Continuation of GARCH(1,1) without initial raw data

[dnyrm]

Hi there,

How do I continue modeling volatility, under GARCH(1,1), using the following key parameters that belong to a successful model (aka I wouldn't have access to the initial raw data anymore)?

mu 0.000961​

omega 4e-06​

alpha 0.2604​

beta 0.721​

long-run volatility 0.0149​

log-likelihood 4691.0025​

New daily values:

'2021-06-25': 4280.700195,​

'2021-06-28': 4290.609863,​

'2021-06-29': 4291.799805,​

'2021-06-30': 4297.500000,​

'2021-07-01': 4319.939941,​

'2021-07-02': 4352.339844​

The GARCH parameters plus these new values belong to the daily returns of the S&P500.

Thanks!

 

[lourano.x]

For the best results, I’d suggest refitting your GARCH once you have new values. Rather than fitting the model from the initial dataset every time, consider using a rolling window approach to select the optimal training period. In my practise, previously estimated parameters become less accurate for second, third, ... steps.