Geodesic
Estimation of parameters of autoregressive models with fractional differences in the presence of additive noise
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 29 (2023) no. 3, pp. 93-99

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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.
Keywords: Fractional difference, autoregressive model, total least squares, additive noise, unknown ratio of variances, generalized instrumental variables, long run memory. 
@article{VSGU_2023_29_3_a10,
     author = {D. V. Ivanov},
     title = {Estimation of parameters of autoregressive models with fractional differences in the presence of additive noise},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {93--99},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2023_29_3_a10/}
}
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D. V. Ivanov. Estimation of parameters of autoregressive models with fractional differences in the presence of additive noise. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 29 (2023) no. 3, pp. 93-99. http://geodesic.mathdoc.fr/item/VSGU_2023_29_3_a10/