# Market Sentiments Distribution Law

## Abstract

**:**

## 1. Introduction

_{o}·exp(−λx)

## 2. Literature Review

## 3. Methodology

- Let x be the size of a candlestick
- Let I be an interval of width equal to x centered x, which is calculated as follows:I = [x − Δx/2, x + Δx/2]
- Let N be the number of candlesticks found in the interval I
- Then, we affirm that: N = N
_{o}·exp(−λx)

## 4. Data Preprocessing

“When the maximum Lyapunov exponent exceeds zero, the system exhibits chaos. If it is greater than one, the predictable limit is less than the sampling frequency. Thus, the chaotic time series predictions are only of practical use when the chaotic system with the maximum Lyapunov exponent is between zero and one. If the positive exponent approaches zero, long-term predictions are possible.”

## 5. Results

^{2}value was equal to 0.9980.

^{2}value was equal to 0.9775.

^{2}value was equal to 0.9712.

^{2}value was equal to 0.9357.

## 6. Discussion

- (i)
- Black candlestick is equal to bearish sentiments.
- (ii)
- White candlestick is equal to bullish sentiments.
- (iii)
- The intensity of the sentiment is measured by the length of the candlestick. That is, the greater the length of the candlestick, the greater the intensity of the sentiment because each candlestick is observed in the same time unit (“day”, in our case).

- (i)
- Section 4 shows that the extension or peak to peak amplitude has more information than the price of the studied financial instrument
- (ii)
- It proved to be lawful to measure the market sentiments intensity in standard deviation units of E length.
- (iii)
- Section 5 shows that the working hypothesis is supported by the coefficient of correlation whose values fluctuate between 0.9357 and 0.9980.

## 7. Conclusions

^{2}values ranging between 0.9354 and 0.9981.

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Candlesticks distribution for USA30 with E length; (

**b**) Market sentiments intensity for USA30 in σ units (σ = 107).

Financial Instrument | LLE for Extension (E) | LLE for Median Price |
---|---|---|

USA30 | 0.599 | 0.318 |

GBPUSD | 0.719 | 0.396 |

IBM | 0.714 | 0.235 |

Copper | 0.585 | 0.321 |

Financial Instrument | Entropy for Extension (E) | Entropy for Median Price |
---|---|---|

USA30 | 0.589 | 0.363 |

GBPUSD | 0.586 | 0.398 |

IBM | 0.472 | 0.196 |

Copper | 0.585 | 0.218 |

Interval | E (Class Mark) | N |
---|---|---|

[100, 200[ | 150 | 498 |

[200, 300[ | 250 | 180 |

[200, 300[ | 350 | 74 |

[400, 500[ | 450 | 23 |

≥500 | 550 | 10 |

Interval | E (Class Mark) | N |
---|---|---|

[1, 3[ | 2 | 1519 |

[3, 5[ | 4 | 388 |

[5, 7[ | 6 | 57 |

[7, 9[ | 8 | 18 |

≥9 | 10 | 1 |

Interval | E (Class Mark) | N |
---|---|---|

[0.5, 1.5[ | 1 | 1200 |

[1.5, 2.5[ | 2 | 415 |

[2.5, 3.5[ | 3 | 55 |

[3.5, 4.5[ | 4 | 4 |

≥4.5 | 5 | 2 |

Interval | E (Class Mark) | N |
---|---|---|

[4, 8[ | 6 | 303 |

[8, 12[ | 10 | 46 |

[12, 16[ | 14 | 10 |

[16, 20[ | 18 | 2 |

≥20 | 22 | 3 |

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**MDPI and ACS Style**

Reyes-Molina, J.
Market Sentiments Distribution Law. *Entropy* **2016**, *18*, 324.
https://doi.org/10.3390/e18090324

**AMA Style**

Reyes-Molina J.
Market Sentiments Distribution Law. *Entropy*. 2016; 18(9):324.
https://doi.org/10.3390/e18090324

**Chicago/Turabian Style**

Reyes-Molina, Jorge.
2016. "Market Sentiments Distribution Law" *Entropy* 18, no. 9: 324.
https://doi.org/10.3390/e18090324