Methods for estimation of dynamical noise

Authors

  • Diudin M.S. Krasnodar branch of Finanical University, Krasnodar, Russian Federation
  • Kalaidin E.N. Kuban State University, Krasnodar, Russian Federation

UDC

330.42

DOI:

https://doi.org/10.31429/vestnik-15-4-6-11

Abstract

The article discusses methods for measuring the random component of time series. Existing random noise processing methods work poorly in the case of dynamic noise even for regular dynamics. We consider the existing methods for measuring dynamic noise and propose to use an algorithm based on the Grassberger and Procaccia method. Analysis of the geometric structure of the reconstruction of the attractor (according to the Takens theorem) allows us to determine the scale at which the deterministic signal begins to exceed the noise. The resulting noise estimate allows us to estimate the accuracy of the prediction of the deterministic component. Random deviation grows in proportion to the root of time, complicating an accurate prediction even with accurate simulation of the deterministic component. Measurement of random noise allows us to estimate the possible horizon of the forecast. Methods based on measuring the correlation integral require a large number of points for analysis and take a lot of time for calculations, but have no alternative in the study of dynamic noise.

Keywords:

correlation integral, fractal dimension, nonlinear dynamics, time series, Taken's theorem

Author Infos

Mikhail S. Diudin

старший преподаватель кафедры математики и информатики Краснодарский филиал Финансового университета при Правительстве РФ

e-mail: diudin.m@yandex.ru

Eugeniy N. Kalaidin

профессор кафедры теоретической экономики Кубанского государственного университета

e-mail: kalaidin@econ.kubsu.ru

References

  1. Kantz H., Schreiber T. Nonlinear time series analysis. Cambridge University Press, Cambridge, MA, 1997.
  2. Sase T. et al. Estimating the level of dynamical noise in time series by using fractal dimensions. Physics Letters A, 2016, vol. 380, no. 11, pp. 1151–1163. DOI: 10.1016/j.physleta.2016.01.014
  3. Grassberger P., Procaccia I. Measuring the strangeness of strange attractors. Physica D: Nonlinear Phenomena, 1983, vol. 9, iss. 1–2, pp. 189–208. DOI: 1016/0167-2789(83)90298-1
  4. Yu D. et al. Efficient implementation of the Gaussian kernel algorithm in estimating invariants and noise level from noisy time series data. Physical Review E, 2000, vol. 61, iss. 4, pp. 3750.DOI: 10.1103/PhysRevE.61.3750
  5. Urbanowicz K., Hołyst J. A. Noise-level estimation of time series using coarse-grained entropy. Physical Review E, 2003, vol. 67, iss. 4, pp. 046218. DOI: 10.1103/PhysRevE.67.046218
  6. Yanovskij L.P., Filatov D.A. Analiz sostoyaniya finansovykh rynkov na osnove metodov nelineynoy dinamiki [Analysis of financial markets based on non-linear dynamic methods]. Financy i kredit [Finance and credit], 2005, no. 32 (200). pp. 2–13. (In Russian)
  7. Kalaidin E.N., Diudin M.S. Otsenka riska v ramkakh gipotezy fraktal'nogo rynka [Risk assessment in the framework of the fractal market hypothesis]. Finansy i kredit [Finance and credit], 2013, no. 22 (550), pp. 31–34. (In Russian)
  8. Kalaidin E.N., Diudin M.S. Izmerenie stokhasticheskoy sostavlyayushchey v dinamike aktivov rossiyskogo rynka kapitala [Measurement of the stochastic component in the dynamics of the assets of the Russian capital market]. Ekonomika ustojchivogo razvitiya [Economics of Sustainable Development], 2012, no. 11, pp. 126–132. (In Russian)

Downloads

Issue

2018. Vol. 15. No. 4

Section

Mathematics

Pages

6-11

Submitted

2018-11-29

Published

2018-12-21

How to Cite

Diudin M.S., Kalaidin E.N. Methods for estimation of dynamical noise. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2018, vol. 15, no. 4, pp. 6-11. DOI: https://doi.org/10.31429/vestnik-15-4-6-11 (In Russian)

Copyright (c) 2018 Diudin M.S., Kalaidin E.N.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.