We present a stochastic volatility modeling method that enables flexible and computationally efficient estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. Our approach uses a white noise process with conditionally log-Laplace volatility. In contrast to other, similar stochastic volatility frameworks, this process has analytic expressions for its probabilistic structure that enable straightforward and computationally inexpensive estimation of dynamically changing extreme event probabilities. The process is conditionally power law-tailed, with tail exponent defined by the log-volatility’s mean absolute innovation. This modeling method can accommodate a wide variety of time series or covariate-based dependence, as well as conditional tail behavior ranging from weakly non-Gaussian to Cauchy-like tails. We provide a straightforward, moment-based estimation procedure, which uses an asymptotic approximation of the process’ dynamic large deviation probabilities. We show that this simple modeling method can be effectively used for dynamic and predictive tail inference in nonlinear and financial time series.

中文翻译：

---

具有log-Laplace波动率的动态尾部推断

我们提出了一种随机波动率建模方法，该方法能够灵活且计算有效地估计在重尾和非线性相关的时间序列中随时间变化的极端事件概率。我们的方法使用白噪声过程，并有条件地进行对数拉普拉斯波动。与其他类似的随机波动率框架相比，此过程针对其概率结构具有解析表达式，可以对动态变化的极端事件概率进行简单且计算上便宜的估算。该过程有条件地按幂定律尾部，尾指数由对数波动率的平均绝对创新定义。这种建模方法可以适应各种时间序列或基于协变量的依赖性，以及从弱非高斯到柯西式尾巴的条件尾巴行为。我们提供了一个简单的基于矩的估计程序，该程序使用过程的动态大偏差概率的渐近逼近。我们表明，这种简单的建模方法可以有效地用于非线性和财务时间序列中的动态和预测尾部推理。