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ON QML-ESTIMATION OF MULTIVARIATE CONSTANT CONDITIONAL CORRELATION HYPERBOLIC GARCH MODELS
Keywords:
HGARCH model, multivariate long memory models, strong consistency, asymptotic normalityDOI:
https://doi.org/10.17654/0972086325004Abstract
The purpose of this paper is to present a theoretical methodology for estimation of a multivariate constant conditional correlation hyperbolic GARCH (CCC-HGARCH) model. The proposed model captures correlations between several time series exhibiting long memory property in volatility and finite variance observed on the same time period. This model extends the class of hyperbolic GARCH processes with finite variance to a multivariate framework. The goal of this work is to model volatility of multivariate hyperbolic GARCH processes by conditional covariance matrix based on a time invariant correlation matrix. We first provide a sufficient condition for the existence of strictly stationary solution of the CCC-HGARCH model. Secondly, the asymptotic properties of the quasi-maximum likelihood estimator are established.
Received: August 9, 2024
Accepted: October 21, 2024
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