78.93 | 95.33 | 61.4 | 70.80 | 94.02 |

n = 2048 | 64.8 | 100 | 100 | 93.4 | 81.13 | 95.13 | 62.78 | 73.61 | 93.84 |

n = 4096 | 62.8 | 100 | 100 | 91.2 | 80.13 | 94.47 | 56.9 | 72.25 | 92.91 |

overall | 64.2 | 100 | 99.95 | 92.64 | 80.13 | 94.85 | 60.99 | 72.35 | 92.92 |

S3t | |||||||||

n = 512 | 87 | 98.6 | 99.2 | 89 | 88.73 | 97.13 | 72.68 | 81.56 | 94.56 |

n = 1024 | 89 | 99.8 | 99.8 | 90.73 | 87.4 | 96.67 | 76.95 | 80.77 | 94.25 |

n = 2048 | 93.4 | 100 | 100 | 92.53 | 85.87 | 96.47 | 82.71 | 78.63 | 94.17 |

n = 4096 | 96.2 | 100 | 100 | 93.33 | 87.6 | 96.73 | 86.16 | 80.94 | 94.6 |

overall | 91.4 | 99.6 | 99.75 | 91.39 | 87.4 | 96.75 | 79.63 | 80.48 | 94.4 |

S3n | |||||||||

n = 512 | 81 | 100 | 100 | 85.8 | 85.4 | 96 | 64.62 | 78.17 | 93.23 |

n = 1024 | 87.4 | 100 | 100 | 78.13 | 87.53 | 96.4 | 60.14 | 80.83 | 93.98 |

n = 2048 | 90.4 | 100 | 100 | 75.6 | 90.27 | 96.53 | 59.77 | 84.66 | 94.07 |

n = 4096 | 94.8 | 100 | 100 | 67.33 | 89.53 | 97 | 54.87 | 83.48 | 95 |

overall | 88.4 | 100 | 100 | 76.72 | 88.18 | 96.48 | 59.85 | 81.79 | 94.07 |

S3b | |||||||||

n = 512 | 100 | 93 | 84.6 | 73.07 | 92.47 | 94.13 | 64.03 | 82.2 | 83.68 |

n = 1024 | 100 | 100 | 99.4 | 68.67 | 91.2 | 93.87 | 59.74 | 85.64 | 91.43 |

n = 2048 | 100 | 100 | 100 | 65.73 | 90.60 | 95.8 | 57.13 | 84.94 | 92.68 |

n = 4096 | 100 | 100 | 100 | 62.27 | 90.73 | 95.13 | 54.24 | 85.01 | 91.58 |

overall | 100 | 98.25 | 96 | 67.44 | 91.25 | 94.73 | 58.79 | 84.45 | 89.84 |

S3g | |||||||||

n = 512 | 82 | 100 | 99.8 | 84.13 | 87.2 | 94.67 | 63.64 | 80.66 | 91.07 |

n = 1024 | 89.4 | 100 | 100 | 77.2 | 86.4 | 96.53 | 61.47 | 79.56 | 94.27 |

n = 2048 | 94 | 100 | 100 | 73.93 | 89.13 | 96.8 | 60.78 | 83.21 | 94.58 |

n = 4096 | 96.6 | 100 | 100 | 67.73 | 89.6 | 96.6 | 56.91 | 83.74 | 94.25 |

overall | 90.5 | 100 | 99.95 | 75.75 | 88.08 | 96.15 | 60.7 | 81.79 | 93.54 |

S3f | |||||||||

n = 512 | 71 | 95.8 | 91.8 | 87 | 81.6 | 93.87 | 58.16 | 70.82 | 84.04 |

n = 1024 | 73.2 | 97.6 | 96 | 83.33 | 78.8 | 93.8 | 53.81 | 68.76 | 87.12 |

n = 2048 | 76.6 | 99.2 | 98.8 | 80.60 | 76.93 | 90.67 | 53.82 | 67.76 | 84.34 |

n = 4096 | 78.8 | 99.6 | 99.8 | 77.13 | 76.07 | 87.6 | 50.86 | 67.46 | 80.73 |

overall | 74.9 | 98.05 | 96.6 | 82.02 | 78.35 | 91.49 | 54.16 | 68.7 | 84.06 |

**Table 5.**Mutual information between the variables of various S2 systems for n = 4096 (the values for the respective systems are denoted in different colors).

