Statistical analysis of multivariate binary time series based on a neural network model
https://doi.org/10.29235/1561-8323-2024-68-4-271-281
Abstract
This article is devoted to the statistical analysis of multivariate binary time series. For solving this problem a parsimonious neural network model of Markov’s ergodic chain of order s was determined. Consistent statistical estimators for model parameters and estimation algorithms of parameters and forecasting algorithms of future states of time series were developed. The results of computer experiments on simulated and real data are presented.
About the Authors
Yu. S. KharinBelarus
Kharin Yuriy S. – Academician, D. Sc. (Physics and Mathematics), Professor, Director
4, Nezavisimosti Ave., Minsk, 220030
S. A. Shibalko
Belarus
Shibalko Siarhei A. – Student
4, Nezavisimosti Ave., Minsk, 220030
References
1. Anderson T. W. The Statistical Analysis of Time Series. New York, 1971. 704 p. https://doi.org/10.1002/9781118186428
2. Nelder J., Wedderburn R. Generalized linear models. Journal of the Royal Statistical Society. Series A, 1972, vol. 135, no. 3, pp. 370–384. https://doi.org/10.2307/2344614
3. Biswas A., Song P. X.-K. Discrete-valued ARMA processes. Statistics and Probability Letters, 2009, vol. 79, no. 17, pp. 1884–1889. https://doi.org/10.1016/j.spl.2009.05.025
4. Cameron A. C., Trivedi P. K. Regression Analysis of Count Data. Cambridge, 2013. 567 p. https://doi.org/10.1017/cbo9781139013567
5. Kim C. Dynamic linear models with Markov-switching. Journal of Econometrics, 1994, vol. 60, no. 1–2, pp. 1–22. https://doi.org/10.1016/0304-4076(94)90036-1
6. Hamilton J. D. Time Series Analysis. Princeton, NJ, 1994. 799 p. https://doi.org/10.1515/9780691218632
7. Fokianos K., Fried R., Kharin Yu., Voloshko V. Statistical analysis of multivariate discrete-valued time series. Journal of Multivariate Analysis, 2022, vol. 188, art. 104805. https://doi.org/10.1016/j.jmva.2021.104805
8. Kharin Yu. S. Neural network-based models of binomial time series in data analysis problems. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 2021, vol. 65, no. 6, pp. 654–660 (in Russian). https://doi.org/10.29235/1561-8323-2021-65-6-654-660
9. Billingsley P. Statistical methods in Markov chains. The Annals of Mathematical Statistics, 1961, vol. 32, no. 1, pp. 12–40. https://doi.org/10.1214/aoms/1177705136
10. Kharin Yu., Voloshko V. Robust estimation for binomial conditionally nonlinear autoregressive time series based on multivariate conditional frequencies. Journal of Multivariate Analysis, 2021, vol. 185, art. 104777. https://doi.org/10.1016/j.jmva.2021.104777
11. Shiryaev A. N. Probability, in 2 books. Moscow, 2004 (in Russian).
12. Kollo T., Rosen D. Advanced Multivariate Statistics and Matrices. Dordrecht, 2005. 506 p. https://doi.org/10.1007/1- 4020-3419-9
13. Magnus J., Neudecker H. Matrix Differential Calculus with Applications in Statistics and Econometrics. New York, 2019. 482 p.
14. Kharin Yu. S. Optimality and Robustness in Statistical Forecasting. Minsk, 2008. 263 p. (in Russian).