IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/49921.html
   My bibliography  Save this paper

Some thoughts on accurate characterization of stock market indexes trends in conditions of nonlinear capital flows during electronic trading at stock exchanges in global capital markets

Author

Listed:
  • Ledenyov, Dimitri O.
  • Ledenyov, Viktor O.

Abstract

This research represents some thoughts on the accurate characterization of the stock market indexes trends in the conditions of the nonlinear capital flows at the stock exchanges in the global capital markets. We make our original research proposal that the nonlinear capital flows in the process of the electronic trading can originate the nonlinear changes of the stock market indexes at the stock exchanges in the global capital markets. We suggest that the econophysics techniques can be used to precisely characterize the nonlinearities in the finances. We performed the research of the nonlinearities in Matlab, researching: 1) the ideal dependence of the stock market index over the time, 2) the linear dependence of the stock market index over the time, 3) the quadratic dependence of the stock market index over the time, 2) the exponential dependence of the stock market index over the time. We researched the following indexes: 1) The Dow Jones Industrial Average (DJIA) index; 2) The Standard and Poor’s 500 (S&P 500) index; 3) The NYSE Composite index; 4) The Hong Kong Hang Seng index; 5) The Shanghai Composite index; 6) The Financial Times Securities Exchange (FTSE100) index; 7) The Deutscher Aktienindex (DAX) index; 8) The Nikkei 225 Stock Average index over the certain time periods. The selected time periods were: 6 months; 12 months; 24 months. We assumed that, in every considered case, there are the complex changes of the company valuation, foreign exchange rates, interest rates, prices of strategic commodities over the specified time period. We found that there are the nonlinearities in the characteristic dependences of the stock exchanges indexes on the time. Our research results are in a good agreement with the research findings in Abhyankar, Copeland, Wong (1995, 1997), however the multiple evidences of quantum chaos were found in the researched stock market indexes dependences for the first time.

Suggested Citation

  • Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "Some thoughts on accurate characterization of stock market indexes trends in conditions of nonlinear capital flows during electronic trading at stock exchanges in global capital markets," MPRA Paper 49921, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:49921
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/49921/1/MPRA_paper_49921.pdf
    File Function: original version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/49964/8/MPRA_paper_49964.pdf
    File Function: revised version
    Download Restriction: no

