I am really trying to invest some time to estimate a GARCH(1,1) method, I know there is many statistical packages that will do this for me (Eviews, MATLAB, R), but I am trying to do this by hand, so that I can really understand the model.

Following the theory from Verbeek. 'A guide to modern econometrics',

I first estimate an AR(1) model,

$$Y_t= \alpha +\theta Y_{t-1} +\varepsilon_t $$

And then I save the residuals, $\varepsilon_t$,

I then want to model a GARCH(1,1) with these residuals.

$$\sigma_t^2=\omega+\alpha \varepsilon_{t-1}^2 +\beta\sigma_{t-1}^2$$

This is where I am struggling, I understand a few things, I understand how I can get the lagged $\varepsilon_{t-1}^2$, I already have it from the first equation, however my major question is how do I get a value for $\sigma_{t-1}^2$ this is what I am trying to estimate, so I am really struggling about how I derive this part. I suppose I need a series for $\sigma_{t-1}^2$, which in matrix terms is a long as the $\varepsilon_{t-1}^2$.

I am thinking I may need to use a for loop to get this $\sigma_{t-1}^2$, but any suggestions on how I might go about this would be helpful.

Second, when I do realise how to do the above step, I need to estimate the thing my maximum likelihood estimation. I think I read around this and try my best to solve it.

I would really like help on step one if anyone has got the time or direction to a good reference?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.