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Estimating Liu, Ji, and Fan’s Four Tail-Dependence Functions

Article Quant Q&A · Author: user75474
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Summary

The document asks how to estimate the time-varying tail-dependence functions proposed by Liu, Ji, and Fan. It distinguishes four dependence directions: upper–upper, lower–lower, lower–upper, and upper–lower, noting that the latter two extend the conventional pair of tail measures. The post focuses on the gap between population definitions and practical sample estimation, especially for different copula families.

It also asks whether cross-tail estimates should be interpreted like conventional estimates under copula rotations, where signs or orientation may change. No estimator, derivation, empirical results, or resolution is provided; the text is a request for methodological guidance. Readers should therefore treat it as a statement of an open estimation question rather than a validated procedure. The cited related paper concerns extreme risk dependence, but the post does not report its findings or establish that its methods apply here.

Key ideas

  • The proposed framework considers upper–upper and lower–lower dependence as well as both cross-tail directions.
  • The post asks how population tail-dependence definitions can be converted into sample estimators.
  • It raises the question of how cross-tail estimates relate to conventional estimates under copula rotations.
  • No estimation method or empirical evidence is supplied.

Tags

StatisticsRisk managementMulti-asset
Full text
# How to estimate the time-varying tail-dependence functions of Liu, Ji, and Fan's 2016 Paper?


# How to estimate the time-varying tail-dependence functions of Liu, Ji, and Fan's 2016 Paper?














- Paper's Authors: BING-YUE LIU, QIANG JI, and YING FAN



- Paper's DOI: http://dx.doi.org/10.1080/14697688.2016.1205208

LIU, JI, and FAN's Tail-Dependence Functions investigate the Upper-Upper, Lower-Lower, Lower-Upper, and Upper-Lower Dependences. Unlike the conventional tail-dependence functions, the suggested methodology has 2 additional tail-dependence functions.

Similar Paper with an Open Access

- Paper's Title: Extreme risk dependence between green bonds and financial markets

- Paper's Authors: Sitara Karim, Brian M. Lucey, Muhammad A. Naeem, Larisa Yarovaya

- Paper's DOI: https://doi.org/10.1111/eufm.12458

Any programming codes for the estimation in R or Python would be highly appreciated.

Currently, the paper shows population format of the tail-dependence functions. As far as I know, these populations equations cannot be used to estimate the respective tail-dependence functions for each copula families. Consequently, If the authors obtained cross-tail-dependence functions (i.e., upper-lower, lower-upper), how does this affect the sample estimation? Will it be consistent with the normal sample estimates that obtains the conventional tail-dependence functions (i.e., Upper-upper, Lower-lower) with varying negative or positive sign to indicate rotation?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.