I read a paper a few years ago that specifies a multivariate GARCH model with a particular form of rolling correlations. The GARCH literature is full of abbreviations and differing terminology which is probably why I have not been able to track down this particular model.

In this model, variances are modeled separately according to the usual univariate GARCH(1,1) process: $\sigma_{i,t}^2=\omega_i+\alpha_i e_{i,t-1}^2+\beta_i \sigma_{i,t-1}^2$. $e_{i,t}$ is the residual at time $t$ for the $i$th variable/component and $\sigma_{i,t}^2$ is the associated conditional variance.

Time-varying correlations $R_t$ are modeled as $R_t=(1-\theta_1-\theta_2)\overline{R}+\theta_1\Psi+\theta_2 R_{t-1}$. $\overline{R}$ is a constant correlation matrix and $\Psi$ is the empirical correlation matrix of the residuals in the previous $k$ periods before time $t$.

What is this model called?


1 Answer 1


At a glance, this looks like the time-varying correlation (TVC) / varying correlation (VC) / varying conditional correlation (VCC) GARCH model of Tse and Tsui (2002) as mentioned on p. 21 in Bauwens et al. (2006) and on p. 10 in Silvennoinen and Terasvirta (2009).


  • $\begingroup$ Thank you for the answer. This looks right so I am making as "accepted". The paper I recall was different, but there is no doubt Tse and Tsui (2002) describes this exact model. Now that I have this citation I will add a comment later if I happen to find the exact one that I was thinking of. $\endgroup$
    – R Small
    Commented Oct 13, 2022 at 0:20
  • $\begingroup$ @RSmall, sounds good. $\endgroup$ Commented Oct 13, 2022 at 8:36

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