On Analysis of Fractional Order System Identification

This paper focuses on analyzing systems with long-range memory properties. Towards this goal, autoregressive fractionally integrated moving average (ARFIMA) model which is a well-known class of long-memory models, is employed as they capture long-range dependence (LRD) through its fractional differencing parameter as well as short-range dependence (SRD) through autoregressive (AR) model and moving average (MA) model parameters. The coefficients of the ARFIMA model are estimated based on both the exact likelhood and its Whittle approximation. Using a numerical example, it is illustrated that ARFIMA model provides an excellent fit to data that exhibits long-range memory.