    References listed on IDEAS

    as
    1. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "To the problem of evaluation of market risk of global equity index portfolio in global capital markets," MPRA Paper 47708, University Library of Munich, Germany, revised 20 Jun 2013.
    2. Thai-Ha LE & Youngho CHANG, 2011. "The Impact of Oil Price Fluctuations on Stock Markets in Developed and Emerging Economies," Economic Growth Centre Working Paper Series 1103, Nanyang Technological University, School of Social Sciences, Economic Growth Centre.
    3. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2012. "On the Risk Management with Application of Econophysics Analysis in Central Banks and Financial Institutions," Papers 1211.4108, arXiv.org.
    4. Park, Jungwook & Ratti, Ronald A., 2008. "Oil price shocks and stock markets in the U.S. and 13 European countries," Energy Economics, Elsevier, vol. 30(5), pages 2587-2608, September.
    5. Pirrong, Craig, 2000. "A Theory of Financial Exchange Organization," Journal of Law and Economics, University of Chicago Press, vol. 43(2), pages 437-471, October.
    6. Goetzmann, William N. & Ibbotson, Roger G. & Peng, Liang, 2001. "A new historical database for the NYSE 1815 to 1925: Performance and predictability," Journal of Financial Markets, Elsevier, vol. 4(1), pages 1-32, January.
    7. Baumol, William J & Benhabib, Jess, 1989. "Chaos: Significance, Mechanism, and Economic Applications," Journal of Economic Perspectives, American Economic Association, vol. 3(1), pages 77-105, Winter.
    8. Viktor O. Ledenyov & Dimitri O. Ledenyov, 2012. "Shaping the international financial system in century of globalization," Papers 1206.2022, arXiv.org.
    9. Barnett, William A. & Gallant, A. Ronald & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1997. "A single-blind controlled competition among tests for nonlinearity and chaos," Journal of Econometrics, Elsevier, vol. 82(1), pages 157-192.
    10. Stuart Hyde, 2007. "The response of industry stock returns to market, exchange rate and interest rate risks," Managerial Finance, Emerald Group Publishing, vol. 33(9), pages 693-709, August.
    11. Barnett, William A. & Serletis, Apostolos, 2000. "Martingales, nonlinearity, and chaos," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 703-724, June.
    12. Sjaastad, Larry A. & Scacciavillani, Fabio, 1996. "The price of gold and the exchange rate," Journal of International Money and Finance, Elsevier, vol. 15(6), pages 879-897, December.
    13. Emmanuel De Veirman, 2009. "What Makes the Output-Inflation Trade-Off Change? The Absence of Accelerating Deflation in Japan," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(6), pages 1117-1140, September.
    14. Basher, Syed A. & Sadorsky, Perry, 2006. "Oil price risk and emerging stock markets," Global Finance Journal, Elsevier, vol. 17(2), pages 224-251, December.
    15. Pierre-Cyrille Hautcoeur & Angelo Riva, 2007. "The Paris financial market in the 19th century: an efficient multi-polar organization?," PSE Working Papers halshs-00587812, HAL.
    16. Paul Alagidede & Theodore Panagiotidis & Xu Zhang, 2011. "Causal relationship between stock prices and exchange rates," The Journal of International Trade & Economic Development, Taylor & Francis Journals, vol. 20(1), pages 67-86.
    17. Le, Thai-Ha & Chang, Youngho, 2011. "Dynamic relationships between the price of oil, gold and financial variables in Japan: a bounds testing approach," MPRA Paper 33030, University Library of Munich, Germany.
    18. Abhyankar, A & Copeland, L S & Wong, W, 1997. "Uncovering Nonlinear Structure in Real-Time Stock-Market Indexes: The S&P 500, the DAX, the Nikkei 225, and the FTSE-100," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 1-14, January.
    19. Jeremy Piger & James Morley & Chang-Jin Kim, 2005. "Nonlinearity and the permanent effects of recessions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(2), pages 291-309.
    20. Georgios Chortareas & George Kapetanios & Merih Uctum, 2003. "A Nonlinear Approach to Public Finance Sustainability in Latin America," Working Papers 486, Queen Mary University of London, School of Economics and Finance.
    21. Marmer, Vadim, 2008. "Nonlinearity, nonstationarity, and spurious forecasts," Journal of Econometrics, Elsevier, vol. 142(1), pages 1-27, January.
    22. Prasad, Anita Mehra & Rajan, Murli, 1995. "The role of exchange and interest risk in equity valuation: A comparative study of international stock markets," Journal of Economics and Business, Elsevier, vol. 47(5), pages 457-472, December.
    23. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2013. "To the problem of turbulence in quantitative easing transmission channels and transactions network channels at quantitative easing policy implementation by central banks," Papers 1305.5656, arXiv.org, revised May 2013.
    24. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2013. "On the accurate characterization of business cycles in nonlinear dynamic financial and economic systems," Papers 1304.4807, arXiv.org.
