The IGARCH model

IGARCH means Integrated Generalized Autoregressive Conditional Heteroskedasticity and is a special form of the more general GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model. In order to understand the IGARCH model, it essential to have a basic undertanding of the concept of unit roots. Unit roots or non-stationarity are by no means easy to grasp and you might consider reading about integration first. For those familiar with the term, just a short reminder of what unit roots are. A stochastic process has a unit root if it is non-stationary, that means it is not mean reverting. It is equally difficult to understand an IGARCH model without understanding the basic principles of GARCH and ARCH models.

An IGARCH model tries to specify the second moment of a time series. Particularly financial time series are often not homoskedastic and the development of the volatility itself is of interest for a researcher. The mathematical expression of the IGARCH model looks as follows:

This looks exactly like a regular GARCH model. In order for this model to be an IGARCH model, it has to fulfill the following condition:

Hence, the conditional variance of the IGARCH model is clearly non-stationary. This has important implications for interpreting the volatility of such a time series. If α₁and α₂ indeed sum up to 1, the volatility of the model is not mean-reverting. External shocks leading to a change in volatility are permanent.

Modern computing makes it quick and easy to compute IGARCH models with statistical software packages. Note that OLS cannot be used to estimate the IGARCH model. In addition, the estimation is the same as for a regular GARCH model. After obtaining estimates for α₁and α₂ the model can be tested for stationarity. If the second equation from above holds, the model is an IGARCH model.

Unfortunately, the formulas didn't come out well. See the picture below.