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Dynamic conditional eigenvalue GARCH

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  • Hetland, Simon
  • Pedersen, Rasmus Søndergaard
  • Rahbek, Anders

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.

Suggested Citation

  • Hetland, Simon & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2023. "Dynamic conditional eigenvalue GARCH," Journal of Econometrics, Elsevier, vol. 237(2).
    • Handle: RePEc:eee:econom:v:237:y:2023:i:2:s0304407621002141
    DOI: 10.1016/j.jeconom.2021.09.003
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    Cited by:

    1. Eric A. Beutner & Yicong Lin & Andre Lucas, 2023. "Consistency, distributional convergence, and optimality of score-driven filters," Tinbergen Institute Discussion Papers 23-051/III, Tinbergen Institute.

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    More about this item

    Keywords

    Multivariate GARCH; GO-GARCH; Reduced rank; Asymptotic theory;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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