    25. Mehtap Kesriyeli & Denise R. Osborn & Marianne Sensier, 2004. "Nonlinearity and Structural Change in Interest Rate Reaction Functions for the US, UK and Germany," Working Papers 0414, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
    26. Lutz Kilian & Cheolbeom Park, 2009. "The Impact Of Oil Price Shocks On The U.S. Stock Market," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(4), pages 1267-1287, November.
    27. Hartmann, Daniel & Pierdzioch, Christian, 2006. "Nonlinear Links between Stock Returns and Exchange Rate Movements," MPRA Paper 558, University Library of Munich, Germany.
    28. Apostolos Serletis & Anastasios Malliaris & Melvin Hinich & Periklis Gogas, 2012. "Episodic Nonlinearity in Leading Global Currencies," Open Economies Review, Springer, vol. 23(2), pages 337-357, April.
    29. Pirrong, Craig, 1999. "The organization of financial exchange markets: Theory and evidence," Journal of Financial Markets, Elsevier, vol. 2(4), pages 329-357, November.
    30. Giovannini, Alberto & Jorion, Philippe, 1989. " The Time Variation of Risk and Return in the Foreign Exchange and Stock Markets," Journal of Finance, American Finance Association, vol. 44(2), pages 307-325, June.
    31. Theodore Panagiotidis, 2010. "An Out-of-Sample Test for Nonlinearity in Financial Time Series: An Empirical Application," Computational Economics, Springer;Society for Computational Economics, vol. 36(2), pages 121-132, August.
    32. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    33. Chow, Edward H & Lee, Wayne Y & Solt, Michael E, 1997. "The Exchange-Rate Risk Exposure of Asset Returns," The Journal of Business, University of Chicago Press, vol. 70(1), pages 105-123, January.
    34. Gisser, Micha & Goodwin, Thomas H, 1986. "Crude Oil and the Macroeconomy: Tests of Some Popular Notions: A Note," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 18(1), pages 95-103, February.
    35. Statman, Meir, 1987. "How Many Stocks Make a Diversified Portfolio?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(03), pages 353-363, September.
    36. Jorion, Philippe, 1991. "The Pricing of Exchange Rate Risk in the Stock Market," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 363-376, September.
    37. Hart, Oliver & Moore, John, 1996. "The Governance of Exchanges: Members' Cooperatives versus Outside Ownership," Oxford Review of Economic Policy, Oxford University Press, vol. 12(4), pages 53-69, Winter.
    38. Wymer, Clifford R., 1997. "Structural Nonlinear Continuous-Time Models In Econometrics," Macroeconomic Dynamics, Cambridge University Press, vol. 1(02), pages 518-548, June.
    39. Busch, Thomas & Christensen, Bent Jesper & Nielsen, Morten Ørregaard, 2011. "The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange, stock, and bond markets," Journal of Econometrics, Elsevier, vol. 160(1), pages 48-57, January.
    40. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    41. Neill Fortune, J., 1987. "The inflation rate of the price of gold, expected prices and interest rates," Journal of Macroeconomics, Elsevier, vol. 9(1), pages 71-82.
    42. Andreas Breitenfellner & Jesus Crespo Cuaresma, 2008. "Crude Oil Prices and the USD/EUR Exchange Rate," Monetary Policy & the Economy, Oesterreichische Nationalbank (Austrian Central Bank), issue 4.
    43. Scheinkman, Jose A, 1990. "Nonlinearities in Economic Dynamics," Economic Journal, Royal Economic Society, vol. 100(400), pages 33-48, Supplemen.
    44. Kelsey, David, 1988. "The Economics of Chaos or the Chaos of Economics," Oxford Economic Papers, Oxford University Press, vol. 40(1), pages 1-31, March.
    45. Kolari, James W. & Moorman, Ted C. & Sorescu, Sorin M., 2008. "Foreign exchange risk and the cross-section of stock returns," Journal of International Money and Finance, Elsevier, vol. 27(7), pages 1074-1097, November.
    46. repec:tcd:wpaper:tep4 is not listed on IDEAS
    47. Bailey, Warren & Chung, Y. Peter, 1995. "Exchange Rate Fluctuations, Political Risk, and Stock Returns: Some Evidence from an Emerging Market," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(04), pages 541-561, December.
    48. Lizardo, Radhamés A. & Mollick, André V., 2010. "Oil price fluctuations and U.S. dollar exchange rates," Energy Economics, Elsevier, vol. 32(2), pages 399-408, March.
    49. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2013. "On the optimal allocation of assets in investment portfolio with application of modern portfolio and nonlinear dynamic chaos theories in investment, commercial and central banks," Papers 1301.4881, arXiv.org, revised Feb 2013.
    50. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2012. "On the new central bank strategy toward monetary and financial instabilities management in finances: Econophysical analysis of nonlinear dynamical financial systems," Papers 1211.1897, arXiv.org.
    51. Dimitri O. Ledenyov & Viktor O. Ledenyov, 2013. "On the theory of firm in nonlinear dynamic financial and economic systems," Papers 1302.6721, arXiv.org, revised Mar 2013.
