Whittle estimation in multivariate CCC-GARCH processes

Abstract

In this paper, we explore some probabilistic properties and statistical analysis of multivariate constant conditional correlation GARCH (CCC-GARCH for short) model. So, in the first part we give the conditions for the model stationarity and its finite moments up to some orders. In the second part, the Whittle estimator is proposed for the parameters CCC-GARCH model based on a transformation. This Whittle estimator is shown to be consistent when the data have finite 4th moment, and its asymptotic normality is established when the data have finite 8th moment. Finite sample properties of this Whittle estimator are further examined through Monte-Carlo experiments.

KEYWORD:

• Multivariate CCC-GARCH models
• stationarity
• whittle estimator
• consistency
• asymptotic normality

2010 Mathematics Subject Classifications:

• Primary 62M10
• Secondary 62F10
• 62F12
• 62P20

Acknowledgement

The authors would like to express their gratitude to the anonymous referee for the constructive comments which led to an improved presentation of this paper. This could not have been done without his/her honest dedication.