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the questions are about GARCH-t (1,1) [t-distribution].

The first question in GARCH-t (1,1) model, the alpha (ARCH) is insignificant. How to rewrite the model?

The second one, in case of insignificant alpha. How to verify stationarity? I know that the alpha + beta < 1 model is stationary. In this case, should I take the only beta? 0 + beta < 1?

The last question concerns the formal side of my paper. I have 9 variables, according to AIC, for all except 2 of them the GARCH (1,1) is the best. Can I assume that for all times series GARCH(1,1) taking into account that for most of the cases GARCH (1,1) is the best and only this model is used in the order to compare properties of times series?

Thank You for an answer!

Dawid
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  • See my answer in [this thread](https://stats.stackexchange.com/questions/113294/) illustrating that a GARCH model with $\alpha=0$ does not really make sense. Also be aware that significance testing of parameters in GARCH models is nontrivial and the $p$-values supplied by your favourite software may be wrong; see my answer [here](https://stats.stackexchange.com/questions/256146/testing-parameter-significance-in-a-garch-model) for more information. – Richard Hardy Sep 20 '19 at 08:12

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If the coefficient Alpha is not significant then it is not a Garch, anyway you have to set Alpha equal to 0 and, if the info criteria that you are using tell that this is the best possible specification of the model for your data, then use it.

Theoretically it would be more appropriate to test Alpha+beta instead of disjointed testing alpha and beta and then calculate the sum. But if your package of interest does not allow you to do that, then it is acceptable to look at the absolute value of beta only as you are doing.

Theoretically you should choose the best specification for each model if you are fitting and testing 9 univariate models disjointly. However, if you wish to simplify, just highlight in the paper that for convenience you are simplifying and are extending the use of Garch to everyone.

Fr1
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  • Regarding your first paragraph: see [this thread](https://stats.stackexchange.com/questions/113294/) illustrating that a GARCH model with $\alpha=0$ does not really make sense. Also be aware that significance testing of parameters in GARCH models is nontrivial and the $p$-values supplied by your favourite software may be wrong; see my answer [here](https://stats.stackexchange.com/questions/256146/testing-parameter-significance-in-a-garch-model) for more information. – Richard Hardy Sep 20 '19 at 08:14