Fractionally integrated time varying GARCH model

This paper introduces the new FITVGARCH model to describe both long memory and structural change behaviour in the volatility process by allowing for time varying dynamic structure in the conditional variance. The parameters of the conditional variance in the FIGARCH model are allowed to change smoothly over time. We derive an LM-type test for parameter constancy of the FIGARCH model against the alternative of time dependent parameters. Simulation analysis shows that both empirical size and power of the constancy test are quite good. An empirical application to the stock market volatility indicates that this new class of model seems to outperform the FIGARCH model in the description of the daily NASDAQ composite index returns.