# Cross-Sectoral Information Transfer in the Chinese Stock Market around Its Crash in 2015

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Transfer Entropy

#### 2.2. Effective Transfer Entropy

#### 2.3. Kernel Density Estimation

## 3. Data

## 4. Results and Discussion

#### 4.1. ETE between Sectors

#### 4.2. Centrality of Sectors

#### 4.3. Directed Maximum Spanning Tree

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Theoretical ${{\displaystyle TE}}_{X\to Y}$ and calculated ${{\displaystyle ETE}}_{X\to Y}$ of the two linear autoregressive processes in Formula (11). $\gamma $ increases from 0 to 1 with a step of 0.1.

**Figure 2.**Shanghai stock exchange composite index (SSECI) and the four sub-periods around the time of the crash of 2015. The horizontal axis is the sample time ranging from 1 July 2013 to 28 February 2017. The red lines correspond to the dates of 1 July 2014, 12 June 2015, and 29 February 2016 from left to right.

**Figure 3.**Colormaps of the effective transfer entropy (ETE) between the 10 sectors during the (

**a**) tranquil, (

**b**) bull, (

**c**) crash, and (

**d**) post-crash periods. The range of the colorbars is from 0 to 0.1533.

**Figure 4.**Weighted betweenness centrality (WBC) for the 10 stock sectors during the (

**a**) tranquil, (

**b**) bull, (

**c**) crash, and (

**d**) post-crash periods. The horizontal axis is the number of the sectors.

**Figure 5.**Directed maximum spanning trees (MSTs) of the 10 stock sectors during the (

**a**) tranquil, (

**b**) bull, (

**c**) crash, and (

**d**) post-crash periods. The values on the edges are their weights.

No. | Index Name | No. | Index Name |
---|---|---|---|

1 | CSI Energy | 6 | CSI Health Care |

2 | CSI Materials | 7 | CSI Financials |

3 | CSI Industrials | 8 | CSI Information Technology |

4 | CSI Consumer Discretionary | 9 | CSI Telecommunication Services |

5 | CSI Consumer Staples | 10 | CSI Utilities |

**Table 2.**Results of the augmented Dickey-Fuller (ADF) and Jarque-Bera tests for the whole return series of the 10 sectors.

No. | ADF Statistic | Jarque-Bera Statistic | No. | ADF Statistic | Jarque-Bera Statistic |
---|---|---|---|---|---|

1 | −28.6154 *** | 765.3783 *** | 6 | −28.4199 *** | 902.8109 *** |

2 | −28.2453 *** | 823.1612 *** | 7 | −28.7902 *** | 953.3962 *** |

3 | −26.7147 *** | 783.1250 *** | 8 | −27.1013 *** | 351.2834 *** |

4 | −27.7279 *** | 753.9022 *** | 9 | −27.6364 *** | 548.0041 *** |

5 | −23.0576 *** | 867.0495 *** | 10 | −27.9620 *** | 970.4217 *** |

Tranquil | Bull | Crash | Post-crash | |
---|---|---|---|---|

Average ETE | 0.0049 | 0.0384 | 0.0619 | 0.0123 |

No. | Sector Name | Pre-Bull | Bull | Crash | Post-Crash |
---|---|---|---|---|---|

1 | Energy | 0.0474 | 0.4301 | 0.7006 | 0.0396 |

2 | Materials | 0.0811 | 0.3366 | 0.6279 | 0.0392 |

3 | Industrials | 0.0407 | 0.3985 | 0.5149 | 0.1133 |

4 | Consumer Discretionary | 0.0714 | 0.3055 | 0.4283 | 0.1918 |

5 | Consumer Staples | 0.0316 | 0.1557 | 0.5451 | 0.0471 |

6 | Health Care | 0.0682 | 0.2251 | 0.3525 | 0.1048 |

7 | Financials | 0 | 0.3147 | 0.7130 | 0.0965 |

8 | Information Technology | 0.0628 | 0.3573 | 0.7729 | 0.0989 |

9 | Telecommunication Services | 0.0361 | 0.3045 | 0.3194 | 0.2176 |

10 | Utilities | 0 | 0.6259 | 0.5983 | 0.1565 |

No. | Sector Name | Pre-Bull | Bull | Crash | Post-Crash |
---|---|---|---|---|---|

1 | Energy | 0.1509 | 0.2314 | 0.3450 | 0 |

2 | Materials | 0.1156 | 0.3289 | 0.6136 | 0 |

3 | Industrials | 0 | 0.3278 | 0.6609 | 0 |

4 | Consumer Discretionary | 0.0345 | 0.3319 | 0.4932 | 0.1367 |

5 | Consumer Staples | 0 | 0.0435 | 0.7335 | 0.0521 |

6 | Health Care | 0.0393 | 0.2888 | 0.4924 | 0.0396 |

7 | Financials | 0 | 0.2835 | 0.5885 | 0.4808 |

8 | Information Technology | 0.0337 | 0.6807 | 0.6157 | 0.0832 |

9 | Telecommunication Services | 0.0653 | 0.3646 | 0.4743 | 0.1325 |

10 | Utilities | 0 | 0.5725 | 0.5558 | 0.1806 |

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**MDPI and ACS Style**

Wang, X.; Hui, X.
Cross-Sectoral Information Transfer in the Chinese Stock Market around Its Crash in 2015. *Entropy* **2018**, *20*, 663.
https://doi.org/10.3390/e20090663

**AMA Style**

Wang X, Hui X.
Cross-Sectoral Information Transfer in the Chinese Stock Market around Its Crash in 2015. *Entropy*. 2018; 20(9):663.
https://doi.org/10.3390/e20090663

**Chicago/Turabian Style**

Wang, Xudong, and Xiaofeng Hui.
2018. "Cross-Sectoral Information Transfer in the Chinese Stock Market around Its Crash in 2015" *Entropy* 20, no. 9: 663.
https://doi.org/10.3390/e20090663