# The Hurst Exponent as an Indicator to Anticipate Agricultural Commodity Prices

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Hurst Exponent

#### 2.2. Days to Mean Reversion

#### 2.3. Dataset

## 3. Results

#### 3.1. Evolution of the Hurst Exponent

#### 3.2. Mean Reversion

#### 3.3. Paired t-Test

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The figure shows the evolution of the price and its corresponding moving average for different rolling windows $RW$ for (

**a**) aubergine, (

**b**) zucchini, (

**c**) pepper, and (

**d**) cucumber.

**Figure 2.**(

**a**) The evolution of the local Hurst exponent for aubergine and different rolling windows. (

**b**) Histogram of aubergine local Hurst exponent values. In both panels the dashed lines reflect the selected thresholds of 0.45 and 0.55.

**Figure 3.**(

**a**) Probability mass distribution of days to MR for the aubergine time series and for various RW. (

**b**) The corresponding cumulative probability distributions.

**Figure 4.**Cumulative probability of days to MR for the price time series of aubergine for different rolling windows $RW$. The blue curve represents the antipersistent regime, while the green curve represents the persistent regime. The horizontal line shows the 50% of probability, and the vertical one marks 6 days. The figure also shows the 95% level of confidence for the 500 random sub-samples.

**Figure 5.**Results of the paired t-test for the persistence ($H\ge 0.55$) and antipersistence ($H\le 0.45$) experiments. The figure shows the t-statistic, measured in days, for both experiments and the different RWs (RW = 4, 8, 16, 32 weeks). The significant differences have been marked with a red cross (p-value < 0.01).

**Table 1.**Total Hurst, H, and mean and standard deviation of price for the four time series shown in Figure 1.

Aubergine | Zucchini | Green Pepper | Cucumber | |
---|---|---|---|---|

H | 0.36 | 0.40 | 0.18 | 0.32 |

$\overline{p}\pm {\sigma}_{p}$ | $0.70\pm 0.53$ | $0.75\pm 0.63$ | $0.85\pm 0.22$ | $0.64\pm 0.33$ |

${p}_{\mathrm{max}}-{p}_{\mathrm{min}}$ | 3.99 | 3.89 | 1.45 | 2.08 |

**Table 2.**This table shows the median of days to MR and mean local Hurst ($\overline{H}$) for the studied rolling windows RW $=4,8,15,32,52$ weeks for aubergine and zucchini. The global value of H of each product is also shown in the top row.

Aubergine ($\mathit{H}=0.36$) | Zucchini ($\mathit{H}=0.40$) | |||
---|---|---|---|---|

$\mathit{RW}$ | Days to MR | $\overline{\mathit{H}}\pm \sigma $_{H} | Days to MR | $\overline{\mathit{H}}\pm \sigma $_{H} |

4 | 10 | 0.57 ± 0.18 | 10 | $0.57\pm 0.20$ |

8 | 11 | $0.56\pm 0.14$ | 12 | $0.57\pm 0.15$ |

16 | 15 | $0.54\pm 0.12$ | 22 | $0.55\pm 0.12$ |

32 | 20 | $0.58\pm 0.08$ | 24 | $0.52\pm 0.10$ |

52 | 14 | $0.46\pm 0.06$ | 17 | $0.49\pm 0.07$ |

**Table 3.**This table shows the median of days to MR and mean local Hurst ($\overline{H}$) for the studied rolling windows $RW=4,8,16,32,52$ weeks for green pepper and cucumber. The global Hurst of each product is also shown in the top row.

Green Pepper ($\mathit{H}=0.18$) | Cucumber ($\mathit{H}=0.32$) | |||
---|---|---|---|---|

$\mathit{RW}$ | Days to MR | $\overline{\mathit{H}}\pm \sigma $_{H} | Days to MR | $\overline{\mathit{H}}\pm \sigma $_{H} |

4 | 3 | $0.32\pm 0.16$ | 11 | $0.52\pm 0.19$ |

8 | 4 | $0.28\pm 0.10$ | 11 | $0.53\pm 0.12$ |

16 | 5 | $0.26\pm 0.07$ | 14 | $0.50\pm 0.07$ |

32 | 5 | $0.25\pm 0.05$ | 15 | $0.46\pm 0.05$ |

52 | 4 | $0.22\pm 0.04$ | 14 | $0.41\pm 0.06$ |

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**MDPI and ACS Style**

Pérez-Sienes, L.; Grande, M.; Losada, J.C.; Borondo, J.
The Hurst Exponent as an Indicator to Anticipate Agricultural Commodity Prices. *Entropy* **2023**, *25*, 579.
https://doi.org/10.3390/e25040579

**AMA Style**

Pérez-Sienes L, Grande M, Losada JC, Borondo J.
The Hurst Exponent as an Indicator to Anticipate Agricultural Commodity Prices. *Entropy*. 2023; 25(4):579.
https://doi.org/10.3390/e25040579

**Chicago/Turabian Style**

Pérez-Sienes, Leticia, Mar Grande, Juan Carlos Losada, and Javier Borondo.
2023. "The Hurst Exponent as an Indicator to Anticipate Agricultural Commodity Prices" *Entropy* 25, no. 4: 579.
https://doi.org/10.3390/e25040579