Skip to main content

2018 | OriginalPaper | Buchkapitel

Chaotic Business Cycles within a Kaldor-Kalecki Framework

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This chapter, after providing some background on business cycles, Kaldor’s original model and related literature, presents an original specification Orlando (Math Comput Simul 125:83–98, 2016) which adds to the cyclical behaviour some peculiar characteristics such as an asymmetric investment and consumption function, lagged investments and integration of economic shocks. A further section proves the chaotic behaviour of the model and adds some insights derived from recurrence quantification analysis. The final part draws some concluding remarks and makes some suggestions for future research. This work investigates chaotic behaviours within a Kaldor-Kalecki framework. This can be achieved by an original specification of the functions describing the investments and consumption as variants of the hyperbolic tangent function rather than the usual arctangent. Therefore fluctuations of economic systems (i.e. business cycles) can be explained by the shape of the investment and saving functions which, in turn, are determined by the behaviour of economic agents. In addition it is explained how the model can accommodate those cumulative effects mentioned by Kaldor which may have the effect of translating the saving and investment functions. This causes the so-called shocks which may be disruptive to the economy or that may have the effect of helping the system to recover from a crisis.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
1
On some issues related to the arctg see for example Bradford and Davenport (2002), Collicott (2012), Walter (2010), Gonnet and Scholl (2009).
 
2
Which has the following advantages: (a) does not require any subjective parameters except for the time-delay for the embedding; (b) does not strongly depend on the number of data points; (c) is able to distinguish between deterministic and stochastic signals; (d) it is computationally efficient and works well in presence of high-dimensional attractors.
 
3
By contrast in the proposed model determinism is ensured by construction.
 
Literatur
Zurück zum Zitat Adachi M (1993) Embeddings and immersions. American Mathematical Society Adachi M (1993) Embeddings and immersions. American Mathematical Society
Zurück zum Zitat Addo PM, Billio M, Guegan D (2013) Nonlinear dynamics and recurrence plots for detecting financial crisis. N Am J Econ Finan 26:416–435CrossRef Addo PM, Billio M, Guegan D (2013) Nonlinear dynamics and recurrence plots for detecting financial crisis. N Am J Econ Finan 26:416–435CrossRef
Zurück zum Zitat Agliari A, Dieci R, Gardini L (2007) Homoclinic tangles in a Kaldor-like business cycle model. J Econ Behav Organ 62:324–347CrossRef Agliari A, Dieci R, Gardini L (2007) Homoclinic tangles in a Kaldor-like business cycle model. J Econ Behav Organ 62:324–347CrossRef
Zurück zum Zitat Arya S, Mount DM (1993) Approximate nearest neighbor searching. In: Proceedings of 4th annual ACM-SIAM symposium on discrete algorithms (SODA’93), pp 271–280 Arya S, Mount DM (1993) Approximate nearest neighbor searching. In: Proceedings of 4th annual ACM-SIAM symposium on discrete algorithms (SODA’93), pp 271–280
Zurück zum Zitat Arya S, Mount DM, Netanyahu NS, Silverman R, Wu AY (1998) An optimal algorithm for approximate nearest neighbor searching. J ACM 45(6):891–923MathSciNetCrossRefMATH Arya S, Mount DM, Netanyahu NS, Silverman R, Wu AY (1998) An optimal algorithm for approximate nearest neighbor searching. J ACM 45(6):891–923MathSciNetCrossRefMATH
Zurück zum Zitat Benson H (2008) University physics. Wiley Benson H (2008) University physics. Wiley
Zurück zum Zitat Bischi GI, Dieci R, Rodano G, Saltari E (2001) Multiple attractors and global bifurcations in a kaldor-type business cycle model. J Evolut Econ 11:527–554CrossRef Bischi GI, Dieci R, Rodano G, Saltari E (2001) Multiple attractors and global bifurcations in a kaldor-type business cycle model. J Evolut Econ 11:527–554CrossRef
