An Improved FIGARCH Model with The Difference Operator (1-Vl)D

We propose a new model called the product memory GARCH model by replacing (1-L)d in the FIGARCH model with (1-vL)d for 0≤v≤1, where the impulse response function in its ARCH(infinity) process has a decay rate in the form of the product of a geometric memory rate and a hyperbolic memory rare when the lags increase. The non-negativity constraints, the existence of the second, fourth, sixth and eighth moments, and the memory length are investigated, and the Gaussian quasi-maximum likelihood estimation is also discussed. The improved model is of great significance in the evolution of GARCH-type models