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Recurrence quantification analysis on a Kaldorian business cycle model

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Abstract

Business cycles denote oscillations in economy as a result of downturns and expansions. The macroeconomic variable under our investigation is income as derived by the dynamic interaction with capital, consumption and investment. In this paper, a Kaldorian business cycle model is used to simulate real dynamics so that nonlinear techniques such as recurrence quantification analysis, Poincaré Plot and related quantifiers can be applied. Analysis of chaos brings evidences on fractal dimension and entropy measures for both real data and model’s simulations. The final goal is to discover whether real and simulated business cycle dynamics have similar characteristics and validate the model as a suitable tool to simulate reality.

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References

  1. Addo, P.M., Billio, M., Guegan, D.: Nonlinear dynamics and recurrence plots for detecting financial crisis. N. Am. J. Econ. Finance 26, 416–435 (2013)

    Google Scholar 

  2. Agliari, A., Dieci, R., Gardin, L.: Homoclinic tangles in a Kaldor-like business cycle model. J. Econ. Behav. Organ. 62, 324–347 (2007)

    Google Scholar 

  3. Bajo-Rubio, O., Fernández-Rodríguez, F., Sosvilla-Rivero, S.: Chaotic behaviour in exchange-rate series: first results for the Peseta—U.S. dollar case. Econ. Lett. 39(2), 207–211 (1992)

    MATH  Google Scholar 

  4. Bastos, A.J., Caiado, J.: Recurrence quantification analysis of global stock. Physica A 390, 1315–1325 (2011)

    Google Scholar 

  5. BEA: USA Recessions, Gross Domestic Product [A191RP1Q027SBEA]—US Bureau of Economic Analysis. Retrieved from FRED, Federal Reserve Bank of St. Louis; 10 Nov 2016 (2016)

  6. Bensaïda, A., Litimi, H.: High level chaos in the exchange and index markets. Chaos Solitons Fractals 54, 90–95 (2013)

    MathSciNet  MATH  Google Scholar 

  7. Blanco, S., Garcia, H., Quiroga, R.Q., Romanelli, L., Rosso, O.: Stationarity of the EEG series. IEEE Eng. Med. Biol. Mag. 14(4), 395–399 (1995)

    Google Scholar 

  8. Brock, W.A., Sayers, C.L.: Is the business cycle characterized by deterministic chaos? J. Monetary Econ. 22(1), 71–90 (1988)

    Google Scholar 

  9. Chen, W.-S.: Use of recurrence plot and recurrence quantification analysis in Taiwan unemployment rate time series. Physica A 390(7), 1332–1342 (2011)

    Google Scholar 

  10. Crowley, P.M.: Analyzing convergence and synchronicity of business and growth cycles in the euro area using cross recurrence plots. Eur. Phys. J. Spec. Top. 164(1), 67–84 (2008)

    Google Scholar 

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

    Google Scholar 

  12. Fabretti, A., Ausloos, M.: Recurrence plot and recurrence quantification analysis techniques for detecting a critical regime. Examples from financial market inidices. Int. J. Mod. Phys. C 16(05), 671–706 (2005)

    MATH  Google Scholar 

  13. Faggini, M., Bruno, B., Parziale, A.: Does chaos matter in financial time series analysis? Int. J. Econ. Financ. Issues 9(4), 18 (2019)

    Google Scholar 

  14. Federici, D., Gandolfo, G.: Chaos in economics. J. Econ. Develop. Stud. 2(1), 51–79 (2014)

  15. Fishman, M., Jacono, F.J., Park, S., Jamasebi, R., Thungtong, A., Loparo, K.A., Dick, T.E.: A method for analyzing temporal patterns of variability of a time series from poincare plots. J. Appl. Physiol. 113(2), 297–306 (2012)

    Google Scholar 

  16. Gneiting, T., Genton, M.G., Guttorp, P.: Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry, Chapter 4. World Scientific, Singapore (2006)

    MATH  Google Scholar 

  17. Golestani, A., Gras, R.: Can we predict the unpredictable? Sci. Rep. 4, 6834 (2014)

    Google Scholar 

  18. Goodfriend, M.: Interest rate smoothing and price level trend-stationarity. J. Monetary Econ. 19(3), 335–348 (1987)

    Google Scholar 

  19. Gorban, A.N., Smirnova, E.V., Tyukina, T.A.: Correlations, risk and crisis: from physiology to finance. Physica A 389(16), 3193–3217 (2010)

    Google Scholar 

  20. Granger, C.W.: Is chaotic economic theory relevant for economics? A review article of: Jess Benhabib: cycles and chaos in economic equilibrium. J. Int. Comp. Econ. 3, 139–145 (1994)