Zurück zum Zitat Bradford R, Davenport JH (2002) Towards better simplification of elementary functions. In: ISSAC ’02 Proceedings of the 2002 international symposium on symbolic and algebraic computation, New York. ACM, pp 16–22 Bradford R, Davenport JH (2002) Towards better simplification of elementary functions. In: ISSAC ’02 Proceedings of the 2002 international symposium on symbolic and algebraic computation, New York. ACM, pp 16–22
Zurück zum Zitat Burns AF, Mitchell WC (1946) Measuring business cycles. In: National bureau of economic research Burns AF, Mitchell WC (1946) Measuring business cycles. In: National bureau of economic research
Zurück zum Zitat Calvo O, Cartwright JHE (1998) Fuzzy control of chaos. Int J Bifurc Chaos 8:1743–1747CrossRefMATH Calvo O, Cartwright JHE (1998) Fuzzy control of chaos. Int J Bifurc Chaos 8:1743–1747CrossRefMATH
Zurück zum Zitat Cao L (1997) Practical method for determining the minimum embedding dimension of a scalar time series. Phys D 110(1–2):43–50CrossRefMATH Cao L (1997) Practical method for determining the minimum embedding dimension of a scalar time series. Phys D 110(1–2):43–50CrossRefMATH
Zurück zum Zitat Cao L (2002) Determining minimum embedding dimension from scalar time series. In: Soofi A, Cao L (eds) Modelling and forecasting financial data, vol 2. Studies in computational finance. US, Springer, pp 43–60CrossRef Cao L (2002) Determining minimum embedding dimension from scalar time series. In: Soofi A, Cao L (eds) Modelling and forecasting financial data, vol 2. Studies in computational finance. US, Springer, pp 43–60CrossRef
Zurück zum Zitat Chen W-S (2011) Use of recurrence plot and recurrence quantification analysis in taiwan unemployment rate time series. Phys A Stat Mech Appl 390(7):1332–1342CrossRef Chen W-S (2011) Use of recurrence plot and recurrence quantification analysis in taiwan unemployment rate time series. Phys A Stat Mech Appl 390(7):1332–1342CrossRef
Zurück zum Zitat Chiarella C (1990) The elements of a nonlinear theory of economic dynamic. Springer, Berlin-Heidelberg-New YorkCrossRefMATH Chiarella C (1990) The elements of a nonlinear theory of economic dynamic. Springer, Berlin-Heidelberg-New YorkCrossRefMATH
Zurück zum Zitat Crowley PM (2008) Analyzing convergence and synchronicity of business and growth cycles in the euro area using cross recurrence plots. Eur Phys J Spec Topics 164(1):67–84CrossRef Crowley PM (2008) Analyzing convergence and synchronicity of business and growth cycles in the euro area using cross recurrence plots. Eur Phys J Spec Topics 164(1):67–84CrossRef
Zurück zum Zitat Crowley PM, Schultz A (2010) A new approach to analyzing convergence and synchronicity in growth and business cycles: cross recurrence plots and quantification analysis. Bank of Finland research discussion paper (16) Crowley PM, Schultz A (2010) A new approach to analyzing convergence and synchronicity in growth and business cycles: cross recurrence plots and quantification analysis. Bank of Finland research discussion paper (16)
Zurück zum Zitat Eroglu D, Peron TKD, Marwan N, Rodrigues FA, Costa LdF, Sebek M, Kiss, IZ, Kurths J (2014) Entropy of weighted recurrence plots. Phys Rev E 90(4):042919 Eroglu D, Peron TKD, Marwan N, Rodrigues FA, Costa LdF, Sebek M, Kiss, IZ, Kurths J (2014) Entropy of weighted recurrence plots. Phys Rev E 90(4):042919
Zurück zum Zitat Fabretti A, Ausloos M (2005) Recurrence plot and recurrence quantification analysis techniques for detecting a critical regime. Examples from financial market indices. Int J Mod Phys C 16(05):671–706CrossRefMATH Fabretti A, Ausloos M (2005) Recurrence plot and recurrence quantification analysis techniques for detecting a critical regime. Examples from financial market indices. Int J Mod Phys C 16(05):671–706CrossRefMATH
Zurück zum Zitat Gonnet GH, Scholl R (2009) Scientific computation. Cambridge University Press, CambridgeCrossRefMATH Gonnet GH, Scholl R (2009) Scientific computation. Cambridge University Press, CambridgeCrossRefMATH
