Estimation of limiting conditional distributions for the heavy tailed long memory stochastic volatility process

TL;DR

This paper investigates the limiting behavior of future extreme events in heavy-tailed, long memory stochastic volatility models, introducing estimators and analyzing their asymptotic properties.

Contribution

It introduces estimators for limiting conditional distributions in heavy-tailed, long memory stochastic volatility processes and studies their asymptotic behavior, accounting for long memory effects.

Findings

Limiting conditional distributions differ from i.i.d. cases.

Estimator convergence rates depend on the long memory parameter.

Asymptotic properties are characterized for processes with long memory.

Abstract

We consider Stochastic Volatility processes with heavy tails and possible long memory in volatility. We study the limiting conditional distribution of future events given that some present or past event was extreme (i.e. above a level which tends to infinity). Even though extremes of stochastic volatility processes are asymptotically independent (in the sense of extreme value theory), these limiting conditional distributions differ from the i.i.d. case. We introduce estimators of these limiting conditional distributions and study their asymptotic properties. If volatility has long memory, then the rate of convergence and the limiting distribution of the centered estimators can depend on the long memory parameter (Hurst index).