COVID-19: Tail Risk and Predictive Regressions

厚尾与预测能力检验

Heavy Tails and Predictive Ability Testing

本文研究了在预测误差具有厚尾时广泛使用的预测准确性评估和比较检验的渐近行为，发现当损失差异具有无限方差时，Diebold-Mariano检验统计量收敛于非标准极限，涉及非高斯稳定随机变量，传统临界值可能导致严重失真推断。为此，作者开发了新的稳定极限定理，并基于此理论提出了一种子采样推断方法，该方法在尾部厚重时仍有效且无需估计长期方差或尾部指数。对新兴市场汇率风险预测的应用表明，考虑厚尾可显著改变预测性能的结论。

使用逐节点分位数预测回归模型进行带尾部估计的协方差结构统计估计

Statistical Estimation for Covariance Structures with Tail Estimates using Nodewise Quantile Predictive Regression Models

本文针对带尾部估计的协方差结构，提出用分位数预测回归估计VaR-CoVaR风险矩阵，还构建了无调优参数、具有一致性的FOCE变量选择算法，经真实与模拟数据集验证可用于网络系统性风险建模。

Financial Return Distributions: Past, Present, and COVID-19

We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017--2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and $q$-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called "inverse-cubic power…

Dynamic tail inference with log-Laplace volatility

We propose a family of models that enable predictive estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. The models are a white noise process with conditionally log-Laplace stochastic volatility. In contrast to other, similar stochastic volatility formalisms, this process has analytic expressions for its conditional probabilistic structure that enable straightforward estimation of dynamically changing extreme event probabilities. The process and volatility are conditionally Pareto-tailed, with tail exponent given by the reciprocal of th…