Hello,

So I'm learning about GARCH and ARIMA models and am curious as to how to apply these models in real life.  Like what do people in real life do with them?  So let's say I want to model the returns of some asset using a GARCH model.  I have historical daily returns up until T0, which is end of day yesterday.  I fit a GARCH model to my data.  

Question 1: My GARCH(1,1) model is only good for 1 step prediction correct?  So it's only good for predicting T+1.  It seems like in class, two step predictions and predictions after that are very close if not equal to my 1 step prediction that it doesn't seem to tell me anything.  For T+2, you are using your forecasted residual of T+1 and the forecasted variance of T+1, which end up being the same?

Question 2: Because of that, I'm guessing in practice, people re-estimate the coefficients each day, as yesterday's return becomes observable.  Is this true?  Do people re-estimate the coefficients of their time series model as often as the period of their data?  Or, do they keep the same coefficients and just take the error from yesterday's return (now that it's observable), and use that input to predict tomorrow's return.

Thanks!

1. here is Engle on applications. His putative application is banks doing VaR. Do they actually use GARCH in VaR? I don't know, but it's plausible. When all is said and done, I will guess 90+% of applications are "academic". As a pure volatility predictor (say for trading), it's going to be sub-optimal unless combined with forward looking measures like VIX -- there is more discussion in my recent book on that. (use the link below to follow up on that).

2. say your data is daily observations over the last 5 years, so roughly 1250 obs. Adding a day isn't going to change the estimated coefs much. So, it is only necessary to re-estimate  whenever it is convenient for the application or workflow.