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Nonstationary response of a nonlinear economic cycle model under random disturbance

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  • Zhao, Jun

Abstract

Stochastic mechanics is widely applied in the field of economics and econometrics. One important application is to study economic fluctuations in economic cycle theory. However, nonstationary response of nonlinear economic cycles with random disturbance is less investigated. This paper is devoted to studying the nonstationary response of a nonlinear economic cycle model. First, a nonlinear economic cycle model is developed according to the Goodwin model and the Puu nonlinear economic cycle model. Gaussian white noise is regarded as a spontaneous function in the developed nonlinear economic cycle model. Then, a path integration method is adopted based on Gauss–Legendre scheme and short-time Gaussian approximation for obtaining the nonstationary probability density function (PDF) of the nonlinear economic cycle model. The obtained results are verified by the simulation result. Finally, the evolution of the nonstationary PDF is studied in detail in the numerical analysis. The effects of system parameters are compared and discussed. The results show that the addition of the quadratic term of income velocity leads to the nonzero means of the PDFs of income and income velocity. Due to the presence of the quadratic and cubic terms, these PDFs have non-Gaussian distributions.

Suggested Citation

  • Zhao, Jun, 2019. "Nonstationary response of a nonlinear economic cycle model under random disturbance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 409-421.
    • Handle: RePEc:eee:phsmap:v:517:y:2019:i:c:p:409-421
    DOI: 10.1016/j.physa.2018.11.036
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    References listed on IDEAS

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    1. Paolinelli, Giovanni & Arioli, Gianni, 2018. "A path integral based model for stocks and order dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 387-399.
    2. Liu, Wei-han, 2018. "Hidden Markov model analysis of extreme behaviors of foreign exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1007-1019.
    3. Nasiri, S. & Bektas, E. & Jafari, G.R., 2018. "The impact of trading volume on the stock market credibility: Bohmian quantum potential approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1104-1112.
    4. Giovanni Paolinelli & Gianni Arioli, 2018. "A path integral based model for stocks and order dynamics," Papers 1803.07904, arXiv.org.
    5. Li, Wei & Xu, Wei & Zhao, Junfeng & Jin, Yanfei, 2007. "Stochastic stability and bifurcation in a macroeconomic model," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 702-711.
    6. Gil-Alana, Luis A. & Gupta, Rangan & Shittu, Olanrewaju I. & Yaya, OlaOluwa S., 2018. "Market efficiency of Baltic stock markets: A fractional integration approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 251-262.
    7. Heiberger, Raphael H., 2018. "Predicting economic growth with stock networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 489(C), pages 102-111.
    8. Giovanni Paolinelli & Gianni Arioli, 2018. "A model for stocks dynamics based on a non-Gaussian path integral," Papers 1809.01342, arXiv.org, revised Oct 2018.
    9. Iryna Sushko & Tönu Puu & Laura Gardini, 2006. "A Goodwin-Type Model with Cubic Investment Function," Springer Books, in: Tönu Puu & Iryna Sushko (ed.), Business Cycle Dynamics, chapter 11, pages 299-316, Springer.
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