# Gutenberg–Richter B-Value Time Series Forecasting: A Weighted Likelihood Approach

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## Abstract

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## 1. Introduction

## 2. Methods

## 3. Data

## 4. Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Comparison of the estimated b-value (with uncertainties, +/− sigma, shaded areas) for the WL method (red) and rolling window (black) applied to the TABOO testing dataset; panel (

**a**) represents the rolling window method using 100 observations, and in panel (

**b**) using 200 observations.

**Figure 5.**Comparison of the estimated b-value (with uncertainties, +/− sigma, shaded areas) for the WL method (red) and rolling window (black) applied to the CMT testing dataset; panel (

**a**) represents the rolling window method using 100 observations, and in panel (

**b**) using 200 observations.

**Table 1.**Bayes Factor (BF) for the comparison of fixed number b-value estimation and the weighted likelihood approach for TABOO (2nd column) and CMT (3rd column) catalogues; bold is used for “strong evidence” of the BF (ln(BF) > 3).

Number of Events | Ln(BF) TABOO | Ln(BF) CMT |
---|---|---|

50 | 22.1 | 4.9 |

75 | 13.5 | 4.0 |

100 | 7.4 | 2.4 |

150 | 0.3 | 1.8 |

200 | 3.6 | 1.2 |

400 | −1.2 | −0.2 |

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**MDPI and ACS Style**

Taroni, M.; Vocalelli, G.; De Polis, A.
Gutenberg–Richter B-Value Time Series Forecasting: A Weighted Likelihood Approach. *Forecasting* **2021**, *3*, 561-569.
https://doi.org/10.3390/forecast3030035

**AMA Style**

Taroni M, Vocalelli G, De Polis A.
Gutenberg–Richter B-Value Time Series Forecasting: A Weighted Likelihood Approach. *Forecasting*. 2021; 3(3):561-569.
https://doi.org/10.3390/forecast3030035

**Chicago/Turabian Style**

Taroni, Matteo, Giorgio Vocalelli, and Andrea De Polis.
2021. "Gutenberg–Richter B-Value Time Series Forecasting: A Weighted Likelihood Approach" *Forecasting* 3, no. 3: 561-569.
https://doi.org/10.3390/forecast3030035