Model of probabilistic assessment of trend stability at financial market

Authors

  • Oleg Lutsenko Dnipropetrovsk Nationsl University Oles Honchar K.Marks avenue, 35, Dnipropetrovsk, Ukraine, 49010, Ukraine
  • Oleg Baybuz Dnipropetrovsk Nationsl University Oles Honchar K.Marks avenue, 35, Dnipropetrovsk, Ukraine, 49010, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.19527

Keywords:

probability, B-spline, probability density estimation, change-point detection, financial market

Abstract

The probabilistic model of assessing the state of the financial market, allowing to assess the probability of the trend reversal at the financial market was developed. A distinctive feature of the risk evaluation method, proposed in this paper, is that the time series of currency quotations are considered not as a set of individual points, but as a set of segments of stationarity, into which it is split by change-points. Finding of the change-points of the series allows to divide the series into the segments with similar statistical properties that corresponds to one of the main paradigms of the technical analysis – the division of the time series into segments with a constant trend. For the solution of the problem of the series splitting, two methods are used, such as the graphical method for finding the inflection points of the diagram, aimed at finding the reversal points a posteriori, and the CUSUM algorithm, relating to the methods of sequential detection of change-points. Splitting the diagram into segments using the change-points generates the random vector, comprising the segment duration in time and the difference between the prices at the beginning and the end of the segment. For the estimation of the probability density function of the vector, B-splines, constructed on a rectangular grid with the restoration of the intermediate points, were used. Based on the basic principles of financial market functioning, the assumptions were accepted, allowing to calculate the probability of the next change-point during the time interval in the future at each step of observation

Author Biographies

Oleg Lutsenko, Dnipropetrovsk Nationsl University Oles Honchar K.Marks avenue, 35, Dnipropetrovsk, Ukraine, 49010

Post-graduate student

Department of Mathematical Software

Oleg Baybuz, Dnipropetrovsk Nationsl University Oles Honchar K.Marks avenue, 35, Dnipropetrovsk, Ukraine, 49010

