Asymmetric excitation of left- and right-tail extreme events probed using a Hawkes model: Application to financial returns.

@article{Tomlinson2021AsymmetricEO,
  title={Asymmetric excitation of left- and right-tail extreme events probed using a Hawkes model: Application to financial returns.},
  author={Matthew F. Tomlinson and David Greenwood and Marcin Mucha-Kruczyński},
  journal={Physical review. E},
  year={2021},
  volume={104 2-1},
  pages={
          024112
        }
}
We construct a two-tailed peaks-over-threshold Hawkes model that captures asymmetric self- and cross-excitation in and between left- and right-tail extreme values within a time series. We demonstrate its applicability by investigating extreme gains and losses within the daily log-returns of the S&P 500 equity index. We find that the arrivals of extreme losses and gains are described by a common conditional intensity to which losses contribute twice as much as gains. However, the contribution of… 
2T-POT Hawkes model for dynamic left- and right-tail quantile forecasts of financial returns: out-of-sample validation of self-exciting extremes versus conditional volatility
Matthew F. Tomlinson, 2, ∗ David Greenwood, and Marcin Mucha-Kruczyński 4 Department of Physics, University of Bath, Bath BA2 7AY, United Kingdom Centre for Networks and Collective Behaviour,

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