Zurück zum Zitat Goodwin RM (1951) The nonlinear accelerator and the persistence of business cycle. Econometrica 19(1) Goodwin RM (1951) The nonlinear accelerator and the persistence of business cycle. Econometrica 19(1)
Zurück zum Zitat Gorban AN, Smirnova EV, Tyukina TA (2010) Correlations, risk and crisis: from physiology to finance. Phys A Stat Mech Appl 389(16):3193–3217CrossRef Gorban AN, Smirnova EV, Tyukina TA (2010) Correlations, risk and crisis: from physiology to finance. Phys A Stat Mech Appl 389(16):3193–3217CrossRef
Zurück zum Zitat Grassberger P (1986) Estimating the fractal dimension and entropies of strange attractors. In: Holden AV (ed) Chaos. Manchester University Press, Manchester, pp 291–311 Grassberger P (1986) Estimating the fractal dimension and entropies of strange attractors. In: Holden AV (ed) Chaos. Manchester University Press, Manchester, pp 291–311
Zurück zum Zitat Grassberger P, Procaccia I (1983b) Estimation of the Kolmogorov entropy from a chaotic signal. Phys Rev A 28:2591–2593CrossRef Grassberger P, Procaccia I (1983b) Estimation of the Kolmogorov entropy from a chaotic signal. Phys Rev A 28:2591–2593CrossRef
Zurück zum Zitat Grassberger P, Procaccia I (1983c). Measuring the strangeness of strange attractors. Physica D 9:189–208 Grassberger P, Procaccia I (1983c). Measuring the strangeness of strange attractors. Physica D 9:189–208
Zurück zum Zitat Hicks JR (1950) A contribution to the theory of the trade cycle. Clarendon Press, Oxford Hicks JR (1950) A contribution to the theory of the trade cycle. Clarendon Press, Oxford
Zurück zum Zitat Hillinger C, Sebold-Bender M (1992) Cyclical growth in market and planned economies. Oxford University Press, Oxford Hillinger C, Sebold-Bender M (1992) Cyclical growth in market and planned economies. Oxford University Press, Oxford
Zurück zum Zitat Ichimura S (1955a) Notes on non-linear business cycle theories. Osaka economic papers Ichimura S (1955a) Notes on non-linear business cycle theories. Osaka economic papers
Zurück zum Zitat Ichimura S (1955b) Toward a general nonlinear macrodynamic theory of economic fluctuations. In: Kurihara KK (ed) Post-Keynesian economics, chapter 8. George Allen & Unwin Ltd., London, pp 192–226 Ichimura S (1955b) Toward a general nonlinear macrodynamic theory of economic fluctuations. In: Kurihara KK (ed) Post-Keynesian economics, chapter 8. George Allen & Unwin Ltd., London, pp 192–226
Zurück zum Zitat Januário C, Grácio C, Duartea J (2009) Measuring complexity in a business cycle model of the Kaldor type. Chaos, Solitons Fractals 42(5):2890–2903 Januário C, Grácio C, Duartea J (2009) Measuring complexity in a business cycle model of the Kaldor type. Chaos, Solitons Fractals 42(5):2890–2903
Zurück zum Zitat Januário C, Grácio C, Ramos JS (2005) Chaotic behaviour in a two-dimensional business cycle model. In: Elaydi S, Cushing J, Lasser R, Ruffing A, Papageorgiou V, Assche WV (eds) Proceedings of the international conference, difference equations, special functions and orthogonal polynomials, pp 294–304, Munich Januário C, Grácio C, Ramos JS (2005) Chaotic behaviour in a two-dimensional business cycle model. In: Elaydi S, Cushing J, Lasser R, Ruffing A, Papageorgiou V, Assche WV (eds) Proceedings of the international conference, difference equations, special functions and orthogonal polynomials, pp 294–304, Munich
Zurück zum Zitat Kaddar A, Alaoui HT (2009) Global existence of periodic solutions in a delayed Kaldor-Kalecki model. Nonlinear Anal Model Control 14(4):463–472MathSciNetMATH Kaddar A, Alaoui HT (2009) Global existence of periodic solutions in a delayed Kaldor-Kalecki model. Nonlinear Anal Model Control 14(4):463–472MathSciNetMATH
Zurück zum Zitat Kalecki M (1966) Studies in the theory of business cycles, 1933–1939. New York, A.M, Kelley Kalecki M (1966) Studies in the theory of business cycles, 1933–1939. New York, A.M, Kelley
Zurück zum Zitat Karagianni S, Kyrtsou C (2011) Analysing the dynamics between US inflation and Dow Jones index using non-linear methods. Stud Nonlinear Dyn Econom 15(2) Karagianni S, Kyrtsou C (2011) Analysing the dynamics between US inflation and Dow Jones index using non-linear methods. Stud Nonlinear Dyn Econom 15(2)
