Skip to main content
SpringerLink
Log in

Global recurrence quantification analysis and its application in financial time series

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This study proposes a modified recurrence quantification analysis, called global recurrence quantification analysis (GRQA). It is well known that the recurrence threshold is an important parameter in traditional recurrence quantification analysis. However, in existing researches, the selection of recurrence thresholds is often based on ‘rules of thumb.’ As many studies have shown, recurrence analysis and its quantifiers are strongly dependent on the evaluation of the vicinity threshold parameter, which indicates that a selected threshold may have an adverse effect on exploring signal inherent information and the interrelationship between different sequences. Therefore, GRQA is initialized in this paper to measure the vertical and diagonal structures of recurrence plots in a more objective way, because it considers all the information carried by all potential values of the threshold. The information described by GRQA is determined by the sequence itself and is not affected by specific thresholds. GQRA can also clearly depict the dynamical similar characteristics and recursive trajectories between sequences, which have not appeared in previous researches. We apply this method to the financial time series to find some useful information. It reveals that SZSE and SSE show similar inherent dynamic characteristics via GQRA statistics curves, and DJI and NASDAQ are similar to each other as well, while HSI is like a combination of these two groups with both of their characteristics, which is consistent with its financial background.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35
Fig. 36
Fig. 37
Fig. 38
Fig. 39
Fig. 40
Fig. 41
Fig. 42
Fig. 43
Fig. 44
Fig. 45
Fig. 46
Fig. 47
Fig. 48
Fig. 49
Fig. 50
Fig. 51
Fig. 52
Fig. 53
Fig. 54
Fig. 55
Fig. 56
Fig. 57
Fig. 58
Fig. 59
Fig. 60
Fig. 61
Fig. 62
Fig. 63
Fig. 64

Similar content being viewed by others

Notes

  1. It means if we let \(\sigma \) as a unit of ‘gap,’ N plays an important role to ensure all the data in \(\mathrm{vec}\_R^{m,\tau }\) can be covered in \(N*\sigma \) gaps.

References

  1. Eckmann, J.P., Kamphorst, S.O., Ruelle, D.: Recurrence plots of dynamical systems. Europhys. Lett. 4(9), 973–977 (1987)

    Article  Google Scholar 

  2. Webber, J.C., Zbilut, J.P.: Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76(2), 965 (1994)

    Article  Google Scholar 

  3. Zbilut, J.P., Webber, L.C.: Embeddings and delays as derived from quantification of recurrence plots. Phys. Lett. A 171, 199–203 (1992)

    Article  Google Scholar 

  4. Marwan, N., Wessel, N., Meyerfeldt, U., Schirdewan, A., Kurths, J.: Recurrence plot based measures of complexity and their application to heart-rate-variability data. Phys. Rev. E 66(2), 026702 (2002)

    Article  MATH  Google Scholar 

  5. Naschitz, J.E., Sabo, E., Naschitz, S., Rosner, I., Rozenbaum, M., Priselac, R.M., Gaitini, L., Zukerman, E., Yeshurun, D.: Fractal analysis and recurrence quantification analysis of heart rate and pulse transit time for diagnosing chronic fatigue syndrome. Clin. Auton. Res. 12(4), 264–272 (2002)

    Article  Google Scholar 

  6. Naschitz, J.E., Itzhak, R., Shaviv, N., Khorshidi, I., Sundick, S., Isseroff, H., Fields, M., Priselac, R.M., Yeshurun, D., Sabo, E.: Assessment of cardiovascular reactivity by fractal and recurrence quantification analysis of heart rate and pulse transit time. J. Hum. Hypertens. 17(2), 111–118 (2003)

    Article  Google Scholar 

  7. Acharya, U.R., Sree, S.V., Chattopadhyay, S., Yu, W., Ang, P.C.A.: Application of recurrence quantification analysis for the automated identification of epileptic eeg signals. Int. J. Neural Syst. 21(03), 199–211 (2011)

    Article  Google Scholar 

  8. Bastos, J.A., Caiado, J.: Recurrence quantification analysis of global stock markets. Phys. A 390(7), 1315–1325 (2012)

    Article  Google Scholar 

  9. Bastos, J.A.: Recurrence quantification analysis of financial markets. Chaos Complex. Theory Manag. Nonlinear Dyn. 57(6), 857–62 (2013)

    Google Scholar 

  10. Guhathakurta, K., Bhattacharya, B., Chowdhury, A.R.: Using recurrence plot analysis to distinguish between endogenous and exogenous stock market crashes. Phys. A 389(9), 1874–1882 (2010)

    Article  Google Scholar 

  11. Nichols, J.M., Trickey, S.T., Seaver, M.: Damage detection using multivariate recurrence quantification analysis. Mech. Syst. Signal Process. 20(2), 421–437 (2006)

