Extremal local linear quantile regression for heavy-tailed time series with near epoch dependence

This paper develops a data-driven inference procedure for extreme analysis of data with near epoch dependence (NED), a condition less restrictive than traditional dependence structures like α-mixing, making it particularly useful for analyzing heavy-tailed time series data. To capture nonlinear data structures, we propose a new framework that combines local linear quantile regression with extreme value theory. We first study the asymptotic properties of the local-linear intermediate conditional quantile (IQR) estimators under NED by establishing the Bahadur representation. While we show the IQR estimator exhibits the desired asymptotic normality for NED data, it is unstable and inaccurate for estimation at extreme quantile levels. Therefore, we develop an enhanced Hill method to estimate the nonlinear extreme value index (EVI) and, consequently, the extreme conditional quantiles (ECQ) based on the tail properties and extrapolation. We show that the proposed EVI and ECQ estimators have the same asymptotic bias. We further develop a bias correction approach to refine these estimators. We thoroughly study the properties of the proposed EVI and ECQ estimators under NED, and their bias-corrected counterparts. Simulation studies and real data analyses demonstrate the effectiveness and applicability of the proposed methods

Linear regression · Quantile · Quantile regression · Regression · Time series · Advanced Statistical Methods and Models · Financial Risk and Volatility Modeling · Statistical Methods and Inference

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