    Google Scholar 

  21. Harrod, R.F.: Towards a Dynamic Economics: Some Recent Developments of Economic Theory and Their Application to Policy. MacMillan and Company, London (1948)

    Google Scholar 

  22. Ho, K.K., Moody, G.B., Peng, C.-K., Mietus, J.E., Larson, M.G., Levy, D., Goldberger, A.L.: Predicting survival in heart failure case and control subjects by use of fully automated methods for deriving nonlinear and conventional indices of heart rate dynamics. Circulation 96(3), 842–848 (1997)

    Google Scholar 

  23. Hommes, C.H., Manzan, S.: Comments on testing for nonlinear structure and chaos in economic time series. J. Macroecon. 28(1), 169–174 (2006)

    Google Scholar 

  24. Januario, C., Gracio, C., Duarte, J.: Measuring complexity in a business cycle model of the Kaldor type. Chaos Solitons Fractals 42(5), 2890–2903 (2009)

    MathSciNet  MATH  Google Scholar 

  25. Kaddar, A., Alaoui, H.T.: Global existence of periodic solutions in a delayed Kaldor–Kalecki model. Nonlinear Anal.: Model. Control 14(4), 463–472 (2009)

    MathSciNet  MATH  Google Scholar 

  26. Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econom.: J. Econom. Soc. 47(2), 263–291 (1979)

    MathSciNet  MATH  Google Scholar 

  27. Kaldor, N.: A model of trade cycle. Econ. J. 50(197), 78–92 (1940)

    Google Scholar 

  28. Kalecki, M.: A theory of the business cycle. Rev. Econ. Stud. 4(2), 77–97 (1937)

    Google Scholar 

  29. Kyrtsou, C., Serletis, A.: Univariate tests for nonlinear structure. J. Macroecon. 28, 154–168 (2006)

    Google Scholar 

  30. Lange, O.: Introduction to Economic Cybernetics. Elsevier, Amsterdam (2014)

    Google Scholar 

  31. Lorenz, H.W.: Nonlinear Dynamical Economics and Chaotic Motion, 2nd edn. Springer, Berlin (1993)

    MATH  Google Scholar 

  32. Mandic, D., Chen, M., Gautama, T., Van Hulle, M., Constantinides, A.: On the characterization of the deterministic/stochastic and linear/nonlinear nature of time series. Proc. R. Soc. A: Math. Phys. Eng. Sci. 464(2093), 1141–1160 (2008)

    MathSciNet  MATH  Google Scholar 

  33. Mandic, D.P., Chambers, J.: Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures and Stability. Wiley, Hoboken (2001)

    Google Scholar 

  34. Mircea, G., Neamtu, M., Opris, D.: The Kaldor–Kalecki stochastic model of business cycle. Nonlinear Anal. 16(2), 191–205 (2011)

    MathSciNet  MATH  Google Scholar 

  35. Moloney, K., Raghavendra, S.: A linear and nonlinear review of the arbitrage-free parity theory for the CDS and bond markets. In: Cummins, M., Murphy, F., Miller, J. (eds.) Topics in Numerical Methods for Finance, pp. 177–200. Springer, Boston, MA (2012)

    MATH  Google Scholar 

  36. National Bureau of Economic Research. The NBER’s recession dating procedure business cycle dating committee (2008)

  37. Orlando, G.: A discrete mathematical model for chaotic dynamics in economics: Kaldor’s model on business cycle. Math. Comput. Simul. 125, 83–98 (2016)

    MathSciNet  Google Scholar 

  38. Orlando, G.: Chaotic business cycles within a Kaldor–Kalecki framework. In: Pham, V.T., Vaidyanathan, S., Volos, C., Kapitaniak, T. (eds.) Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors, pp. 133–161. Springer, Cham (2018)

    Google Scholar 

  39. Orlando, G., Della Rossa, F.: An empirical test on Harrod’s open economy dynamics. Mathematics 7(6), 524 (2019)

    Google Scholar 

  40. Orlando, G., Zimatore, G.: RQA correlations on real business cycles time series. Proc. Conf. Perspect. Nonlinear Dyn. 2016(1), 35–41 (2017)

    Google Scholar 

  41. Orlando, G., Zimatore, G.: Recurrence quantification analysis of business cycles. Chaos Solitons Fractals 110, 82–94 (2018)

    MathSciNet  Google Scholar 

  42. Orlando, G., Zimatore, G.: RQA correlations on business cycles: A comparison between real and simulated data. In: Advances on Nonlinear Dynamics of Electronic Systems, pp. 62–68 (2019). https://doi.org/10.1142/9789811201523_0012