    Article  Google Scholar 

  12. Zbilut, J.P., Giuliani, A., Webber, C.L., Colosimo, A.: Recurrence quantification analysis in structure-function relationships of proteins: an overview of a general methodology applied to the case of tem-1 beta-lactamase. Protein Eng. 11(2), 87 (1998)

    Article  Google Scholar 

  13. Roma, G., Nogueira, W., Herrera, P.: Recurrence quantification analysis features for environmental sound recognition. BMC Public Health 9(1), 1–9 (2013)

    Google Scholar 

  14. Fabretti, A., Ausloos, M.: Recurrence plot and recurrence quantification analysis techniques for detecting a critical regime. Int. J. Mod. Phys. C 16(05), 671–706 (2011)

    Article  MATH  Google Scholar 

  15. Mosdorf, R., Dzienis, P., Litak, G.: The loss of synchronization between air pressure fluctuations and liquid flow inside the nozzle during the chaotic bubble departures. Meccanica 52(11–12), 2641–2654 (2017)

    Article  MathSciNet  Google Scholar 

  16. Ren, W., Jin, N.: Vector visibility graph from multivariate time series: a new method for characterizing nonlinear dynamic behavior in two-phase flow. Nonlinear Dyn. 97(4), 2547–2556 (2019)

    Article  MATH  Google Scholar 

  17. Rusinek, R., Zaleski, K.: Dynamics of thin-walled element milling expressed by recurrence analysis. Meccanica 51(6), 1275–1286 (2016)

    Article  Google Scholar 

  18. Knight, A.P., Kennedy, D.M., McComb, S.A.: Using recurrence analysis to examine group dynamics. Group Dyn. Theory Res. Pract. 20(3), 223 (2016)

    Article  Google Scholar 

  19. Bianchi, F.M., Livi, L., Alippi, C.: Investigating echo-state networks dynamics by means of recurrence analysis. IEEE Trans. Neural Netw. Learn. Syst. 29(2), 427–439 (2016)

    Article  MathSciNet  Google Scholar 

  20. Piu, P., Serchi, V., Rosini, F., Rufa, A.: A cross-recurrence analysis of the pupil size fluctuations in steady scotopic conditions. Front. Neurosci. 13, 407 (2019)

    Article  Google Scholar 

  21. Sarkar, S., Dey, A.: Classifying recurrent dynamics on emotional speech signals. In: Intelligent Speech Signal Processing, pp. 139–152 (2019)

  22. Stender, M., Oberst, S., Tiedemann, M., Hoffmann, N.: Complex machine dynamics: systematic recurrence quantification analysis of disk brake vibration data. Nonlinear Dyn. 97(4), 2483–2497 (2019)

    Article  Google Scholar 

  23. Eroglu, D., Peron, T.K., Marwan, N., Rodrigues, F.A., Costa, L.D., Sebek, M., Kiss, I.Z., Kurths, J.: Entropy of weighted recurrence plots. Phys. Rev. E 90(4), 042919–042919 (2014)

    Article  Google Scholar 

  24. Ding, H.: Characterization of local complex structures in a recurrence plot to improve nonlinear dynamic discriminant analysis. Phys. Rev. E 89(1), 013313 (2014)

    Article  Google Scholar 

  25. Chen, Y., Yang, H.: Multiscale recurrence analysis of long-term nonlinear and nonstationary time series. Chaos Solitons Fractals 45(7), 978–987 (2012)

    Article  Google Scholar 

  26. Xiang, R., Zhang, J., Xu, X.K., Small, M.: Multiscale characterization of recurrence-based phase space networks constructed from time series. Chaos 22(1), 47 (2012)

    Article  MathSciNet  Google Scholar 

  27. Kraemer, K.H., Donner, R.V., Heitzig, J., Marwan, N.: Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions. Chaos 28(8), 085720 (2018)

    Article  MathSciNet  Google Scholar 

  28. Prado, TdL, dos Santos Lima, G.Z., Lobão-Soares, B., do Nascimento, G.C., Corso, G., Fontenele-Araujo, J., Kurths, J., Lopes, S.R.: Optimizing the detection of nonstationary signals by using recurrence analysis. Chaos 28(8), 085703 (2018)

    Article  MathSciNet  Google Scholar 

  29. Mindlin, G.B., Gilmore, R.: Topological analysis and synthesis of chaotic time series. Phys. D 58, 229–242 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  30. Zbilut, J.P., Koebbe, M., Loeb, H., et al.: Use of recurrence plots in the analysis of heart beat intervals. In: Proceedings Computers in Cardiology, pp. 263–266 (1990)

  31. Marwan, N., Romano, M.C., Thiel, M., Kurths, J.: Recurrence plots for the analysis of complex systems. Phys. Rep. 438, 237–329 (2007)

    Article  MathSciNet  Google Scholar 

  32. Holyst, J.A., Żebrowska, M., Urbanowicz, K.: Observations of deterministic chaos in financial time series by recurrence plots, can one control chaotic economy? Eur. Phys. J. B 20(4), 531–535 (2001)

