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Scaling in the Norwegian stock market

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  • Skjeltorp, Johannes A

Abstract

The main objective of this paper is to investigate the validity of the much-used assumptions that stock market returns follow a random walk and are normally distributed. For this purpose the concepts of chaos theory and fractals are applied. Two independent models are used to examine price variations in the Norwegian and US stock markets. The first model used is the range over standard deviation or R/S statistic which tests for persistence or antipersistence in the time series. Both the Norwegian and US stock markets show significant persistence caused by long-run “memory” components in the series. In addition, an average non-periodic cycle of four years is found for the US stock market. These results are not consistent with the random walk assumption. The second model investigates the distributional scaling behaviour of the high-frequency price variations in the Norwegian stock market. The results show a remarkable constant scaling behaviour between different time intervals. This means that there is no intrinsic time scale for the dynamics of stock price variations. The relationship can be expressed through a scaling exponent, describing the development of the distributions as the time scale changes. This description may be important when constructing or improving pricing models such that they coincide more closely with the observed market behaviour. The empirical distributions of high-frequency price variations for the Norwegian stock market is then compared to the Lévy stable distribution with the relevant scaling exponent found by using the R/S- and distributional scaling analysis. Good agreement is found between the Lévy profile and the empirical distribution for price variations less than ±6 standard deviations, covering almost three orders of magnitude in the data. For probabilities larger than ±6 standard deviations, there seem to be an exponential fall-off from the Lévy profile in the tails which indicates that the second-moment may be finite.

Suggested Citation

  • Skjeltorp, Johannes A, 2000. "Scaling in the Norwegian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(3), pages 486-528.
  • Handle: RePEc:eee:phsmap:v:283:y:2000:i:3:p:486-528
    DOI: 10.1016/S0378-4371(00)00212-0
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Randi Naes & Johannes A. Skjeltorp, 2003. "Strategic Investor Behaviour and the Volume-Volatility Relation in Equity Markets," Working Paper 2003/9, Norges Bank.
    2. Yuan, Ying & Zhuang, Xin-tian, 2008. "Multifractal description of stock price index fluctuation using a quadratic function fitting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 511-518.
    3. Annibal Figueiredo & Iram Gleria & Raul Matsushita & Sergio Da Silva, 2004. "On the origins of truncated Lévy flights," Finance 0404013, University Library of Munich, Germany.
    4. McCauley, Joseph L. & Bassler, Kevin E. & Gunaratne, Gemunu H., 2008. "Martingales, detrending data, and the efficient market hypothesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 202-216.
    5. Matsushita, Raul & Gleria, Iram & Figueiredo, Annibal & Rathie, Pushpa & Da Silva, Sergio, 2004. "Exponentially damped Lévy flights, multiscaling, and exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 353-369.
    6. Pablo Su'arez-Garc'ia & David G'omez-Ullate, 2012. "Scaling, stability and distribution of the high-frequency returns of the IBEX35 index," Papers 1208.0317, arXiv.org.
    7. Romanovsky, M.Yu. & Vidov, P.V., 2011. "Analytical representation of stock and stock-indexes returns: Non-Gaussian random walks with various jump laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3794-3805.
    8. repec:agr:journl:v:3(612):y:2017:i:3(612):p:71-82 is not listed on IDEAS
    9. Yuan, Ying & Zhuang, Xin-tian & Jin, Xiu, 2009. "Measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(11), pages 2189-2197.
    10. Juan Benjamín Duarte Duarte & Juan Manuel Mascare?nas Pérez-Iñigo, 2014. "Comprobación de la eficiencia débil en los principales mercados financieros latinoamericanos," ESTUDIOS GERENCIALES, UNIVERSIDAD ICESI, November.
    11. Ho, Ding-Shun & Lee, Chung-Kung & Wang, Cheng-Cai & Chuang, Mang, 2004. "Scaling characteristics in the Taiwan stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 448-460.
    12. Bucsa, G. & Jovanovic, F. & Schinckus, C., 2011. "A unified model for price return distributions used in econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3435-3443.
    13. Sergio Da Silva, 2004. "International Finance, Levy Distributions, and the Econophysics of Exchange Rates," International Finance 0405018, University Library of Munich, Germany.
    14. Yuan, Ying & Zhuang, Xin-tian & Liu, Zhi-ying, 2012. "Price–volume multifractal analysis and its application in Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3484-3495.
    15. Yang, ChunXia & Hu, Sen & Xia, BingYing, 2012. "The endogenous dynamics of financial markets: Interaction and information dissemination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3513-3525.
    16. Abounoori, Esmaiel & Shahrazi, Mahdi & Rasekhi, Saeed, 2012. "An investigation of Forex market efficiency based on detrended fluctuation analysis: A case study for Iran," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3170-3179.
    17. McCauley, Joseph L. & Bassler, Kevin E. & Gunaratne, Gemunu H., 2007. "Martingales, Detrending Data, and the Efficient Market Hypothesis," MPRA Paper 2256, University Library of Munich, Germany.
    18. Gu, Rongbao & Xiong, Wei & Li, Xinjie, 2015. "Does the singular value decomposition entropy have predictive power for stock market? — Evidence from the Shenzhen stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 103-113.
    19. Suárez-García, Pablo & Gómez-Ullate, David, 2013. "Scaling, stability and distribution of the high-frequency returns of the Ibex35 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1409-1417.
    20. Zhuang, Xin-tian & Huang, Xiao-yuan & Sha, Yan-li, 2004. "Research on the fractal structure in the Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 293-305.
    21. Goddard, John & Onali, Enrico, 2012. "Self-affinity in financial asset returns," International Review of Financial Analysis, Elsevier, vol. 24(C), pages 1-11.
    22. Juan Benjamín Duarte Duarte & Juan Manuel Mascareñas Pérez-Iñigo, 2014. "¿Han sido los mercados bursátiles eficientes informacionalmente?," REVISTA APUNTES DEL CENES, UNIVERSIDAD PEDAGOGICA Y TECNOLOGICA DE COLOMBIA, June.
    23. Stanley, H.E & Amaral, L.A.N & Gopikrishnan, P & Plerou, V, 2000. "Scale invariance and universality of economic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(1), pages 31-41.
    24. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    25. Du, Guoxiong & Ning, Xuanxi, 2008. "Multifractal properties of Chinese stock market in Shanghai," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 261-269.

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