Abstract
The awareness that phenomena (social, natural) are for the most part complex and consequently require more realistic models has led to the development of powerful new concepts and tools to detect, analyse, and understand non-stationarity and apparently random behaviour. Almost all existing linear and nonlinear techniques used for the study of time series presume some kind of stationarity, but the application of such tools to non-stationarity and apparently random time series produces misleading results. Recurrence analysis is an advanced technique for nonlinear data analysis used to identify the general structure, non-stationarity, and hidden recurring elements in a time series. Differently from traditional time series techniques that previously assume the nature of the series, the recurrence analysis can be conceived as a diagnostic tool which provides an exploratory analysis identifying the structure of the series. After a general overview of the epistemological and technical underpinnings for the emergent concepts of complexity and nonlinearity, this paper examines the main features of the technique through theoretical examples and a significant review of the main applications.
The original version of this chapter was revised: Author name has been included. The erratum to this chapter is available at https://doi.org/10.1007/978-3-319-55477-8_28
This is a preview of subscription content, log in via an institution to check access.
Notes
- 1.
The time delay is calculated by the minimum of the mutual information which is a measure of the link between the following values of the series.
- 2.
Chaos is aperiodic, deterministic system and sensitive to the initial conditions.
- 3.
A more deeper analysis has also allowed to discover some nonlinear elements and to carry out a short-term prediction [20].
- 4.
In this research, the macroeconomic time series were already analysed by Frank et al. (1988) with traditional tests for chaos. The analysis carried out through the RA provided different conclusions from the previous research.
- 5.
The comparison between the original time series and its shuffling is an usual practice in order to confirm a possible regular structure of the original series.
References
Addo, P. M., Billio, M., & Guegan, D. (2013). Nonlinear dynamics and recurrence plots for detecting financial crisis. The North American Journal of Economics and Finance, 26, 416–435.
Bertuglia, C. S., & Vaio, F. (2003). Non linearità, caos, complessità. le dinamiche dei sistemi naturali e sociali. Torino: Bollati Boringhieri.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327.
Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis: Forecasting and control. San Francisco: Holden Day.
Box, G. E., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis: Forecasting and control. Wiley.
Byrne, D. (2013). Evaluating complex social interventions in a complex world. Evaluation, 19(3), 217–228.
Byrne, D., & Callaghan, G. (2013). Complexity theory and the social sciences: The state of the art. Abingdon: Routledge.
Castellani, B., & Hafferty, F. W. (2009). Sociology and complexity science: A new field of inquiry. Berlin: Springer Science and Business Media.
Caraiani, P., & Haven, E. (2013). The role of recurrence plots in characterizing the output-unemployment relationship: An analysis. PloS One, 8(2).
Catone, M. C. (2013). Chaos and non-linear tools in website visits. In T. Gilbert, M. Kirkiolionis & G. Nicolis (Eds.), Proceedings of the European Conference on Complex Systems 2012 (pp. 87–91). Springer.
Ceja, L., & Navarro, J. (2011). Dynamic patterns of flow in the workplace: Characterizing within individual variability using a complexity science approach. Journal of Organizational Behavior, 32(4), 627–651.
Chatfield, C. (2013). The analysis of time series: An introduction. Boca Raton: CRC Press.
Chen, W. S. (2011). Use of recurrence plot and recurrence quantification analysis in Taiwan unemployment rate time series. Physica A: Statistical Mechanics and Its Applications, 390(7), 1332–1342.
De Gooijer, J. G., & Hyndman, R. J. (2006). 25 years of time series forecasting. International Journal of Forecasting, 22(3), 443–473.
Eckmann, J. P., Kamphorst, S. O., & Ruelle, D. (1987). Recurrence plots of dynamical systems. Europhysics Letters, 4(9), 973–977.
Eve, R. A., Horsfall, S., & Lee, M. E. (Eds.). (1997). Chaos, complexity, and sociology: Myths, models, and theories. London: Sage.
Faggini, M. (2007). Visual recurrence analysis: Application to economic time series. In M. Salzano & D. Colader (Eds.), Complexity hints for economy policy (pp. 69–92). Springer.
Frank, M., Gencay, R., & Stengos, T. (1988). International chaos? European Economic Review, 32(8), 1569–1584.
Fusaroli, R., Konvalinka, I., & Wallot, S. (2014). Analyzing social interactions: The promises and challenges of using cross recurrence quantification analysis. In N. Marwan, M. Riley, A. Giuliani & C. L. Webber Jr. (Eds.) Translational recurrences (pp. 137–155). Springer.
Giannerini, S. (2012). The quest for nonlinearity in time series. Handbook of Statistics: Time Series, 30, 43–63.
Iwayama, K., Hirata, Y., Suzuki, H., & Aihara, K. (2013). Change-point detection with recurrence networks. Nonlinear Theory and Its Applications, IEICE, 4(2), 160–171.
Kantz, H., & Schreiber, T. (2004). Nonlinear time series analysis. Cambridge: Cambridge University Press.
Kennel, M. B., Brown, R., & Abarbanel, H. D. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical Review A, 45(6), 3403–3411.
Marwan, N. (2003). Encounters with neighbours: Current developments of concepts based on recurrence plots and their applications. Germany: Postdam.
Neacşu, E. L., & Todoni, M. D. (2014). A way to determine chaotic behaviour in Romanian stock Market. Review of Economic and Business Studies, 207–217.
Strozzi, F., Zaldı́var, J. M., & Zbilut, J. P. (2002). Application of nonlinear time series analysis techniques to high-frequency currency exchange data. Physica A: Statistical Mechanics and Its Applications, 312(3), 520–538.
Tong, H. (1990). Non-linear time series: A dynamical system approach. Claredon Press.
Webber, C. L., Jr., & Zbilut, J. P. (2005). Recurrence quantification analysis of nonlinear dynamical systems. Tutorials in contemporary nonlinear methods for the behavioral sciences, 26–94.
Webber, C. L., Jr., & Marwan, N. (Eds.). (2015). Recurrence quantification analysis—Theory and best practices. Cham: Springer International Publishing.
Zbilut, J. P., & Webber, C. L., Jr. (1992). Embeddings and delays as derived from quantification of recurrence plots. Physics Letters A, 171(3–4), 199–203.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Catone, M.C., Diana, P., Faggini, M. (2017). Recurrence Analysis: Method and Applications. In: Lauro, N., Amaturo, E., Grassia, M., Aragona, B., Marino, M. (eds) Data Science and Social Research. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-55477-8_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-55477-8_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-55476-1
Online ISBN: 978-3-319-55477-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)