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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?

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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).

References

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  • $\begingroup$ 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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