Estimation of parameters of autoregressive models with fractional differences in the presence of additive noise

For modeling in time series, models with fractional differences are widely used. The best known model is the ARFIMA (autoregressive fractionally integrated moving average) model. It is known that for integer-order autoregressive models, autoregressive models with additive noise can outperform ARMA and autoregressive models in terms of accuracy. This article considers a class of autoregressive models with fractional order differences. The article presents a new method for estimating parameters autoregressive models with fractional differences in the presence of additive noise with an unknown variance of additive noise. The propose algorithm was realized in Matlab. The simulation results show the high efficiency of the propose algorithm.