Zurück zum Zitat Kennel MB, Brown R, Abarbanel HDI (1992) Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 45(6):3403–3411CrossRef Kennel MB, Brown R, Abarbanel HDI (1992) Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 45(6):3403–3411CrossRef
Zurück zum Zitat Korotayev AV, Sergey TV (2010) A spectral analysis of world gdp dynamics: Kondratieff waves, Kuznets swings, Juglar and Kitchin cycles in global economic development, and the 2008–2009 economic crisis. Struct Dyn 4(1) Korotayev AV, Sergey TV (2010) A spectral analysis of world gdp dynamics: Kondratieff waves, Kuznets swings, Juglar and Kitchin cycles in global economic development, and the 2008–2009 economic crisis. Struct Dyn 4(1)
Zurück zum Zitat Krawiec A, Szydlowski M (1999). The Kaldor-Kalecki business cycle model. Ann Oper Res, 89–100 Krawiec A, Szydlowski M (1999). The Kaldor-Kalecki business cycle model. Ann Oper Res, 89–100
Zurück zum Zitat Lei M, Meng G (2011) Symplectic principal component analysis: a new method for time series analysis. Math Probl Eng 2011. Article ID 793429, 14 p Lei M, Meng G (2011) Symplectic principal component analysis: a new method for time series analysis. Math Probl Eng 2011. Article ID 793429, 14 p
Zurück zum Zitat Lei M, Wang Z, Feng Z (2002) A method of embedding dimension estimation based on symplectic geometry. Phys Lett A 303(2–3):179–189MathSciNetCrossRefMATH Lei M, Wang Z, Feng Z (2002) A method of embedding dimension estimation based on symplectic geometry. Phys Lett A 303(2–3):179–189MathSciNetCrossRefMATH
Zurück zum Zitat Letellier C (2013) Estimating the minimum embedding dimension Letellier C (2013) Estimating the minimum embedding dimension
Zurück zum Zitat Lorenz HW (1993) Nonlinear dynamical economics and chaotic motion, 2nd edn. Springer, Berlin-Heidelberg-New York Lorenz HW (1993) Nonlinear dynamical economics and chaotic motion, 2nd edn. Springer, Berlin-Heidelberg-New York
Zurück zum Zitat McBurnett M (1996) Probing the underlying structure in dynamical systems: an introduction to spectral analysis, chapter 2. The University of Michigan Press, pp 31–51 McBurnett M (1996) Probing the underlying structure in dynamical systems: an introduction to spectral analysis, chapter 2. The University of Michigan Press, pp 31–51
Zurück zum Zitat Mircea G, Neamt M, Opris D (1963) The Kaldor and Kalecki stochastic model of business cycle, nonlinear analysis: modelling and control. J Atmos Sci 16(2):191–205 Mircea G, Neamt M, Opris D (1963) The Kaldor and Kalecki stochastic model of business cycle, nonlinear analysis: modelling and control. J Atmos Sci 16(2):191–205
Zurück zum Zitat Moloney K, Raghavendra S (2012) A linear and nonlinear review of the arbitrage-free parity theory for the cds and bond markets. In: Topics in numerical methods for finance. Springer, pp 177–200 Moloney K, Raghavendra S (2012) A linear and nonlinear review of the arbitrage-free parity theory for the cds and bond markets. In: Topics in numerical methods for finance. Springer, pp 177–200
Zurück zum Zitat Moon FC (1987) Chaotic vibrations: an introduction for applied scientists and engineers. Wiley, New YorkMATH Moon FC (1987) Chaotic vibrations: an introduction for applied scientists and engineers. Wiley, New YorkMATH
Zurück zum Zitat Morishima M (1959) A contribution to the nonlinear theory of the trade cycle. Zeitschrift für Nationalökonomie 18(4):166–170CrossRef Morishima M (1959) A contribution to the nonlinear theory of the trade cycle. Zeitschrift für Nationalökonomie 18(4):166–170CrossRef
Zurück zum Zitat Mullineux AW (1984) The business cycle after Keynes. Wheatsheaf Books Ltd, Brighton, Sussex Mullineux AW (1984) The business cycle after Keynes. Wheatsheaf Books Ltd, Brighton, Sussex
Zurück zum Zitat Orlando G (2016) A discrete mathematical model for chaotic dynamics in economics: Kaldor’s model on business cycle. Math Comput Simul 125:83–98 Orlando G (2016) A discrete mathematical model for chaotic dynamics in economics: Kaldor’s model on business cycle. Math Comput Simul 125:83–98
