Estimate GARCH Model from Time Series

[Niklas Paetzold]

Hallo,

I am a student and new to Stata. For a university course I have to model a GARCH model from time series data (euro-dollar exchange rate by the ECB).

I am not allowed to use the built-in modeling procedure but should do the procedure on my own step-by-step.

1. I load the data.
tsset newdate

2. I generate the first difference of the exchange rate.
gen Dvalue = value - L.value

3. I estimate the mean equation as an AR(1) process.
reg Dvalue L.Dvalue

4. I predict the residuals and square them.
predict Dresid, resid
gen Dresid_sq = Dresid^2

5. Now I run a regression of the squared residuals on its lag as a first step to get to the GARCH model.
reg Dresid_sq L.Dresid_sq

6. From this I want to compute the conditional variance of the time series
gen hsq = _b[_cons] + _b[L1.Dresid_sq]*L.Dresid_sq

7. Now, I want to estimate the GARCH(1,1) model.
reg hsq L.hsq L.Dresid_sq

Unfortunately, I get only coefficients no standard errors or p-values.

Would it be an option to do step 7 as a Maximum Likelihood Estimation? How would this be done?

Any help is appreciated. Thanks.

[Niklas Paetzold]

I want to put my question in a different form. Starting from a time series (euro-dollar exchange rate), how can I compute the conditional variance?