Towards estimating extremal serial dependence via the bootstrapped extremogram
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Davis and Mikosch (2009a) introduced the extremogram as a flexible quantitative tool for measuring various types of extremal dependence in a stationary time series. There we showed some standard statistical properties of the sample extremogram. A major difficulty was the construction of credible confidence bands for the extremogram. In this paper, we employ the stationary bootstrap to overcome this problem. The use of the stationary bootstrap for the extremogram and the resulting interpretations are illustrated with several financial time series.
条件风险价值:半参数估计与推断
Conditional Value-at-Risk (CVaR) plays an important role in financial risk management. Nonparametric CVaR estimation suffers from the “curse of dimensionality” and slow convergence rate. To overcome these issues, we study semiparametric CVaR estimation and inference for parametric model with nonparametric noise distribution. Under a general framework that allows for many widely used time series models, we propose a semiparametric CVaR estimator that achieves the parametric…
厚尾与预测能力检验
We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test statistic converges to a nonstandard limit involving non-Gaussian stable random variables. As a consequence, conventional critical values can yield severely distorted inference: a nominal 5$\%$ test may reject a true null as often as 70$\%$ of…
时间序列分位数与预期短缺回归中的自归一化推断
This paper proposes valid inference tools, based on self-normalization, in time series expected shortfall regressions and, as a corollary, also in quantile regressions. Extant methods for such time series regressions, based on a bootstrap or direct estimation of the long-run variance, are computationally more involved, require the choice of tuning parameters and have serious size distortions when the regression errors are strongly serially dependent. In contrast, our…
动态系统性风险度量的统计推断
Systemic risk measures (SRM) quantify the risk of a system induced by the possible distress of any of its components. Applications in economics and finance are numerous. We define a general dynamic framework for the risk factors, allowing us to obtain explicit expressions of the corresponding dynamic SRM. We deduce an easy-to-implement statistical approach which, based on semi-parametric assumptions, reduces to estimating univariate location-scale models and to computing…
时间序列统计泛函的重叠分批置信区间:分位数、优化与估计应用
We propose a general purpose confidence interval procedure (CIP) for statistical functionals constructed using data from a stationary time series. The procedures we propose are based on derived distribution-free analogues of the $χ^2$ and Student's $t$ random variables for the statistical functional context, and hence apply in a wide variety of settings including quantile estimation, gradient estimation, M-estimation, CVAR-estimation, and arrival process rate estimation,…
基于极端依赖的时间序列模型设定检验
We propose a specification test for conditional location–scale models based on extremal dependence properties of the standardized residuals. We do so comparing the left-over serial extremal dependence—as measured by the pre-asymptotic tail copula—with that arising under serial independence at different lags. Our main theoretical results show that the proposed Portmanteau-type test statistics have nuisance parameter-free asymptotic limits. The test statistics are easy to…