ON TAIL INDEX ESTIMATION FOR DEPENDENT, HETEROGENEOUS DATA

By Jonathan B. Hill. Econometric Theory, 2010

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Pareto Smoothed Importance Sampling (2015, background): “(14) Ionides (2008) proposes an Monte Carlo error estimate which also takes the bias into account.”
MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES (2017, background): “Consistency and asymptotic normality under serial dependence conditions—including -dependence, β-mixing, ARCH—were established by various authors (see e.g., Hill (2010), De Hann, Mercadier, and Zhou (2016) and the references therein).”
Frontiers in VaR forecasting and backtesting (2016, background): “The corresponding VaR forecast is given by V̂ aR HILL t = R(k+1) ( α k/T ) ξ̂ , (7) where ξ̂ = 1k k∑ j=1 ( log(R(j)) log ( R(j+1) )) ; see Peng and Qi (2006b) and Hill (2010) for the asymptotic properties of the tail index estimator for dependent, heterogeneous processes.”
Tail Risk and Asset Prices (2014, unknown): “We conduct inference using the Hodrick’s (1992) standard error correction for overlapping data.”