Professor

Department of Mathematical Software

References

  1. Kahn M.N. Technical Analysis Plain and Simple: Charting the Markets in Your Language [Текст] / M.N. Kahn // FT Press — 2010 — 352 p.
  2. Demark T.R. The New Science of Technical Analysis. / T.R. Demark // John Wiley — 1994 — 247 p.
  3. Kuan C.M. Forecasting exchange rates using feedforward and recurrent neural networks. / C.M. Kuan , T. Liu // Journal of Applied Econometrics — 1995 — 10 — P. 347—364.
  4. Mendes L., Godinho P., Dias J. A Forex trading system based on a genetic algorithm. / L. Mendes, P. Godinho, J. Dias // Journal of Heuristics — 2012 — vol. 18, N 4 — 627—656.
  5. Chan L. Automated Trading with Genetic-Algorithm Neural-Network Risk Cybernetics: An Application on FX Markets. / L. Chan, A. WK Wong // Finamatrix, Research and Markets — 2011 — Режим доступа : WWW/ URL: http://ssrn.com/abstract=1687763 — 01.11.2013.
  6. Ciskowski P. Neural Pattern Recognition with Self-organizing Maps for Efficient Processing of Forex Market Data Streams. / P. Ciskowski, M. Zaton // Artificial Intelligence and Soft Computing — 2010 — 6113 — P. 307—314.
  7. Page, E. S. Continous Inspection Schemes [Текст] / E. S. Page // Biometrika — 1954 — vol. 41, N 1 — P.100—115.
  8. Nadler, J. Some characteristics of Page’s twosided procedure for detecting a change in a location parameter [Текст] / J. Naddler, N.B. Robbins // Ann. Math. Statist. — 1971 — vol. 42, N 2 — P. 538—551.
  9. Kooperberg, C. A study of logspline density estimation [Текст] / C. Kooperang, C. Stone // Computational Statistics & Data Analysis — 1991. — vol. 12, N 3 — P. 327—347.
  10. Гливенко, В. И. Курс теории вероятностей [Текст]: учебник для физико-математических факультетов государственных универсистетов / В. И. Гливенко. — М., Л.: ГОНТИ НКТП СССР, Редакция технико-теоретической литературы — 1939. — 220 с.
  11. Смирнов, Н. В. Приближение законов распределения случайных величин по эмпирическим данным [Текст] / Н. В. Смирнов // Успехи Матем.Наук — 1944 — N 10 — С. 179-206.
  12. Завьялов, Ю. С. Методы сплайн-функций [Текст] / Ю. С. Завьялов, Б. И. Квасов, В. Л. Мирошниченко — М.: "Наука" — 1980. — 352 c.
  13. De Boor, C. Package for Calculating with B-Splines [Текст] / C. De Boor // SJAM J. On Numer. Anal. — 1977 — vol. 14, N3 — p. 441—472.
  14. Koo, J.-Y., Tensor product splines in the estimation of regression, exponential response functions and multivariate densities [Текст]: Ph.D. thesis / J. Y. Koo — Berkeley — 1988 — 132 p.
  15. Stone, C. J. The use of polynomial splines and their tensor products in multivariate function estimation (with discussion) [Текст] / C. J. Stone // Ann. Statist. — 1994 — N 22 — p. 118—184.
  16. Rogers, D. F. An Introduction to NURBS with Historical Perspective [Текст] / D. F. Rogers — San Francisco: Morgan Kaufmann Publishers — 2000 — 344p.
  17. Kahn, M.N. (2010). Technical Analysis Plain and Simple: Charting the Markets in Your Language. FT Press, 352.
  18. Demark, T.R. (1994). The New Science of Technical Analysis. John Wiley, 247.
  19. Kuan, C.M., Liu, T. (1995). Forecasting exchange rates using feedforward and recurrent neural networks. Journal of Applied Econometrics, 10, 347–364.
  20. Mendes, L., Godinho, P., Dias, J. (2012). A Forex trading system based on a genetic algorithm. Journal of Heuristics, 18(4), 627—656.
  21. Chan, L., Wong, WK A. (2011). Automated Trading with Genetic-Algorithm Neural-Network Risk Cybernetics: An Application on FX Markets. Finamatrix, Research and Markets. http://ssrn.com/abstract=1687763
  22. Ciskowski, P., Zaton, M. (2010). Neural Pattern Recognition with Self-organizing Maps for Efficient Processing of Forex Market Data Streams. Artificial Intelligence and Soft Computing 6113, 307—314.
  23. Page, E. S. (1954). Continous Inspection Schemes. Biometrika, 41(1), 100—115.
  24. Nadler, J., Robbins, N. B. (1971). Some characteristics of Page’s twosided procedure for detecting a change in a location parameter. Ann. Math. Statist, 42(2), 538—551.
  25. Kooperberg, C., Stone, C. (1991). A study of logspline density estimation. Computational Statistics & Data Analysis, 12(3), 327—347.
  26. Glivenko, V. I. (1939). Course of Probability Theory. Moscow, Leningrad: Redaction of Technological Theory Literature, 220.
  27. Smirnov N.V. (1944). Estimating of Probability Distributions of Random Values from Empirical Data. Progress of Mathematical Science, 10, 179—206.
  28. Zavyalov, Yu. S., Kvasov, B. I., Miroshnichenko, V. L. (1980). Methods of Spline Functions. Moscow: Nauka, 352.
  29. De Boor, C. (1977) Package for Calculating with B-Splines. SJAM J. On Numer. Anal., 1977, 14(3), 441—472.
  30. Koo, J.-Y. (1988). Tensor product splines in the estimation of regression, exponential response functions and multivariate densities, Ph.D. thesis. Berkeley: Department of Statistics, University of California, 132.
  31. Stone, C. J. (1994). The use of polynomial splines and their tensor products in multivariate function estimation (with discussion). Ann. Statist, 22. 118—184.
  32. Rogers, D. F. (2000). An Introduction to NURBS with Historical Perspective. San Francisco: Morgan Kaufmann Publishers. 344p.

Downloads

Published

2013-12-18

How to Cite

Lutsenko, O., & Baybuz, O. (2013). Model of probabilistic assessment of trend stability at financial market. Eastern-European Journal of Enterprise Technologies, 6(3(66), 50–54. https://doi.org/10.15587/1729-4061.2013.19527

Issue

Vol. 6 No. 3(66) (2013): Control processec

Section

Control processes

License

Copyright (c) 2014 Oleg Lutsenko, Oleg Baybuz

Creative Commons License

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

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.