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
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)
Agliari, A., Dieci, R., Gardin, L.: Homoclinic tangles in a Kaldor-like business cycle model. J. Econ. Behav. Organ. 62, 324–347 (2007)
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)
Bastos, A.J., Caiado, J.: Recurrence quantification analysis of global stock. Physica A 390, 1315–1325 (2011)
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)
Bensaïda, A., Litimi, H.: High level chaos in the exchange and index markets. Chaos Solitons Fractals 54, 90–95 (2013)
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)
Brock, W.A., Sayers, C.L.: Is the business cycle characterized by deterministic chaos? J. Monetary Econ. 22(1), 71–90 (1988)
Chen, W.-S.: Use of recurrence plot and recurrence quantification analysis in Taiwan unemployment rate time series. Physica A 390(7), 1332–1342 (2011)
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)
Eckmann, J.-P., Kamphorst, S.O., Ruelle, D.: Recurrence plots of dynamical systems. EPL (Europhys. Lett.) 4(9), 973 (1987)
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)
Faggini, M., Bruno, B., Parziale, A.: Does chaos matter in financial time series analysis? Int. J. Econ. Financ. Issues 9(4), 18 (2019)
Federici, D., Gandolfo, G.: Chaos in economics. J. Econ. Develop. Stud. 2(1), 51–79 (2014)
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)
Gneiting, T., Genton, M.G., Guttorp, P.: Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry, Chapter 4. World Scientific, Singapore (2006)
Golestani, A., Gras, R.: Can we predict the unpredictable? Sci. Rep. 4, 6834 (2014)
Goodfriend, M.: Interest rate smoothing and price level trend-stationarity. J. Monetary Econ. 19(3), 335–348 (1987)
Gorban, A.N., Smirnova, E.V., Tyukina, T.A.: Correlations, risk and crisis: from physiology to finance. Physica A 389(16), 3193–3217 (2010)
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)
Harrod, R.F.: Towards a Dynamic Economics: Some Recent Developments of Economic Theory and Their Application to Policy. MacMillan and Company, London (1948)
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)
Hommes, C.H., Manzan, S.: Comments on testing for nonlinear structure and chaos in economic time series. J. Macroecon. 28(1), 169–174 (2006)
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)
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)
Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econom.: J. Econom. Soc. 47(2), 263–291 (1979)
Kaldor, N.: A model of trade cycle. Econ. J. 50(197), 78–92 (1940)
Kalecki, M.: A theory of the business cycle. Rev. Econ. Stud. 4(2), 77–97 (1937)
Kyrtsou, C., Serletis, A.: Univariate tests for nonlinear structure. J. Macroecon. 28, 154–168 (2006)
Lange, O.: Introduction to Economic Cybernetics. Elsevier, Amsterdam (2014)
Lorenz, H.W.: Nonlinear Dynamical Economics and Chaotic Motion, 2nd edn. Springer, Berlin (1993)
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)
Mandic, D.P., Chambers, J.: Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures and Stability. Wiley, Hoboken (2001)
Mircea, G., Neamtu, M., Opris, D.: The Kaldor–Kalecki stochastic model of business cycle. Nonlinear Anal. 16(2), 191–205 (2011)
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)
National Bureau of Economic Research. The NBER’s recession dating procedure business cycle dating committee (2008)
Orlando, G.: A discrete mathematical model for chaotic dynamics in economics: Kaldor’s model on business cycle. Math. Comput. Simul. 125, 83–98 (2016)
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)
Orlando, G., Della Rossa, F.: An empirical test on Harrod’s open economy dynamics. Mathematics 7(6), 524 (2019)
Orlando, G., Zimatore, G.: RQA correlations on real business cycles time series. Proc. Conf. Perspect. Nonlinear Dyn. 2016(1), 35–41 (2017)
Orlando, G., Zimatore, G.: Recurrence quantification analysis of business cycles. Chaos Solitons Fractals 110, 82–94 (2018)
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
Piskun, O., Piskun, S.: Recurrence quantification analysis of financial market crashes and crises. arXiv preprint arXiv:1107.5420 (2011)
Robinson, J.: Harrod after twenty-one years. Econ. J. 80(319), 731–737 (1970)
Schouten, J.C., den Bleek, C.M.V.: RRChaos, Software Package for Analysis of (Experimental) Chaotic Time Series. Reactor Research Foundations, Delft (1994)
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)
Sivakumar, B., Berndtsson, R.: Advances in Data-Based Approaches for Hydrologic Modeling and Forecasting, Chapter 9, pp. 411–461. World Scientific, Singapore (2010)
Smith, A.: The Wealth of Nations. W. Strahan and T. Cadell, London (1776)
Solow, R.M.: A contribution to the theory of economic growth. Q. J. Econ. 70(1), 65–94 (1956)
Sportelli, M., Celi, G.: A mathematical approach to Harrod’s open economy dynamics. Metroeconomica 62, 459–493 (2011)
Sportelli, M.C.: Dynamic complexity in a Keynesian growth-cycle model involving Harrod’s instability. J. Econ. 71(2), 167–198 (2000)
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)
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)
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)
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)
Von Mises, L.: Planned Chaos. Ludwig von Mises Institute, Auburn (1947)
Wiener, N.: Cybernetics. Bull. Am. Acad. Arts Sci. 3(7), 2–4 (1950)
Yoshida, H.: Harrod’s ‘knife-edge’ reconsidered: an application of the Hopf bifurcation theorem and numerical simulations. J. Macroecon. 21(3), 537–562 (1999)
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)
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)
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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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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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DOI: https://doi.org/10.1007/s11071-020-05511-y