Abstract
For the financial time series modeling, the models with conditional heteroscedasticity GARCH are most commonly used. The estimation of GARCH models is already implemented in many software products.
However, when working with high-frequency data such as stock market prices or index levels, classical estimation methods often fail, and it is necessary to use a recursive approach. In literature, recursive estimation formulas for several GARCH models have already been suggested.
The aim of this contribution is to modify the GARCH model estimation algorithm for the model IGARCH (Integrated GARCH model), GARCH model with a unit root in the autoregressive polynomial in the volatility equation. This model proves to be useful in situations of high-frequency financial data, where it often happens that the sum of GARCH model parameters is close to one.
This paper includes both mathematical derivation of a recursive algorithm for the IGARCH model and also an application of this algorithm.