Zurück zum Zitat Palus M, Dvorak I (1992) Singular-value decomposition in attractor reconstruction: pitfalls and precautions. Phys D Nonlinear Phenom 55(1–2):221–234MathSciNetCrossRefMATH Palus M, Dvorak I (1992) Singular-value decomposition in attractor reconstruction: pitfalls and precautions. Phys D Nonlinear Phenom 55(1–2):221–234MathSciNetCrossRefMATH
Zurück zum Zitat Pesin YB (1977) Characteristic Lyapunov exponents and smooth ergodic theory. Rus Math Surv 32:55–114CrossRefMATH Pesin YB (1977) Characteristic Lyapunov exponents and smooth ergodic theory. Rus Math Surv 32:55–114CrossRefMATH
Zurück zum Zitat Pettini M (2005) Controlling chaos through parametric excitations. In: Dynamics and stochastic processes theory and applications. Lecture notes in physics, vol 355. Springer, Berlin-Heidelberg-New York, pp 242–250 Pettini M (2005) Controlling chaos through parametric excitations. In: Dynamics and stochastic processes theory and applications. Lecture notes in physics, vol 355. Springer, Berlin-Heidelberg-New York, pp 242–250
Zurück zum Zitat Pham V-T, Volos C, Vaidyanathan S (2017) A chaotic time-delay system with saturation nonlinearity. Int J Syst Dyn Appl (IJSDA) 6(3):111–129 Pham V-T, Volos C, Vaidyanathan S (2017) A chaotic time-delay system with saturation nonlinearity. Int J Syst Dyn Appl (IJSDA) 6(3):111–129
Zurück zum Zitat Purves WK, Orians GH, Sadava D, Heller HC (2003) Life: the science of biology, vol 3. Macmillan Purves WK, Orians GH, Sadava D, Heller HC (2003) Life: the science of biology, vol 3. Macmillan
Zurück zum Zitat Reger D, Goode S, Ball D (2010) Chemistry: principles and practice. Brooks/Cole, 3rd edn Reger D, Goode S, Ball D (2010) Chemistry: principles and practice. Brooks/Cole, 3rd edn
Zurück zum Zitat Romieras FJ, Ott E, Grebogi C, Daiawansa WP (1992) Controlling chaotic dynamical systems. Physica D, 58:165–192 Romieras FJ, Ott E, Grebogi C, Daiawansa WP (1992) Controlling chaotic dynamical systems. Physica D, 58:165–192
Zurück zum Zitat Schumpeter JA (1954) History of economic analysis. George Allen & Unwin, London Schumpeter JA (1954) History of economic analysis. George Allen & Unwin, London
Zurück zum Zitat Schuster H (1988) Deterministic chaos—an introduction. VcH Verlagsgesellschaft mbH Schuster H (1988) Deterministic chaos—an introduction. VcH Verlagsgesellschaft mbH
Zurück zum Zitat Shishkin J (1961) Signals of recession and recovery. NBER Occasional Paper n 77 Shishkin J (1961) Signals of recession and recovery. NBER Occasional Paper n 77
Zurück zum Zitat Sivakumar B, Berndtsson R (2010) Advances in data-based approaches for hydrologic modeling and forecasting, chapter 9. World Scientific, pp 411–461 Sivakumar B, Berndtsson R (2010) Advances in data-based approaches for hydrologic modeling and forecasting, chapter 9. World Scientific, pp 411–461
Zurück zum Zitat Stewart J (2010) Single variable calculus, 4th edn. Brooks/Cole Publishing Company Stewart J (2010) Single variable calculus, 4th edn. Brooks/Cole Publishing Company
Zurück zum Zitat Stoica P, Moses R (2005) Spectral analysis of signals. Prentice Hall Stoica P, Moses R (2005) Spectral analysis of signals. Prentice Hall
Zurück zum Zitat Strozzi F, Gutierrez E, Noè C, Rossi T, Serati M, Zaldivar J (2007) Application of non-linear time series analysis techniques to the nordic spot electricity market data. Libero istituto universitario Carlo Cattaneo Strozzi F, Gutierrez E, Noè C, Rossi T, Serati M, Zaldivar J (2007) Application of non-linear time series analysis techniques to the nordic spot electricity market data. Libero istituto universitario Carlo Cattaneo
Zurück zum Zitat Takens F (1981) Dynamical systems and turbulence. Lecture notes in mathematics, chapter Detecting strange attractors in turbulence, vol 898. Springer, Berlin-Heidelberg-New York, pp 366–381 Takens F (1981) Dynamical systems and turbulence. Lecture notes in mathematics, chapter Detecting strange attractors in turbulence, vol 898. Springer, Berlin-Heidelberg-New York, pp 366–381
