Dynamic conditional eigenvalue GARCH

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