УДК 519.21

М.М. ЛУЗ,
BNP Paribas Cardif, Україна,
 maksim_luz@ukr.net

М.П. МОКЛЯЧУК,
Київський національний університет імені Тараса Шевченка, Київ, Україна,
 moklyachuk@gmail.com

МІНІМАКСНА ФІЛЬТРАЦІЯ ПОСЛІДОВНОСТЕЙ
З ПЕРІОДИЧНО СТАЦІОНАРНИМИ ПРИРОСТАМИ

СПИСОК ЛІТЕРАТУРИ

1. Dudek A., Hurd H., Wojtowicz W. PARMA methods based on Fourier representation of periodic coefficients. Wiley Interdisciplinary Reviews: Computational Statistics. 2016. Vol. 8, N 3. P. 130–149. https://doi.org/10.1002/wics.1380.


2. Johansen S., Nielsen M.O. The role of initial values in conditional sum-of-squares estimation of nonstationary fractional time series models. Econom. Theory. 2016. Vol. 32, N 5. P. 1095–1139. https://doi.org/10.1017/S02664666150001.10.


3. Reisen V.A., Zamprogno B., Palma W., Arteche J. A semiparametric approach to estimate two seasonal fractional parameters in the SARFIMA model. Math. Comput. Simul. 2014. Vol. 98. P. 1–17. https://doi.org/10.1016/j.matcom.2013.11.001.


4. Box G.E.P., Jenkins G.M., Reinsel G.C., Ljung, G.M. Time series analysis, forecasting and control. 5rd ed., Hoboken, NJ: John Wiley and Sons, 2016. 712 p.


5. Porter-Hudak S. An application of the seasonal fractionally differenced model to the monetary aggegrates. J. Am. Stat. Assoc. 1990. Vol. 85, N 410. P. 338–344. https://doi.org/10.1080/01621459.1990.10476206.


6. Гладышев Е.Г. О периодически коррелированных случайных последовательностях. Докл. АН СССР. 1961. Т. 137, № 2. С. 1026–1029.


7. Napolitano A. Cyclostationarity: New trends and applications. Signal Process. 2016. Vol. 120. P. 385–408. https://doi.org/10.1016/j.sigpro.2015.09.011.


8. Lund R. Choosing seasonal autocovariance structures: PARMA or SARMA. In: Bell WR, Holan SH, McElroy TS (eds). Economic time series: modelling and seasonality. London: Chapman and Hall, 2011. P. 63–80. https://doi.org/10.1201/b11823.


9. Basawa I.V., Lund R., Shao Q. First-order seasonal autoregressive processes with periodically varying parameters. Stat. Probab. Lett. 2004. Vol. 67, N 4. P. 299–306. https://doi.org/10.1016/j.spl.2004.02.001.


10. Reisen V.A., Monte E.Z., Franco G.C., Sgrancio A.M., Molinares F.A.F., Bondon P., Ziegelmann F.A., Abraham B. Robust estimation of fractional seasonal processes: Modeling and forecasting daily average SO2 concentrations. Math. Comput. Simul. 2018. Vol. 146. P. 27–43. https://doi.org/10.1016/j.matcom.2017.10.004.


11. Grenander U. A prediction problem in game theory. Ark. Mat. 1957. Vol. 6. P. 371–379. https://doi.org/10.1007/BF02589429.


12. Kassam S.A., Poor H.V. Robust techniques for signal processing: A survey. Proc. IEEE. 1985. Vol. 73, N 3. P. 433–481. https://doi.org/10.1109/PROC.1985.13167.


13. Liu Y., Xue Yu. and Taniguchi M. Robust linear interpolation and extrapolation of stationary time series in Lp. J. Time Ser. Anal. 2020. Vol. 41, N 2. P. 229–248. https://doi.org/10.1111/jtsa.12502.


14. Luz M., Moklyachuk M. Estimation of stochastic processes with stationary increments and cointegrated sequences. London: ISTE; Hoboken, NJ: John Wiley and Sons, 2019. 282 p. https://nlinelibrary.wiley.com/doi/book/10.1002/9781119663539.


15. Moklyachuk M.P. Minimax-robust estimation problems for stationary stochastic sequences. Stat., Optim. Inf. Comput. 2015. Vol. 3, N 4. P. 348–419. https://doi.org/10.19139/soic.v3i4.173.


16. Moklyachuk M.P., Golichenko I.I. Periodically correlated processes estimates. Saarbrucken:LAP Lambert Academic Publishing, 2016. 308 p. https:/www.lap-publishing.com/catalog/details/ store/gb/book/978-3-659-88507-5/periodically-correlated-processes-estimates.


17. Moklyachuk M.P., Masyutka A.Yu. Minimax-robust estimation technique for stationary stochastic processes. Saarbrucken: LAP LAMBERT Academic Publishing, 2012. 296 p. https:/www.amazon.co.uk/Minimax-robust-estimation-technique-Mikhail-nique-Mikhail-Moklyachuk/dp/365919817X.


18. Moklyachuk M.P., Sidei M.I., Masyutka O.Yu. Estimation of stochastic processes with missing observations. New York, NY: Nova Science Publishers, 2019. 334 p. https://novapublishers.com/shop/estimates-of-stochastic-processes-with-missing-observations.


19. Gikhman I.I., Skorokhod A.V. The theory of stochastic processes. I. Berlin: Springer, 2004. 574 p. https://link.springer.com/book/10.1007/978-3-642-61943-4.


20. Kolmogorov A.N. In: Shiryayev A.N. (Ed.) Selected works by A. N. Kolmogorov. Vol. II: Probability theory and mathematical statistics, Dordrecht etc.: Kluwer Academic Publishers. 1992. 579 p. https:/www.springer.com/gp/book/9789401050036.