Abstract
Hawaiian volcanoes such as Kilauea and Mauna Loa have drawn the attention of researchers for quite some time and numerous theories abound hinting at a possible inverse relationship between the two. Most of these analyses are intrinsically qualitative and are bereft of data-driven statistical justification. The present work attempts to address this issue adopting a more mathematical approach and endeavours to examine the existence of such a relationship through the novel use of a smoothing statistic termed as the empirical recurrence rates ratio. Additionally, it is shown that useful knowledge about the possible interplay between these two volcanoes is coded into this single statistic and based on it; construction of new dependence measures such as the two introduced, becomes simpler and much more intuitive. The recent decade is witnessing an increased activity of Kilauea and the methods proposed here can be successfully implemented to safeguard human lives and property against the unpredictable advances of all-engulfing molten lava flow.
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Acknowledgements
The authors gratefully acknowledge the insightful comments from the referee Manuel Nathenson as well as the esteemed editor, which led to a significant improvement of the final research output.
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Ho, CH., Bhaduri, M. A Quantitative Insight into the Dependence Dynamics of the Kilauea and Mauna Loa Volcanoes, Hawaii. Math Geosci 49, 893–911 (2017). https://doi.org/10.1007/s11004-017-9692-z
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DOI: https://doi.org/10.1007/s11004-017-9692-z
Keywords
- Empirical recurrence rate
- Empirical recurrence rates ratio
- Point processes
- Time series
- Time series bootstrapping