Measuring Extreme Tail Association
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917341147693056 |
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| author | Das, Bikramjit Liu, Xiangyu |
| author_facet | Das, Bikramjit Liu, Xiangyu |
| contents | Simultaneous occurrences of extreme events need not imply symmetric or reciprocal tail dependence. However, most existing measures of extremal dependence are inherently symmetric and hence often fail to capture directional influence in tail association. We introduce a rank-based measure of Extreme Tail Association (ETA) for bivariate data quantifying such directional influence of one variable on another in extreme tail regions. The proposed estimator is easily computable, consistent with its population counterpart, and asymptotically normal under mild conditions, allowing for statistical inference. We further develop a formal test for asymmetry in tail association based on a multiplier bootstrap procedure. The practical relevance of the methodology is illustrated using data on extreme price movements in major cryptocurrencies. Beyond providing a flexible tool for extremal association, the proposed framework offers a substantive argument for investigating causal relationships in extreme scenarios. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_13614 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Measuring Extreme Tail Association Das, Bikramjit Liu, Xiangyu Methodology Statistics Theory 62G32, 62G10, 60F05, 62G30 Simultaneous occurrences of extreme events need not imply symmetric or reciprocal tail dependence. However, most existing measures of extremal dependence are inherently symmetric and hence often fail to capture directional influence in tail association. We introduce a rank-based measure of Extreme Tail Association (ETA) for bivariate data quantifying such directional influence of one variable on another in extreme tail regions. The proposed estimator is easily computable, consistent with its population counterpart, and asymptotically normal under mild conditions, allowing for statistical inference. We further develop a formal test for asymmetry in tail association based on a multiplier bootstrap procedure. The practical relevance of the methodology is illustrated using data on extreme price movements in major cryptocurrencies. Beyond providing a flexible tool for extremal association, the proposed framework offers a substantive argument for investigating causal relationships in extreme scenarios. |
| title | Measuring Extreme Tail Association |
| topic | Methodology Statistics Theory 62G32, 62G10, 60F05, 62G30 |
| url | https://arxiv.org/abs/2603.13614 |