Dynamic conditional eigenvalue GARCH

Simon Hetland, Rasmus Søndergaard Pedersen and Anders Rahbek

Journal of Econometrics, 2023, vol. 237, issue 2

Abstract: In this paper we introduce a multivariate generalized autoregressive conditional heteroskedastic (GARCH) class of models with time-varying conditional eigenvalues. The dynamics of the eigenvalues is derived for the cases with underlying Gaussian and Student’s t-distributed innovations based on the general theory of dynamic conditional score models by Creal, Koopman and Lucas (2013) and Harvey (2013). The resulting time-varying eigenvalue GARCH models – labeled ‘λ-GARCH’ models – differ for the two cases of innovations, similar to, and generalizing, univariate linear Gaussian GARCH and Student’s t-based Beta-t-GARCH models. Asymptotic theory is provided for the Gaussian-based quasi-maximum likelihood estimator (QMLE). In addition, and in order to test for the number of (linear combinations of) the time-varying eigenvalues, we consider testing and inference under the hypothesis of reduced rank of the GARCH loading matrices. The conditional Gaussian and Student’s t distributed λ-GARCH models are applied to US return data, and it is found that the eigenvalue structure for the sample considered indeed satisfies the hypothesis of reduced rank. Specifically, it is possible to disentangle time-varying linear combinations of the eigenvalues, or factors, from time-invariant factors which drive the dynamics of the conditional covariance.

Keywords: Multivariate GARCH; GO-GARCH; Reduced rank; Asymptotic theory (search for similar items in EconPapers)
JEL-codes: C32 C51 C58 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:237:y:2023:i:2:s0304407621002141

DOI: 10.1016/j.jeconom.2021.09.003

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