S2, S2t, S2n, S2b, S2g, S2f | X1 | X2 | X3 | X4 | X5 |
---|---|---|---|---|---|

X1 | - | 0.0000 0.0044 0.0294 0.0000 0.0344 0.0099 | 0.0990 0.1366 0.1911 0.1280 0.1830 0.1923 | 0.0053 0.0203 0.0824 0.0000 0.0957 0.0575 | 0.0973 0.1734 0.2493 0.4293 0.2699 0.1980 |

X2 | - | 0.0280 0.0205 0.0568 0.1831 0.0535 0.0405 | 0.7509 0.9407 0.7874 1.2848 0.7892 1.0911 | 0.0818 0.1679 0.2241 0.0536 0.2179 0.2297 | |

X3 | - | 0.0571 0.1070 0.1079 0.2644 0.1160 0.1494 | 0.1020 0.1691 0.1870 0.3169 0.1958 0.3289 | ||

X4 | - | 0.1306 0.2648 0.3131 0.0958 0.3152 0.3562 | |||

X5 | - |

**Table 6.**Mutual information between the variables of the various S3 systems for n = 4096 (the values for the respective systems are denoted in different colors).

S3, S3t, S3n, S3b, S3g, S3f | X1 | X2 | X3 | X4 | X5 |
---|---|---|---|---|---|

X1 | - | 0.0111 0.0059 0.0232 0.7988 0.0269 0.0039 | 0.0022 0.0000 0.0140 0.3140 0.0054 0.0000 | 0.0052 0.0000 0.0259 0.9428 0.0206 0.0148 | 0.0000 0.0000 0.0177 0.6588 0.0104 0.0205 |

X2 | - | 0.0120 0.0053 0.0072 0.2340 0.0000 0.0000 | 0.1329 0.2757 0.2330 1.1917 0.2524 0.6074 | 0.0034 0.0000 0.0301 0.6000 0.0401 0.0350 | |

