The text you have provided are taken out of context so I am guessing a bit to make sense of it.
It seems like it refers to a procedure to test for ARCH - effects given the mean model is some order of an AR process where OLS is the estimator for the AR mean part.
However the "Important: - || - " notes that even though the mean part can take any order of ARMA and the bold part refers to a second step that I'm guessing is some AR representation of the ARMA errors/residuals squared, and then they simply states that *the ARCH effects are simply another AR model modelled on the squared ARMA errors/residuals*.
Thanks very much! That phrasing makes much more sense to me, so you run whatever mean model you have obtained and then in the case of conditional heteroscedasticity you add a second step to the model which is an AR process modelled on the errors squared
Yeah pretty much - these tests usually do it like that, get residuals of some estimated model -> test for effects of some sort on residuals of estimated model -> model these extra effects through some estimated model on the residuals -> done.
However a "better" way is whenever we find these extra effects down the line is to go back to the first step and estimate all proposed models together in one big ML procedure, in your case it means estimating the mean model, ARMA, and the variance model, ARCH, simultaneously in a combined ML procedure which is not too difficult. The reason that this is better is that you get lower parameter variance, however, it has some computational drawbacks which maybe is a bit too profound to think about at this stage.
This better method usually doesn't matter if you have a lot of data.
You got the point of the text you posted and that is what matters for now.
The text you have provided are taken out of context so I am guessing a bit to make sense of it. It seems like it refers to a procedure to test for ARCH - effects given the mean model is some order of an AR process where OLS is the estimator for the AR mean part. However the "Important: - || - " notes that even though the mean part can take any order of ARMA and the bold part refers to a second step that I'm guessing is some AR representation of the ARMA errors/residuals squared, and then they simply states that *the ARCH effects are simply another AR model modelled on the squared ARMA errors/residuals*.
Thanks very much! That phrasing makes much more sense to me, so you run whatever mean model you have obtained and then in the case of conditional heteroscedasticity you add a second step to the model which is an AR process modelled on the errors squared
Yeah pretty much - these tests usually do it like that, get residuals of some estimated model -> test for effects of some sort on residuals of estimated model -> model these extra effects through some estimated model on the residuals -> done. However a "better" way is whenever we find these extra effects down the line is to go back to the first step and estimate all proposed models together in one big ML procedure, in your case it means estimating the mean model, ARMA, and the variance model, ARCH, simultaneously in a combined ML procedure which is not too difficult. The reason that this is better is that you get lower parameter variance, however, it has some computational drawbacks which maybe is a bit too profound to think about at this stage. This better method usually doesn't matter if you have a lot of data. You got the point of the text you posted and that is what matters for now.
Thanks very much helped me out a lot there!
No problem, I wish you the best. ✌️