    52. Munro, John H., 2002. "The medieval origins of the 'Financial Revolution': usury, rentes, and negotiablity," MPRA Paper 10925, University Library of Munich, Germany, revised Sep 2002.
    53. Viktor O. Ledenyov & Dimitri O. Ledenyov, 2012. "Designing the new architecture of international financial system in era of great changes by globalization," Papers 1206.2778, arXiv.org.
    54. Jaiswal, A. K. & Niraj, Rakesh, 2007. "Examining the Nonlinear Effects in Satisfaction-Loyalty-Behavioral Intentions Model," IIMA Working Papers WP2007-11-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    55. Richard A. Ajayi & Mbodja Mougouė, 1996. "On The Dynamic Relation Between Stock Prices And Exchange Rates," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 193-207, June.
    56. Pierre-Cyrille Hautcoeur, 2006. "Why and how to measure stock market fluctuations? The early history of stock market indices, with special reference to the French case," Working Papers halshs-00590522, HAL.
    57. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    58. Dahl, Christian M. & Gonzalez-Rivera, Gloria, 2003. "Testing for neglected nonlinearity in regression models based on the theory of random fields," Journal of Econometrics, Elsevier, vol. 114(1), pages 141-164, May.
    59. Derek Bond & Michael J. Harrison & Niall Hession & Edward J. O'Brien, 2006. "Some Empirical Observations on the Forward Exchange Rate Anomaly," Trinity Economics Papers tep2006, Trinity College Dublin, Department of Economics.
    60. Capie, Forrest & Mills, Terence C. & Wood, Geoffrey, 2005. "Gold as a hedge against the dollar," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 15(4), pages 343-352, October.
    61. DeCoster, Gregory P & Mitchell, Douglas W, 1991. "Nonlinear Monetary Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 455-461, October.
    62. Abhyankar, A & Copeland, L S & Wong, W, 1995. "Nonlinear Dynamics in Real-Time Equity Market Indices: Evidence from the United Kingdom," Economic Journal, Royal Economic Society, vol. 105(431), pages 864-880, July.
    63. Stavarek, Daniel, 2004. "Stock Prices and Exchange Rates in the EU and the USA: Evidence of their Mutual Interactions," MPRA Paper 7297, University Library of Munich, Germany.
    64. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    65. Hamilton, James D, 1983. "Oil and the Macroeconomy since World War II," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 228-248, April.
    66. Jun Cai & Yan‐Leung Cheung & Michael C. S. Wong, 2001. "What moves the gold market?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 21(3), pages 257-278, March.
    67. Akihiko Utsugi & Kazusumi Ino & Masaki Oshikawa, 2003. "Random Matrix Theory Analysis of Cross Correlations in Financial Markets," Papers cond-mat/0312643, arXiv.org.
    68. Wanfeng Yan & Ryan Woodard & Didier Sornette, 2014. "Inferring fundamental value and crash nonlinearity from bubble calibration," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1273-1282, July.
    69. David Chappell & Theodore Panagiotidis, 2005. "Using the correlation dimension to detect non-linear dynamics: Evidence from the Athens Stock Exchange," Econometrics 0504005, University Library of Munich, Germany.
    70. Carmine Di Noia, 2001. "Competition and Integration among Stock Exchanges in Europe: Network Effects, Implicit Mergers and Remote Access," European Financial Management, European Financial Management Association, vol. 7(1), pages 39-72.
    71. Agnon, Yehuda & Golan, Amos & Shearer, Matthew, 1999. "Nonparametric, nonlinear, short-term forecasting: theory and evidence for nonlinearities in the commodity markets," Economics Letters, Elsevier, vol. 65(3), pages 293-299, December.
    72. Pierre-Cyrille Hautcoeur, 2006. "Why and how to measure stock market fluctuations? The early history of stock market indices, with special reference to the French case," PSE Working Papers halshs-00590522, HAL.
    73. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
    74. Hui Guo & Kevin L. Kliesen, 2005. "Oil price volatility and U.S. macroeconomic activity," Review, Federal Reserve Bank of St. Louis, issue Nov, pages 669-684.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "On the Stratonovich – Kalman - Bucy filtering algorithm application for accurate characterization of financial time series with use of state-space model by central banks," MPRA Paper 50235, University Library of Munich, Germany.
    2. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.

    More about this item

    Keywords

    stock exchange; stock indexes trends analysis; nonlinear capital flows at stock exchanges; financial securities market; global capital market; share price volatility; foreign exchange rates; interest rates; prices of strategic commodities; return on investments; equity premium; investment portfolio; econophysics; econometrics; integrative thinking.;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:49921. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.