On studying extreme values and systematic risks with nonlinear time series models and tail dependence measures

This review paper discusses advances of statistical inference in modeling extreme observations from multiple sources and heterogeneous populations.The paper starts briefly reviewing classical univariate/multivariate extreme value theory,tail equivalence,and tail(in)dependence.New extreme value theory for heterogeneous populations is then introduced.Time series models for maxima and extreme observations are the focus of the review.These models naturally form a new system with similar structures.They can be used as alternatives to the widely used ARMA models and GARCH models.Applications of these time series models can be in many fields.The paper discusses two important applications:systematic risks and extreme co-movements/large scale contagions.

Distributed Estimator of Market Beta under Extreme Conditions

Market beta is a measure of the volatility or systematic risk of a security or portfolio compared to the market as a whole. This paper considers the distributed estimation of market beta in the case of massive data, and obtains the consistency and asymptotic normality of the estimator. Further, simulations show the finite sample properties of this estimator.

Estimates for the ruin probability of a time-dependent renewal risk model with dependent by-claims

Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs, with each pair obeying a dependence structure, and so do the by-claim sizes and the delay times. Supposing that the main claim sizes with by-claim sizes form a sequence of dependent random variables with dominatedly varying tails, asymptotic estimates for the ruin probability of the surplus process are investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity.

ALMOST SURE CONVERGENCE OF THE STABLE TAIL EMPIRICAL DEPENDENCE FUNCTION IN MULTIVARIATE EXTREME STATISTICS

In this paper we prove the almost sure convergence of the stable tail empirical dependence function for multivariate extreme values.

Conditional dependence between oil price and stock prices of renewable energy: a vine copula approach

The current paper focusses on the co-movement between oil prices and renewable energy stock markets in a multivariate framework.The vine copula approach that offers a great flexibility in conditional dependence modelling is used.More specifically,we investigate the issue of the average dependence and co-movement between oil prices(West Texas Intermediate[WTI])and renewable energy stock prices(Wilder Hill New Energy Global Innovation Index[NEX],Wilder Hill Clean Energy Index[ECO]and S and P Global Clean Energy Index[SPGCE])by applying the vine copula based threshold generalised autoregressive conditional heteroskedasticity(TGARCH)model.Over the period 2003–2016,empirical findings reveal significant and symmetric dependence between the considered markets.Therefore,there is symmetric tail dependence,indicating the evidence of upper and lower tail dependence.This means that movements in oil prices and renewable energy indices are coupled to the same direction.These empirical insights are of particular interest to policymakers,risk managers and investors in renewable energy sector.

AIEgen containing side-chain liquid crystalline polymers: Photoluminecence or photothermal, which dominate?

Why many luminescent liquid crystalline polymers(LLCPs)containing aggregation-induced emission luminogen(AIEgen)show weak emission is a question still to be answered.Herein,a series of LLCPs(α-Pns,n=4,8,and 12)with polynorbornene as main chain and twoα-dicyanodistyrylbenzene(α-DCS)as side chain are successfully synthesized to solve this issue.Differential scanning calorimetry(DSC),polarized light microscopy(PLM),one-dimentional(1D),two-dimentional(2D)middle-angle and wide-angle X-ray scattering(MAXS and WAXS)results demonstrate that the polymers form smectic A(SmA)phase with the side chains interdigitated packed within the smectic layers.Meanwhile,the photophysical properties ofα-Pns were investigated by ultraviolet-visible(UV-vis)absorption,steady state and time-resolved spectroscopy,and photothermal effect.Results show that the polymers are AIE active,but emit weak emission.The emission peak ofα-Pns film red-shift from 473 to 531 nm,the quantum yield gradually increases from around 1.6%to 14.7%,and the photothermal conversion efficiency decreases from 39%to 19%with the alkyl tail length increased.The photothermal effect,but not photoluminescence,dominates the excited state relaxation.