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Dynamic tail inference with log-Laplace volatility. (English) Zbl 07214716
Summary: 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.
MSC:
62G32 Statistics of extreme values; tail inference
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
60G70 Extreme value theory; extremal stochastic processes
60F10 Large deviations
60H40 White noise theory
91G70 Statistical methods; risk measures
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