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Empirical chaotic dynamics in economics

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Abstract

Barnett and Chen [4–6] have displayed evidence of chaos in certain monetary aggregates, but the tests have unknown statistical sampling properties. Using monthly growth rates in monetary aggregates, we conduct bispectral tests for nonlinearity. Our tests have known sampling properties, and we find deep nonlinearity in some monetary aggregate series.

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References

  1. R. Ashley, D.M. Patterson and M. Hinich, A diagnostic test for nonlinear serial dependence in time series fitting errors, J. Time Series Anal. 7(1986)165–178.

    Google Scholar 

  2. W.A. Barnett, Economic monetary aggregates: An application of index number and aggregation theory, J. Econometrics 14(1980)11–48.

    Google Scholar 

  3. W.A. Barnett, The microeconomic theory of monetary aggregation, in:New Approach to Monetary Economics, Proc. 2nd Int. Symp. on Economic Theory and Econometrics, ed. W.A. Barnett and K. Singleton (Cambridge University Press, Cambridge, 1987), pp. 115–168.

    Google Scholar 

  4. W.A. Barnett and P. Chen, Economic theory as a generator of measurable attractors, Mondes en Developpement, 14(1986)453; reprinted in:Laws of Nature and Human Conduct: Specificities and Unifying Themes, ed. I. Prigogine and M. Sanglier (G.O.R.D.E.S., Brussels), pp. 209–224.

    Google Scholar 

  5. W.A. Barnett and P. Chen, The aggregation-theoretic monetary aggregates are chaotic and have strange attractors: An econometric application of mathematical chaos, in:Dynamic Econometric Modeling, Proc. 3rd Int. Symp. on Economic Theory and Econometrics, ed. W.A. Barnett, E. Berndt, and H. White (Cambridge University Press, Cambridge, 1988), pp. 199–246.

    Google Scholar 

  6. W.A. Barnett and P. Chen, Deterministic chaos and fractal attractors as tools for nonparametric dynamical econometric inference, Math. Comput. Modeling 10(1988)275–296.

    Google Scholar 

  7. W.A. Barnett and S. Choi, A comparison between the conventional econometric approach to structural inference and the nonparametric chaotic attractor approach, in:Economic Complexity: Chaos, Sunspots, Bubbles and Nonlinearity, Proc. 4th Int. Symp. on Economic Theory and Econometrics, ed. W.A. Barnett, J. Geweke and K. Shell (Cambridge University Press, Cambridge, 1989), pp. 141–212.

    Google Scholar 

  8. W.A. Barnett, M.J. Hinich and W.E. Weber, The regulatory wedge between the demand-side and supply-side aggregation-theoretic monetary aggregates, J. Econometrics 33(1986)165–185.

    Google Scholar 

  9. W.A. Barnett, M. Hinich and P. Yue, Monitoring monetary aggregates under risk aversion, in:Monetary Policy on the 75th Anniversary of the Federal Reserve System, Proc. 14th Annual Economic Conf. of the Federal Reserve Bank of St. Louis, ed. M.T. Belongia (Kluwer Academic, Boston, 1991).

    Google Scholar 

  10. G.E.P. Box and G.M. Jenkins,Time Series Analysis — Forecasting and Control (Holden Day, San Francisco, 1970).

    Google Scholar 

  11. D.R. Brillinger, An introduction to polyspectrum, Ann. Math. Statistics 36(1965)1351–1374.

    Google Scholar 

  12. W.A. Brock and W.D. Dechert, Theorems on distinguishing deterministic from random systems, in:Dynamic Econometric Modeling, Proc. 3rd Int. Symp. on Economic Theory and Econometrics, ed. W. Barnett, E. Berndt and H. White (Cambridge University Press, Cambridge, 1988) pp. 247–268.

    Google Scholar 

  13. W.A. Brock and W.D. Dechert, Statistical inference theory, in:Measures of Complexity and Chaos, ed. Abraham et al. (Plenum, New York, 1990) p. 93.

    Google Scholar 

  14. W.A. Brock, W.D. Dechert and J. Scheinkman, A test for independence based on the correlation dimension, University of Wisconsin-Madison and University of Chicago (1987).