Zurück zum Zitat Walter FS (2010) Waves and oscillations: a prelude to quantum mechanics. Oxford University Press, OxfordMATH Walter FS (2010) Waves and oscillations: a prelude to quantum mechanics. Oxford University Press, OxfordMATH
Zurück zum Zitat Wheldon TE (1988) Mathematical models in cancer research. Taylor & Francis Wheldon TE (1988) Mathematical models in cancer research. Taylor & Francis
Zurück zum Zitat Whitney H (1992) Hassler Whitney collected papers. In: Eells J, Toledo D (eds) Hassler Whitney collected papers, volume I II of contemporary mathematicians. Birkhäuser Verlag, Basel-Boston-Stuttgart Whitney H (1992) Hassler Whitney collected papers. In: Eells J, Toledo D (eds) Hassler Whitney collected papers, volume I II of contemporary mathematicians. Birkhäuser Verlag, Basel-Boston-Stuttgart
Zurück zum Zitat Wolf A (1986) Quantifying chaos with Lyapunov exponents. In: Holden AV (ed) Chaos. Manchester University Press, Manchester, pp 273–290 Wolf A (1986) Quantifying chaos with Lyapunov exponents. In: Holden AV (ed) Chaos. Manchester University Press, Manchester, pp 273–290
Zurück zum Zitat Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Determining Lyapunov exponents from a time series. Physica D 16:285–317 Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Determining Lyapunov exponents from a time series. Physica D 16:285–317
Zurück zum Zitat Xie H, Wang Z, Huang H (2005) Identification determinism in time series based on symplectic geometry spectra. Phys Lett A 342(1–2):156–161MathSciNetCrossRefMATH Xie H, Wang Z, Huang H (2005) Identification determinism in time series based on symplectic geometry spectra. Phys Lett A 342(1–2):156–161MathSciNetCrossRefMATH
Zurück zum Zitat Yasui E (1953) Non-linear self-excited oscillations and business cycles. Cowles Comm Discuss Paper 2063:1–20 Yasui E (1953) Non-linear self-excited oscillations and business cycles. Cowles Comm Discuss Paper 2063:1–20
Zurück zum Zitat Zarnowitz V (1992) Business cycles: theory, history, indicators, and forecasting. National bureau of economic research studies in business cycles, vol 27. The University of Chicago Press, Chicago and London Zarnowitz V (1992) Business cycles: theory, history, indicators, and forecasting. National bureau of economic research studies in business cycles, vol 27. The University of Chicago Press, Chicago and London
Zurück zum Zitat Zbilut JP (2005) Use of recurrence quantification analysis in economic time series. In: Economics: complex windows. Springer, pp 91–104 Zbilut JP (2005) Use of recurrence quantification analysis in economic time series. In: Economics: complex windows. Springer, pp 91–104
Zurück zum Zitat Zimatore G, Fetoni AR, Paludetti G, Cavagnaro M, Podda MV, Troiani D (2011) Post-processing analysis of transient-evoked otoacoustic emissions to detect 4 khz-notch hearing impairment—a pilot study. Med Sci Monit Int Med J Experimental Clin Res, 17(6):MT41 Zimatore G, Fetoni AR, Paludetti G, Cavagnaro M, Podda MV, Troiani D (2011) Post-processing analysis of transient-evoked otoacoustic emissions to detect 4 khz-notch hearing impairment—a pilot study. Med Sci Monit Int Med J Experimental Clin Res, 17(6):MT41
Zurück zum Zitat Zimatore G, Garilli G, Poscolieri M, Rafanelli C, Terenzio Gizzi F, Lazzari M (2017) The remarkable coherence between two Italian far away recording stations points to a role of acoustic emissions from crustal rocks for earthquake analysis. Chaos: An Interdisciplinary. J Nonlinear Sci 27(4):043101 Zimatore G, Garilli G, Poscolieri M, Rafanelli C, Terenzio Gizzi F, Lazzari M (2017) The remarkable coherence between two Italian far away recording stations points to a role of acoustic emissions from crustal rocks for earthquake analysis. Chaos: An Interdisciplinary. J Nonlinear Sci 27(4):043101
Metadaten
Titel
Chaotic Business Cycles within a Kaldor-Kalecki Framework
verfasst von
Giuseppe Orlando
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-71243-7_6