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

- Journal title : Communications for Statistical Applications and Methods
- Volume 21, Issue 4, 2014, pp.327-334
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CSAM.2014.21.4.327

Title & Authors

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

Lee, O.;

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 -mixing. The central limit theorem for the process is also obtained.

Keywords

Exponential ergodicity;diffusion limit;Lvy-driven volatility process;modified GARCH(1, 1) process;central limit theorem;

Language

English

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