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I run a standard GARCH (1,1) model and obtain the following results.

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Thereafter, I add an external regressor in the same model and obtain the following results:

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The GARCH coefficient (beta1) is zero and the p-value is 1. The coefficient of the external regressor (vxreg1) is 0.415 with p-value of 0.000.

I use the robust standard errors.

How to interpret the result? Should I concur that the external regressor reduces/removes volatility contemporaneously?

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Interesting. I would not say the external regressor reduces/removes volatility but it is able to fit/explain it better than the previous period's conditional variance $\sigma_{t-1}^2$ can. This reminds me a bit of the realized GARCH model. There, including lagged realized variance into the conditional variance equation tends to make the lagged squared return term not statistically significant; see slide 36 of Peter R. Hansen's "Lecture 3: Realized GARCH Models" (2016). Meanwhile, in your case the external regressor does the same for lagged conditional variance.

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  • $\begingroup$ Thank you very much for this explanation. Much appreciated. $\endgroup$
    – Jyoti Nair
    Commented Nov 2, 2022 at 8:33
  • $\begingroup$ @JyotiNair, you are welcome! I am still thinking why/how this would be happening. $\endgroup$
    – Richard Hardy
    Commented Nov 2, 2022 at 8:56
  • $\begingroup$ I ran a return equation of ARMA (6,3), as the optimised lags with minimum AIC score. If there is anyway I can share the data with you, and if you are keen, I will be more than happy to share. $\endgroup$
    – Jyoti Nair
    Commented Nov 3, 2022 at 7:27
  • $\begingroup$ @JyotiNair, thank you, but I am thinking more in theoretical terms here. $\endgroup$
    – Richard Hardy
    Commented Nov 3, 2022 at 10:55
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    $\begingroup$ @JyotiNair, well, you have a statistically significant $\alpha_1$, so past squared error has something to say about today's conditional variance, too, even when the external regressor is accounted for. $\endgroup$
    – Richard Hardy
    Commented Nov 7, 2022 at 10:52

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