## Dynamic Tail Inference with Log-Laplace Volatility. (arXiv:1901.02419v1 [stat.ME])

We propose a family of stochastic volatility models that enable direct
estimation of time-varying extreme event probabilities in time series with
nonlinear dependence and power law tails. The models are a white noise process
with conditionally log-Laplace stochastic volatility. In contrast to other,
similar stochastic volatility formalisms, this process has an explicit,
closed-form expression for its conditional probability density function, which
enables straightforward estimation of dynamically changing extreme event
probabilities. The process and volatility are conditionally Pareto-tailed, with
tail exponent given by the reciprocal of the log-volatility's mean absolute
innovation. These models thus can accommodate conditional power law-tail
behavior ranging from very weakly non-Gaussian to Cauchy-like tails.
Closed-form expressions for the models' conditional polynomial moments also
allows for volatility modeling. We provide a straightforward, probabilistic
method-of-moments estimat查看全文