Continuous Time Approximations to GARCH(1, 1)-Family Models and Their Limiting Properties

Title & Authors
Continuous Time Approximations to GARCH(1, 1)-Family Models and Their Limiting Properties
Lee, O.;

Abstract
Various modified GARCH(1, 1) models have been found adequate in many applications. We are interested in their continuous time versions and limiting properties. We first define a stochastic integral that includes useful continuous time versions of modified GARCH(1, 1) processes and give sufficient conditions under which the process is exponentially ergodic and $\small{{\beta}}$-mixing. The central limit theorem for the process is also obtained.
Keywords
Exponential ergodicity;diffusion limit;L$\small{\acute{e}}$vy-driven volatility process;modified GARCH(1, 1) process;central limit theorem;
Language
English
Cited by
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