Estimating multivariate GARCH and stochastic correlation models equation by equation

Christian Francq and Jean-Michel Zakoian

MPRA Paper from University Library of Munich, Germany

Abstract: A new approach is proposed to estimate a large class of multivariate volatility models. The method is based on estimating equation-by-equation the volatility parameters of the individual returns by quasi-maximum likelihood in a first step, and estimating the correlations based on volatility-standardized returns in a second step. Instead of estimating a $d$-multivariate volatility model we thus estimate $d$ univariate GARCH-type equations plus a correlation matrix, which is generally much simpler and numerically efficient. The strong consistency and asymptotic normality of the first-step estimator is established in a very general framework. For generalized constant conditional correlation models, and also for some time-varying conditional correlation models, we obtain the asymptotic properties of the two-step estimator. Our estimator can also be used to test the restrictions imposed by a particular MGARCH specification. An application to financial series illustrates the interest of the approach.

Keywords: Constant conditional correlation; Dynamic conditional correlation; Markov switching models; Multivariate GARCH; Quasi maximum likelihood estimation (search for similar items in EconPapers)
JEL-codes: C01 C13 C32 (search for similar items in EconPapers)
Date: 2014
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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Citations: View citations in EconPapers (2)

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