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Nonstationarity of Stock Returns

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Difference Equations, Discrete Dynamical Systems and Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 150))

Abstract

Theoretical framework and an appropriate algorithm is developed to measure the nonstationarity (NS) of data streams. With the nonstationary measure, the properties of stock returns are studied. Three experiments illustrate that: the nonstationarity of stock return can not be diversified with big portfolio; nonstationarity, which can explain the risk premium, is positively related to the investing period.

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Notes

  1. 1.

    The selected indices include S&P 500 from the US; FTSE 100, DAX, CAC 40 and EURO STOXX 50 index from Europe; Nikkei 225, Hang Seng Index, SSE Composite Index, Straits Times Index, and S&P/ASX 200 from Asia; and S&P/TSX Composite Index from Canada. For more information about these indices, please visit http://finance.yahoo.com/stock-center/.

  2. 2.

    The component stocks are as listed on December 01, 2014. For more information about S&P 500 index please visit http://en.wikipedia.org/wiki/List_of_S%26P_500_companies.

  3. 3.

    http://finance.yahoo.com/.

  4. 4.

    http://csmar.gtadata.com/.

  5. 5.

    It is observed that in the beginning of 2001, there are only 985 companies are listed on the two stock exchanges in China. After ten years of development this figure increases to 2028 at the end of 2010.

References

  1. H. Markowitz, Portfolio selection. J. Financ. 7, 77–91 (1952)

    Google Scholar 

  2. W.F. Sharpe, Capital asset prices: a theory of market equilibrium under conditions of risk. J. Financ. 19, 425–442 (1964)

    Google Scholar 

  3. S.A. Ross, The arbitrage theory of capital asset pricing. J. Econ. Theory 13, 341–360 (1976)

    Article  MathSciNet  Google Scholar 

  4. N.F. Chen, R. Roll, S.A. Ross, Economic forces and the stock market. J. Bus. 59, 383–403 (1986)

    Article  Google Scholar 

  5. E.F. Fama, K.R. French, Common risk factors in the returns on stocks and bonds. J. Financ. Econ. 33, 3–56 (1993)

    Article  MATH  Google Scholar 

  6. C.J. Neely, D.E. Rapach, J. Tu, G.F. Zhou, Forecasting the equity risk premium: the role of technical indicators. Manag. Sci. 60, 1772–1791 (2014)

    Article  Google Scholar 

  7. R.M. Gray, J.C. Kieffer, Asymptotically mean stationary measures. Ann. Probab. 8, 962–973 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  8. D.A. Dickey, W.A. Fuller, Distribution of the estimators for autoregressive time series with a unit root. J. Am. Stat. Assoc. 74, 427–431 (1979)

    MathSciNet  MATH  Google Scholar 

  9. T. Schreiber, Detecting and analyzing nonstationarity in a time series using nonlinear cross predictions. Phys. Rev. Lett. 78, 843–846 (1997)

    Article  Google Scholar 

  10. C. Rieke, K. Sternickel, R.G. Andrzejak, C.E. Elger, P. David, K. Lehnertz, Measuring nonstationarity by analyzing the loss of recurrence in dynamical systems, Phys. Rev. Lett. 88 (2002)

    Google Scholar 

  11. N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H.H. Shih, Q. Zheng, N.C. Yen, C.C. Tung, H.H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. A: Math. Phys. Eng. Sci. 454, 903–995 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  12. Y.M. Ding, W.T. Fan, Q.H. Tan, K.K. Wu, Y.J. Zou, Nonstationarity measure of data stream. Acta Mathematica Scientia 30(A), 1364–1376 (2010)

    MathSciNet  MATH  Google Scholar 

  13. Q.H. Tan, The non-stationarity measure of time series and its application, Ph.D. thesis, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, 2013

    Google Scholar 

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Acknowledgments

The author is funded by Zhongnan University of Economics and Law with the Start-Up Grant (No. 31541310516) and the General Research Fund (No. 31541410505).

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Authors and Affiliations

  1. School of Finance, Zhongnan University of Economics and Law, Wuhan, 430073, China

    Kekun Wu

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  1. Kekun Wu
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Correspondence to Kekun Wu .

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Editors and Affiliations

  1. Missouri University of Science and Techn Dept. of Mathematics and Statistics, Rolla, Montana, USA

    Martin Bohner

  2. Chinese Academy of Sciences Wuhan Institute of Physics and Mathemati, Wuhan, China

    Yiming Ding

  3. Faculty of Science, Masaryk University Faculty of Science, Brno, Czech Republic

    Ondřej Došlý

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Wu, K. (2015). Nonstationarity of Stock Returns. In: Bohner, M., Ding, Y., Došlý, O. (eds) Difference Equations, Discrete Dynamical Systems and Applications. Springer Proceedings in Mathematics & Statistics, vol 150. Springer, Cham. https://doi.org/10.1007/978-3-319-24747-2_12

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