Estimation of parameters of autoregressive models with fractional differences in the presence of additive noise
D. V. Ivanov

References
1.	Stiassnie M., “On the application of fractional calculus for the formulation of viscoelastic models”, Applied Mathematical Modelling, 3:4 (1979), 300–302
2.	Bagley R.L., “Fractional calculus - a different approach to the analysis of viscoelastically damped structures”, AIAA Journal, 21:5 (1983), 741–748
3.	Reyes-Melo M.E., Martinez-Vega J.J., Guerrero-Salazar C.A., Ortiz-Mendez U., “Application of fractional calculus to modeling of relaxation phenomena of organic dielectric materials”, Proceedings International Conference Solid Dielectrics, ICSD'04 (Toulouse, 2004), v. 2, 530–533
4.	Vinagre B.M., Feliu V., “Modeling and control of dynamic system using fractional calculus: Application to electrochemical processes and flexible structures”, Proceedings of 41-st IEEE Conference Decision Control (Las Vegas, 2002), 214–239 https://www.researchgate.net/profile/Vicente-Feliu-2/publication/252440774_Modeling_and_control_of_dynamic_system_using_fractional_calculus_Application_to_electrochemical_processes_and_flexible_structures/links/\ldots
5.	Granger C.W., Joyeux R., “An introduction to long-memory time series models and fractional differencing”, Journal of Time Series Analysis, 1:1 (1980), 15–29
6.	Hosking J.R.M., “Fractional differencing”, Biometrika, 68:1 (1981), 165–176
7.	Woodward W.A., Cheng Q., Gray H.L., “A k-factor GARMA long-memory model”, Journal of Time Series Analysis, 19:4 (1998), 485–504
8.	Ivanov D.V., Engelgardt V.V., Sandler I.L., “Genetic Algorithm of Structural and Parametric Identification of Gegenbauer Autoregressive with Noise on Output”, Procedia Computer Science, 131 (2018), 619–625
9.	Giraitis L., Leipus R., “A generalized fractionally differencing approach in long memory modelling”, Lithuanian Mathematical Journal, 35 (1995), 53–65
10.	Reisen V.A., Rodrigues A.L., Palma W., “Estimation of Seasonal Fractionally Integrated Processes”, Computational Statistics & Data Analysis, 50:2 (2006), 568–582
11.	Reisen V.A., Rodrigues A.L., Palma W., “Estimating seasonal long-memory processes: A Monte Carlo study”, Journal of Statistical Computation and Simulation, 76:4 (2006), 305–316
12.	Meerschaert M.M., Sabzikar F., Phanikumar M.S., Zeleke A., “Tempered fractional time series model for turbulence in geophysical flows”, Journal of Statistical Mechanics Theory and Experiment, 2014, P09023
13.	Sabzikar F., Meerschaert M.M., Chen J., “Tempered Fractional Calculus”, Journal of Computational Physics, 293 (2015), 14–28
14.	Ram M., Recent Advances in Time Series Forecasting, 1st ed., eds. Bisht D.C.S., CRC Press, Boca Raton, FL, USA, 2021, 238 pp.
15.	Palma W., Long-memory time series: Theory and Methods, Wiley, Hoboken, NJ, USA, 2006, 304 pp. https://books.google.ru/books?id=NtSbmQyQcSMC&printsec=frontcover&hl=ru#v=onepage&q&f=false
16.	Guidorzi R., Diversi R., Vincenzi L., Simioli V., “AR+ noise versus AR and ARMA models in SHM-oriented identification”, Proceedings of the 23rd Mediterranean Conference on Control and Automation (MED) (Torremolinos, Spain, 16–19 June, 2015), 809–814
17.	Ivanov D., Yakoub Z., “Overview of Identification Methods of Autoregressive Model in Presence of Additive Noise”, Mathematics, 11:3 (2023), 607 pp.
18.	Ivanov D.V., “Identification autoregression non-integer order with noise in output signal”, Interdisciplinary research in the area of mathematical modelling and informatics, Materials of the research and practical internet-conference (Togliatti, June 18-19, 2013), SIMJET, 2013, 64–67 (In Russ.)
19.	Ivanov D.V., Serebryakov A.Yu., Ivanov A.V., “Identification of autoregression described by fractional difference equations with 1/f noise in the output signal”, Vestnik transporta Povolzhya, 2016, no. 5(59), 93–99 (In Russ.)
20.	Ivanov D.V., “Estimation of parameters of linear fractional order ARX systems with noise in the input signal”, Tomsk State University Journal of Control and Computer Science, 2014, no. 2(27), 30–38 (In Russ.)
21.	Diversi R., Guidorzi R., Soverini U., “Identification of autoregressive models in the presence of additive noise”, International Journal of Adaptive Control and Signal Processing, 22 (2007), 465–481
22.	Soderstrom T., “A generalized instrumental variable estimation method for errors-in-variables identification problems”, Automatica, 47:8 (2011), 1656–1666
23.	Ivanov D.V., Sandler I.L., Kozlov E.V., “Identification of Fractional Linear Dynamical Systems with Autocorrelated Errors in Variables by Generalized Instrumental Variables”, IFAC-PapersOnLine, 51:32 (2018), 580–584
24.	Ivanov D., Zhdanov A., “Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares”, Mathematics, 9:24 (2021), 3250