This is known as an ARCH(1) model.
l We can easily extend this to the general case where the error variance depends on q lags of squared errors:
l This is an ARCH(q) model.
l So the GARCH(1,1) model can be written as an infinite order ARCH model.
is termed intergrated GARCH
lFor non-stationarity in variance, the conditional variance forecasts will not converge on their unconditional value as the horizon increases.
- Specify the appropriate equations for the mean and the variance - e.g. an AR(1)- GARCH(1,1) model:
- Specify the log-likelihood function to maximise:
- The computer will maximise the function and give parameter values and their standard errors
l Consider a single parameter, q to be estimated, Denote the MLE as (estimated theta) and a restricted estimate as (congruent theta) .
Presented by Dr. Babar Zaheer Butt to the students of MS/Ph.D at Iqra University Islamabad.