    Article  MathSciNet  Google Scholar 

  33. May, R.: Simple mathematical models with very complicated dynamics. Nature 261(5560), 459–467 (1976)

    Article  MATH  Google Scholar 

  34. Granger, C., Joyeux, R.: An Introduction to Long-Memory Time Series Models and Fractional Differencing. Harvard University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  35. Hosking, J.: Fractional differencing. Biometrika 68(1), 165–176 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  36. Podobnik, B., Horvatic, D., Ng, A.L., Stanley, H.E., Ivanov, P.C.: Modeling long-range cross-correlations in two-component arfima and fiarch processes. Phys. A 387(15), 3954–3959 (2007)

    Article  MathSciNet  Google Scholar 

  37. Yamapi, R., Chabi Orou, J., Woafo, P.: Harmonic oscillations, stability and chaos control in a non-linear electromechanical system. J. Sound Vib. 259(5), 1253–1264 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  38. Hartmann, F.: Harmonic Oscillations, pp. 320–341. Springer, Berlin (1989)

    Google Scholar 

Download references

Acknowledgements

The financial supports from the funds of the Fundamental Research Funds for the Central Universities (2019YJS203, 2019YJS193, 2018JBZ104), the National Natural Science Foundation of China (61771035) and China Scholarship Council (201907090035) are gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, China

    Jiayi He, Pengjian Shang & Yali Zhang

Authors
  1. Jiayi He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pengjian Shang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yali Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiayi He.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

See Figs. 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83.

Fig. 65
figure 65

Recurrence plot of logistic map (\(a=3.8\)) with threshold \(\varepsilon =0.05*\hbox {dev}\)

Full size image
Fig. 66
figure 66

Recurrence plot of logistic map (\(a=3.8\)) with threshold \(\varepsilon =0.1*\hbox {dev}\)

Full size image
Fig. 67
figure 67

Recurrence plot of logistic map (\(a=3.8\)) with threshold \(\varepsilon =0.25*\hbox {dev}\)

Full size image
Fig. 68
figure 68

Recurrence plot of logistic map (\(a=3.8\)) with threshold \(\varepsilon =0.5*\hbox {dev}\)

Full size image
Fig. 69
figure 69

Recurrence plot of logistic map (\(a=4\)) with threshold \(\varepsilon =0.05*\hbox {dev}\)

Full size image
Fig. 70
figure 70

Recurrence plot of logistic map (\(a=4\)) with threshold \(\varepsilon =0.1*\hbox {dev}\)

Full size image
Fig. 71
figure 71

Recurrence plot of logistic map (\(a=4\)) with threshold \(\varepsilon =0.25*\hbox {dev}\)

Full size image
Fig. 72
figure 72

Recurrence plot of logistic map (\(a=4\)) with threshold \(\varepsilon =0.5*\hbox {dev}\)

Full size image
Fig. 73
figure 73

Recurrence plot of ARFIMA1 with threshold \(\varepsilon =0.05*\hbox {dev}\)

Full size image
Fig. 74
figure 74

Recurrence plot of ARFIMA1 with threshold \(\varepsilon =0.1*\hbox {dev}\)

Full size image
Fig. 75
figure 75

Recurrence plot of ARFIMA1 with threshold \(\varepsilon =0.25*\hbox {dev}\)

Full size image
Fig. 76
figure 76

Recurrence plot of ARFIMA1 with threshold \(\varepsilon =0.5*\hbox {dev}\)

Full size image
Fig. 77
figure 77

Recurrence plot of ARFIMA2 with threshold \(\varepsilon =0.05*\hbox {dev}\)

Full size image
Fig. 78
figure 78

Recurrence plot of ARFIMA2 with threshold \(\varepsilon =0.1*\hbox {dev}\)

Full size image
Fig. 79
figure 79

Recurrence plot of ARFIMA2 with threshold \(\varepsilon =0.25*\hbox {dev}\)

Full size image
Fig. 80
figure 80

Recurrence plot of ARFIMA2 with threshold \(\varepsilon =0.5*\hbox {dev}\)

Full size image
Fig. 81
figure 81

Recurrence plot of harmonic oscillations with threshold \(\varepsilon =0.05*\hbox {dev}\)

Full size image
Fig. 82
figure 82

Recurrence plot of harmonic oscillations with threshold \(\varepsilon =0.1*\hbox {dev}\)

Full size image
Fig. 83
figure 83

Recurrence plot of harmonic oscillations with threshold \(\varepsilon =0.5*\hbox {dev}\)

Full size image

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, J., Shang, P. & Zhang, Y. Global recurrence quantification analysis and its application in financial time series. Nonlinear Dyn 100, 803–829 (2020). https://doi.org/10.1007/s11071-020-05543-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-05543-4

Keywords

Search

Navigation