X3 | - | 0.0040 0.0020 0.0113 0.7189 0.0102 0.0005 | 0.0024 0.0024 0.0159 0.5489 0.0116 0.0126 | ||

X4 | - | 0.0000 0.0734 0.0548 1.0924 0.0555 0.1048 | |||

X5 | - |

n = 4000 14/9/2004–30/04/2020 | FP | SAN | OR | BNP | BN |
---|---|---|---|---|---|

Kurtosis | 16.8693 | 8.9997 | 8.8949 | 12.7080 | 7.8091 |

Skewness | −0.3475 | −0.1641 | 0.2020 | −0.0539 | −0.1539 |

n = 200021/06/2012–30/04/2020 | |||||

Kurtosis | 23.7631 | 7.1009 | 6.8242 | 13.3001 | 7.8363 |

Skewness | −1.2257 | −0.4148 | 0.1141 | −0.9696 | −0.3779 |

n = 100002/06/2016–30/04/2020 | |||||

Kurtosis | 36.1905 | 7.3303 | 10.1418 | 19.8451 | 11.8267 |

Skewness | −2.0231 | −0.1469 | 0.1186 | −1.9065 | −0.8756 |

n = 50017/05/2018–30/04/2020 | |||||

Kurtosis | 28.1107 | 7.3561 | 9.4350 | 13.3472 | 13.4247 |

Skewness | −1.9083 | −0.3948 | 0.1157 | −1.5374 | −1.2417 |

n = 4000 14/9/2004–30/04/2020 | FP | SAN | OR | CILPA | BRITANNIA |
---|---|---|---|---|---|

Kurtosis | 16.8693 | 8.9997 | 8.8949 | 7.9616 | 23.1883 |

Skewness | −0.3475 | −0.1641 | 0.2020 | 0.0052 | 1.7592 |

n = 200021/06/2012–30/04/2020 | |||||

Kurtosis | 23.7631 | 7.1009 | 6.8242 | 7.9316 | 11.9245 |

Skewness | −1.2257 | −0.4148 | 0.1141 | 0.4215 | 0.4737 |

n = 100002/06/2016–30/04/2020 | |||||

Kurtosis | 36.1905 | 7.3303 | 10.1418 | 9.5737 | 14.8812 |

Skewness | −2.0231 | −0.1469 | 0.1186 | 0.8919 | 0.1096 |

n = 50017/05/2018–30/04/2020 | |||||

Kurtosis | 28.1107 | 7.3561 | 9.4350 | 9.5488 | 14.1208 |

Skewness | −1.9083 | −0.3948 | 0.1157 | 1.0137 | −0.0525 |

Portfolio A | Samples | FP | SAN | OR | BNP | BN |
---|---|---|---|---|---|---|

FP | 4000 | - | 0.1659 | 0.1928 | 0.2254 | 0.1456 |

2000 | - | 0.1628 | 0.1552 | 0.2257 | 0.1413 | |

1000 | - | 0.0499 | 0.0865 | 0.1816 | 0.0711 | |

500 | - | 0.0555 | 0.0785 | 0.2075 | 0.0737 | |

SAN | 4000 | - | 0.2008 | 0.1463 | 0.1781 | |

2000 | - | 0.2295 | 0.1385 | 0.2169 | ||

1000 | - | 0.1139 | 0.0185 | 0.1143 | ||

500 | - | 0.1251 | 0.0129 | 0.1193 | ||

OR | 4000 | - | 0.1285 | 0.2847 | ||

2000 | - | 0.1171 | 0.3382 | |||

1000 | - | 0.0685 | 0.2455 | |||

500 | - | 0.0784 | 0.2089 | |||

BNP | 4000 | - | 0.1131 | |||

2000 | - | 0.1087 | ||||

1000 | - | 0.0469 | ||||

500 | - | 0.0535 | ||||

BN | 4000 | - | ||||

2000 | - | |||||

1000 | - | |||||

500 | - | |||||

Portfolio B | Samples | FP | SAN | OR | CIPLA | BRITANNIA |

FP | 4000 | - | 0.1659 | 0.1928 | 0.0171 | 0.0044 |

2000 | - | 0.1628 | 0.1552 | 0.2257 | 0.1413 | |

1000 | - | 0.0499 | 0.0865 | 0.0000 | 0.0133 | |

500 | - | 0.0555 | 0.0785 | 0.0177 | 0.0246 | |

SAN | 4000 | - | 0.2008 | 0.0154 | 0.0085 | |

2000 | - | 0.2295 | 0.1385 | 0.2169 | ||

1000 | - | 0.1139 | 0.0006 | 0.0043 | ||

500 | - | 0.1251 | 0.0174 | 0.0124 | ||

OR | 4000 | - | 0.0082 | 0.0138 | ||

2000 | - | 0.1171 | 0.3382 | |||

1000 | - | 0.0022 | 0.0006 | |||

500 | - | 0.0216 | 0.0027 | |||

CIPLA | 4000 | 0.5459 | ||||

2000 | 0.1087 | |||||

1000 | 0.5022 | |||||

500 | 0.5532 | |||||

BRITANNIA | 4000 | - | ||||

2000 | - | |||||

1000 | - | |||||

500 | - |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Kyrtsou, C.; Mikropoulou, C.; Papana, A.
Exploitation of Information as a Trading Characteristic: A Causality-Based Analysis of Simulated and Financial Data. *Entropy* **2020**, *22*, 1139.
https://doi.org/10.3390/e22101139

**AMA Style**

Kyrtsou C, Mikropoulou C, Papana A.
Exploitation of Information as a Trading Characteristic: A Causality-Based Analysis of Simulated and Financial Data. *Entropy*. 2020; 22(10):1139.
https://doi.org/10.3390/e22101139

**Chicago/Turabian Style**

Kyrtsou, Catherine, Christina Mikropoulou, and Angeliki Papana.
2020. "Exploitation of Information as a Trading Characteristic: A Causality-Based Analysis of Simulated and Financial Data" *Entropy* 22, no. 10: 1139.
https://doi.org/10.3390/e22101139