An Introduction to GARCH Models

We give an introduction to the generalized autoregressive conditional heteroskedasticity (GARCH) model.

Specifically, we consider the GARCH(1,1) model. First, we present the model,. Second, we show that the innovations are conditionally normally distributed with a time-varying conditional variance. Third, we show that the GARCH(1,1) model implies an ARMA(1,1) process for the squared innovations, and we derive the unconditional variance of the innovations under the assumption that the condition for weak stationarity is fulfilled. Finally, we show that the conditional variance of the innovations can be rewritten as a function of all the past squared innovations.

[jrm]

Excellent explanation. Basically the only video on Youtube where you finally get why they always say a GARCH is an ARMA. Actually it is an ARMA on the residual and not on the variance itself. Simple rewritting in this video but I saw it nowhere else that was frustrating !

[Kirill-xpjq]

Every single GARCH model I see online is somehow different from every other GARCH model observed in the past. There should be a model to calculate variance of GARCH explanation youtube videos cuz, somehow, none of them are the same.

[pariscatesby]

Can u apply this to a real life example?

[shielareyes]

It would be helpful if you could pls explain each symbol of the Garch model.. not everyone understands the symbols

[sam]

What about the conditional mean? What is the conditional mean of Yt?

[sahilaseeja]

sir will u please tell me how we gonna use volatility in improving the predicted value generated from arima ?

[jgcaap]

do you could, by any chance, assist me on using GARCH to detect seasonal anomalies? having difficulties on it.

[andriamamonjynorofarahery]

can you tell me what is the x't? please!

[andriamamonjynorofarahery]

hey! please tell me about x't ! :(

[earningthomas]

Terrible explanation. I had to just skip this video