  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
the log-volatility's mean absolute innovation. This formalism can accommodate a
wide variety of nonlinear dependence, as well as conditional power law-tail
behavior ranging from weakly non-Gaussian to Cauchy-like tails. We provide a
computationally straightforward estimation procedure that uses an asymptotic
approximation of the process' dynamic large deviation probabilities. We
demonstrate the estimator's utility with a simulation study. We then show the
method's predictive capabilities on a simulated nonlinear time series where the
volatility is driven by the chaotic Lorenz system. Lastly we provide an
empirical application, which shows that this simple modeling method can be
effectively used for dynamic and predictive tail inference in financial time
series.