  15. P.L. Brockett, M. Hinich and G.R. Wilson, Nonlinear and non-Gaussian ocean noise, J. Acoust. Soc. Amer. 82(1987)1386–1394.

    Google Scholar 

  16. P.L. Brockett, M. Hinich and D. Patterson, Bispectral-based test for the detection of Gaussianity and linearity in time series, J. Amer. Statist. Assoc. 83(1988)657–664.

    Google Scholar 

  17. P. Chen, Nonlinear dynamics and business cycles, Ph.D. Dissertation, Department of Physics, University of Texas at Austin (May, 1987).

  18. G.P. DeCoster and D.W. Mitchell, Nonlinear monetary dynamics, J. Bus. Econ. Statist. 9(1991) 455–462.

    Google Scholar 

  19. W.E. Diewert, Exact and superlative index numbers, J. Econometrics 4(1976)115–145.

    Google Scholar 

  20. M.J. Hinich, Testing for Gaussianity and linearity of a stationary time series, J. Time Series Anal. 3(1982)169–176.

    Google Scholar 

  21. M.J. Hinich and D. Patterson, Identification of the coefficients in a non-linear time series of the quadratic type, in: J. Econometrics 30(1985)269–288; reprinted in:New Approaches to Modelling, Specification Selection, and Econometric Inference, Proc. 1st Int. Symp. on Economic Theory and Econometrics, ed. W. Barnett and R. Gallant (Cambridge University Press, Cambridge, 1989).

    Google Scholar 

  22. M.J. Hinich and D. Patterson, Evidence of nonlinearity in the trade-by-trade stock market return generating process, in:Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity, Proc. 4th Int. Symp. on Economic Theory and Econometrics, ed. W. Barnett, J. Geweke, and K. Shell (Cambridge University Press, Cambridge, 1989) pp. 383–409.

    Google Scholar 

  23. C.R. Hulten, Divisia index numbers, Econometrica 63(1973)1017–1026.

    Google Scholar 

  24. G. Jenkins and D. Watts,Spectral Analysis and its Applications (Holden-Day, San Francisco, 1968).

    Google Scholar 

  25. H. Minsky,John Maynard Keynes (Columbia University Press, New York, 1975).

    Google Scholar 

  26. J.M. Poterba and J.J. Rotemberg, Money in the utility function: An empirical implementation, in:New Approach to Monetary Economics, Proc. 2nd Int. Symp. on Economic Theory and Econometrics, ed. W. Barnett and K. Singleton (Cambridge University Press, Cambridge, 1987) pp. 219–240.

    Google Scholar 

  27. M. Priestly,Spectral Analysis and Time Series, Vol. 2 (Academic Press, New York, 1981).

    Google Scholar 

  28. J.B. Ramsey, C.L. Sayers, and P. Rothman, The statistical properties of dimension calculations using small data sets: Some economic applications, Int. Econ. Rev. 31(1990)991–1020.

    Google Scholar 

  29. J. Scheinkman and B. LeBaron, Nonlinear dynamics and GNP data, in:Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity, Proc. 4th Int. Symp. on Economic Theory and Econometrics, ed. W. Barnett, J. Geweke and K. Shell (Cambridge University Press, Cambridge, 1989) pp. 213–227.

    Google Scholar 

  30. W. Semmler, Financial crisis as bifurcation in a limit cycle model: A nonlinear approach to Minsky crisis, Department of Economics, New School for Social Research, 65 Fifth Avenue, New York (1985).

    Google Scholar 

  31. T. Subba Rao and M. Gabr, A test for linearity of stationary time series, J. Time Series Anal. 1(1980)145–158.

    Google Scholar 

  32. M. Woodford, Imperfect financial intermediation and complex dynamics, in:Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity, Proc. 4th Int. Symp. on Economic Theory and Econometrics, ed. W. Barnett, J. Geweke and K. Shell (Cambridge University Press, Cambridge, 1989), pp. 309–338.

    Google Scholar 

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Barnett, W.A., Hinich, M.J. Empirical chaotic dynamics in economics. Ann Oper Res 37, 1–15 (1992). https://doi.org/10.1007/BF02071045

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