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尾过程推断及其在金融时间序列建模中的应用AI 解读

To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees et al., (2015) proposed nonparametric estimators of the spectral tail process. The methodology can be extended to the more general setting of a stationary, regularly varying time series. The large-sample distribution of the estimators is derived via empirical process theory for cluster functionals. The finite-sample performance of these estimators is evaluated via Monte Carlo…

利用自助法极值相关图估计极端序列依赖AI 解读

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…

非负 Lévy 驱动 CARMA 过程的估计AI 解读

Continuous-time autoregressive moving average (CARMA) processes with a nonnegative kernel and driven by a nondecreasing Lévy process constitute a useful and very general class of stationary, nonnegative continuous-time processes that have been used, in particular, for the modeling of stochastic volatility. Brockwell, Davis, and Yang (2007) derived efficient estimates of the parameters of a nonnegative Lévy-driven CAR(1) process and showed how the realization of the…

重尾过程的样本自相关及其在 ARCH 模型中的应用AI 解读

We study the sample ACVF and ACF of a general stationary sequence under a weak mixing condition and in the case that the marginal distributions are regularly varying. This includes linear and bilinear processes with regularly varying noise and ARCH processes, their squares and absolute values. We show that the distributional limits of the sample ACF can be random, provided that the variance of the marginal distribution is infinite and the process is nonlinear. This is in…