  43. Piskun, O., Piskun, S.: Recurrence quantification analysis of financial market crashes and crises. arXiv preprint arXiv:1107.5420 (2011)

  44. Robinson, J.: Harrod after twenty-one years. Econ. J. 80(319), 731–737 (1970)

    Google Scholar 

  45. Schouten, J.C., den Bleek, C.M.V.: RRChaos, Software Package for Analysis of (Experimental) Chaotic Time Series. Reactor Research Foundations, Delft (1994)

    Google Scholar 

  46. Shintani, M., Linton, O.: Is there chaos in the world economy? A nonparametric test using consistent standard errors. Int. Econ. Rev. 44(1), 331–357 (2003)

    MathSciNet  Google Scholar 

  47. Sivakumar, B., Berndtsson, R.: Advances in Data-Based Approaches for Hydrologic Modeling and Forecasting, Chapter 9, pp. 411–461. World Scientific, Singapore (2010)

    Google Scholar 

  48. Smith, A.: The Wealth of Nations. W. Strahan and T. Cadell, London (1776)

  49. Solow, R.M.: A contribution to the theory of economic growth. Q. J. Econ. 70(1), 65–94 (1956)

    Google Scholar 

  50. Sportelli, M., Celi, G.: A mathematical approach to Harrod’s open economy dynamics. Metroeconomica 62, 459–493 (2011)

    MATH  Google Scholar 

  51. Sportelli, M.C.: Dynamic complexity in a Keynesian growth-cycle model involving Harrod’s instability. J. Econ. 71(2), 167–198 (2000)

    MATH  Google Scholar 

  52. Strozzi, F., Gutierrez, E., Noè, C., Rossi, T., Serati, M., Zaldivar, J.: Application of Non-linear Time Series Analysis Techniques to the Nordic Spot Electricity Market Data. Libero istituto universitario Carlo Cattaneo, Castellanza (2007)

    Google Scholar 

  53. Theiler, J., Galdrikian, B., Longtin, A., Eubank, S., Farmer, J.D.: Testing for nonlinearity in time series: the method of surrogate data. Physica D 58, 77–94 (1992)

    MATH  Google Scholar 

  54. Tulppo, M.P., Makikallio, T., Takala, T., Seppanen, T., Huikuri, H.V.: Quantitative beat-to-beat analysis of heart rate dynamics during exercise. Am. J. Physiol. Heart Circ. Physiol. 271(1), H244–H252 (1996)

    Google Scholar 

  55. Vassilicos, J.C., Demos, A., Tata, F.: No evidence of chaos but some evidence of multifractals in the foreign exchange and the stock markets. In: Crilly, A.J., Earnshaw, R.A., Jones, H. (eds.) Applications of Fractals and Chaos, pp. 249–265. Springer, Berlin (1993)

    Google Scholar 

  56. Von Mises, L.: Planned Chaos. Ludwig von Mises Institute, Auburn (1947)

    Google Scholar 

  57. Wiener, N.: Cybernetics. Bull. Am. Acad. Arts Sci. 3(7), 2–4 (1950)

    Google Scholar 

  58. Yoshida, H.: Harrod’s ‘knife-edge’ reconsidered: an application of the Hopf bifurcation theorem and numerical simulations. J. Macroecon. 21(3), 537–562 (1999)

    Google Scholar 

  59. Zimatore, G., Fetoni, A.R., Paludetti, G., Cavagnaro, M., Podda, M.V., Troiani, D.: Post-processing analysis of transient-evoked otoacoustic emissions to detect 4 kHz-notch hearing impairment—a pilot study. Med Sci. Monit.: Int. Med. J. Exper. Clin. Res. 17(6), MT41 (2011)

    Google Scholar 

  60. Zimatore, G., Garilli, G., Poscolieri, M., Rafanelli, C., Terenzio Gizzi, F., Lazzari, M.: The remarkable coherence between two Italian far away recording stations points to a role of acoustic emissions from crustal rocks for earthquake analysis. Chaos: Interdiscip. J. Nonlinear Sci. 27(4), 043101 (2017)

    Google Scholar 

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Acknowledgements

The authors are very grateful to the antonymous referees for their feedbacks and recommendations. Special thanks go to Carlo Lucheroni (University of Camerino) for his comments.

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Correspondence to Giuseppe Orlando.

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Orlando, G., Zimatore, G. Recurrence quantification analysis on a Kaldorian business cycle model. Nonlinear Dyn 100, 785–801 (2020). https://doi.org/10.1007/s11071-020-05511-y

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