IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2206.11933.html
   My bibliography  Save this paper

Chaotic time series in financial processes consisting of savings with piecewise constant monthly contributions

Author

Listed:
  • Jos'e Pedro Gaiv~ao
  • Benito Pires

Abstract

We investigate the time series generated by an elementary and deterministic financial process that consists in making monthly contributions to a savings account subjected to the devaluation by a monthly negative real interest rate. The monthly contribution is a piecewise constant function of the account balance. We show that a dichotomy holds for such a financial time series: either the financial time series are asymptotic to finitely many periodic sequences or the financial time series have an uncountable (Cantor) set of {\omega}-limit points. We also provide explicit parameters for which the financial process is chaotic in the sense that the financial time series have sensitive dependence on initial conditions at points of a Cantor attractor.

Suggested Citation

  • Jos'e Pedro Gaiv~ao & Benito Pires, 2022. "Chaotic time series in financial processes consisting of savings with piecewise constant monthly contributions," Papers 2206.11933, arXiv.org, revised Feb 2023.
    • Handle: RePEc:arx:papers:2206.11933
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2206.11933
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Schittenkopf Christian & Dorffner Georg & Dockner Engelbert J., 2000. "On Nonlinear, Stochastic Dynamics in Economic and Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 4(3), pages 1-23, October.
    2. Kiminori Matsuyama & Iryna Sushko & Laura Gardini, 2018. "A piecewise linear model of credit traps and credit cycles: a complete characterization," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 119-143, November.
    3. Small Michael & Tse Chi K., 2003. "Determinism in Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 7(3), pages 1-31, October.
    4. Blake LeBaron, 1994. "Chaos and Nonlinear Forecastability in Economics and Finance," Finance 9411001, University Library of Munich, Germany.
    5. Florian Heider & Farzad Saidi & Glenn Schepens, 2021. "Banks and Negative Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 13(1), pages 201-218, November.
    6. Hommes,Cars, 2015. "Behavioral Rationality and Heterogeneous Expectations in Complex Economic Systems," Cambridge Books, Cambridge University Press, number 9781107564978, November.
    7. Asano, Takao & Yokoo, Masanori, 2019. "Chaotic dynamics of a piecewise linear model of credit cycles," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 9-21.
    8. Umezuki, Yosuke & Yokoo, Masanori, 2019. "A simple model of growth cycles with technology choice," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 164-175.
    9. Corneille, O. & D’Hondt, C. & De Winne, R. & Efendic, E. & Todorovic, A., 2021. "What leads people to tolerate negative interest rates on their savings?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 93(C).
    10. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, June.
    11. Kelsey, David, 1988. "The Economics of Chaos or the Chaos of Economics," Oxford Economic Papers, Oxford University Press, vol. 40(1), pages 1-31, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gardini, Laura & Radi, Davide & Schmitt, Noemi & Sushko, Iryna & Westerhoff, Frank, 2023. "Sentiment-driven business cycle dynamics: An elementary macroeconomic model with animal spirits," Journal of Economic Behavior & Organization, Elsevier, vol. 210(C), pages 342-359.
    2. Mikhail Anufriev & Davide Radi & Fabio Tramontana, 2018. "Some reflections on past and future of nonlinear dynamics in economics and finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 91-118, November.
    3. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, June.
    4. Carolina Castaldi & Giovanni Dosi, 2003. "The Grip of History and the Scope for Novelty: Some Results and Open Questions on Path Dependence in Economic Processes," LEM Papers Series 2003/02, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    5. Nijkamp, P. & Poot, J., 1991. "Lessons from non-linear dynamic economics," Serie Research Memoranda 0105, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    6. Nijkamp, Peter & Reggiani, Aura, 1995. "Non-linear evolution of dynamic spatial systems. The relevance of chaos and ecologically-based models," Regional Science and Urban Economics, Elsevier, vol. 25(2), pages 183-210, April.
    7. Nijkamp, P. & Reggiani, A., 1989. "Logit models and chaotic behaviour," Serie Research Memoranda 0054, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    8. Takao Asano & Akihisa Shibata & Masanori Yokoo, 2024. "Technology choice, externalities in production, and a chaotic middle-income trap," Journal of Economics, Springer, vol. 141(1), pages 29-56, January.
    9. Marisa Faggini & Bruna Bruno & Anna Parziale, 2019. "Does Chaos Matter in Financial Time Series Analysis?," International Journal of Economics and Financial Issues, Econjournals, vol. 9(4), pages 18-24.
    10. Schmitt, Noemi & Tuinstra, Jan & Westerhoff, Frank, 2017. "Side effects of nonlinear profit taxes in an evolutionary market entry model: Abrupt changes, coexisting attractors and hysteresis problems," Journal of Economic Behavior & Organization, Elsevier, vol. 135(C), pages 15-38.
    11. Rosser, J. Jr. & Ahmed, Ehsan & Hartmann, Georg C., 2003. "Volatility via social flaring," Journal of Economic Behavior & Organization, Elsevier, vol. 50(1), pages 77-87, January.
    12. Sandubete, Julio E. & Escot, Lorenzo, 2020. "Chaotic signals inside some tick-by-tick financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    13. Takao Asano & Akihisa Shibata & Masanori Yokoo, 2021. "Polarization and Permanent Fluctuations: Quasi-Periodic Motions in a Two-Class OLG Model (Revised version with a new title "Quasi-Periodic Motions in a Polarized Overlapping Generations Model wit," KIER Working Papers 1063, Kyoto University, Institute of Economic Research.
    14. Takao Asano & Akihisa Shibata & Masanori Yokoo, 2021. "Quasi-Periodic Motions in a Polarized Overlapping Generations Model with Technology Choice," KIER Working Papers 1070, Kyoto University, Institute of Economic Research.
    15. Frédéric Lordon, 1991. "Théorie de la croissance : quelques développements récents [Première partie : la croissance récente]," Revue de l'OFCE, Programme National Persée, vol. 36(1), pages 157-211.
    16. Laura Gardini & Noemi Schmitt & Iryna Sushko & Fabio Tramontana & Frank Westerhoff, 2019. "Necessary and sufficient conditions for the roots of a cubic polynomial and bifurcations of codimension-1, -2, -3 for 3D maps," Working Papers 1908, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2019.
    17. Viktor Avrutin & Iryna Sushko & Fabio Tramontana, 2014. "Bifurcation Structure in a Bimodal Piecewise Linear Business Cycle Model," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, November.
    18. Citera, Emanuele & Sau, Lino, 2019. "Complexity, Conventions and Instability: the role of monetary policy," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201924, University of Turin.
    19. Fausto, Cavalli, 2016. "A cobweb model with alternating demand and supply functions," Working Papers 325, University of Milano-Bicocca, Department of Economics, revised 07 Feb 2016.
    20. Dimitrios Varvarigos, 2020. "Cultural Transmission, Education-Promoting Attitudes, and Economic Development," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 37, pages 173-194, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2206.11933. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.