# Replication in Energy Markets: Use and Misuse of Chaos Tools

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## Abstract

**:**

## 1. Introduction

## 2. The “Core” of Chaos: Its Definition

## 3. Methodologies

#### 3.1. Phase Space Reconstruction

#### 3.2. Modified Correlation Entropy

#### 3.3. Noise Level

#### 3.4. Recurrence Analysis

## 4. Implications of the New Approach

- The KS entropy estimated with a noise-oblivious approach is much smaller than the MCE;
- The CE decays as the size of the correlation window increases, whereas the MCE is rather steady.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Type I intermittency, positioning of the rectangles in the RP (see Figure 8 in [52]).

Futures Contract | Time Delay | Embedding Dimension |
---|---|---|

Crude oil Contract 1 | 4 | 11 |

Crude oil Contract 3 | 4 | 10 |

Heating oil Contract 1 | 1 | 13 |

Heating oil Contract 3 | 1 | 11 |

Natural gas | 1 | 14 |

Commodity Contract | $\overline{\mathit{\sigma}}$ | Noise Level % |
---|---|---|

Crude oil C1 | $0.02363634$ | $57.9\%$ |

Crude oil C3 | $0.02432642$ | $57.1\%$ |

Heating oil C1 | $0.02032667$ | $51.7\%$ |

Heating oil C3 | $0.02334584$ | $53.5\%$ |

Natural gas | $0.02591293$ | $40.1\%$ |

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Mastroeni, L.; Vellucci, P. Replication in Energy Markets: Use and Misuse of Chaos Tools. *Entropy* **2022**, *24*, 701.
https://doi.org/10.3390/e24050701

**AMA Style**

Mastroeni L, Vellucci P. Replication in Energy Markets: Use and Misuse of Chaos Tools. *Entropy*. 2022; 24(5):701.
https://doi.org/10.3390/e24050701

**Chicago/Turabian Style**

Mastroeni, Loretta, and Pierluigi Vellucci. 2022. "Replication in Energy Markets: Use and Misuse of Chaos Tools" *Entropy* 24, no. 5: 701.
https://doi.org/10.3390/e24050701