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A model for stock market returns: non-Gaussian fluctuations and financial factors

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Abstract

While there are various theories to account for the large variations in stock prices, some observed statistical aspects require further analysis. A model is proposed for aggregate stock prices, based on observed data, rather than any efficient market hypothesis, and considering jumps in statistical parameters between phases of generally increasing, or generally decreasing, aggregate stock prices. The model relates a critical parameter for short-term behaviour directly to financial factors, especially interest rates, to explain large short-term variations which follow a non-Gaussian distribution. Economic fundamentals may affect changes over longer periods.

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References

  • Andersen TG, Bollerslev T (1998) Answering the sceptics: yes, standard volatility models do provide accurate forecasts. Int Econ Rev 39(4):885–905

    Article  Google Scholar 

  • Baillie RTG, Bollerslev T, Mikkelsen HO (1996) Fractionally integrated generalized autoregressive heteroscedastity. J Econ 74(1):3–30

    Google Scholar 

  • Bollerslev T (1986) Generalized autoregressive conditional heteroskedastity. J Econ 3(3):307–337

    Google Scholar 

  • Bradford de Long J, Schleifer A, Summers LH, Waldmann RJ (1990) Positive feedback investment strategies and destabilizing rational speculation. J Finance 45(2):379–395

    Article  Google Scholar 

  • Cai J (1994) A Markov model of swithing-regime ARCH. J Bus Econ Stat 12(3):309–316

    Article  Google Scholar 

  • Christiansen C (2005) Level-ARCH short-rate models with regime switching: bivariate modeling of US and European short rates, Aarhus School of Business, Department of Accounting, Finance and Logistics, Working paper 05.3

  • Cuthbertson K (1996) Quantitative financial economics: stocks, bonds, and foreign exchange. Wiley, Chichester

    Google Scholar 

  • Eguíluz VM, Zimmermann MG (2000) Transmission of information and herd behavior: an application to financial markets. Phys Rev Lett 25(26):5659–5662

    Article  Google Scholar 

  • Feller W (1966) An introduction to probability theory and its applications, Vol II. Wiley, New York

    Google Scholar 

  • Fernandes M (2006) Financial crashes as endogenous jumps: estimation, testing and forecasting. J Econ Dyn Control 30:111–141

    Google Scholar 

  • Fitzherbert R (2003) The identification and measurement of speculative risk. Institute of Actuaries, Australia (25 August, 2003)

    Google Scholar 

  • Gabaix X, Gopikrishnan P, Plerou V, Stanley HE (2005) Institutional investors and stock market stability, NBER Working Paper No. 11722

  • Gopikrishnan P, Plerou V, Amaral LA Nunes, Meyer M, Stanley HE (1999) Scaling of the distribution of fluctuations of financial market indices. Phys Rev E 60(5):5305–5316

    Article  Google Scholar 

  • Hamilton JD (1994) Time Series Analysis. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Hurst H (1951) Long term storage capacity of reservoirs. Trans Am Soc Civil Eng 116:770–799

    Google Scholar 

  • Islam SMN, Watanapalachaikul S (2005) Empirical finance modelling and analysis of emerging financial and stock markets. Physica-Verlag, Heidelberg

  • Kalimikpalli M, Susmel R (2001) Regime-switching stochastic volatility and short-term interest rates, CEMA Working Paper 192, http://www.cema.edu.ar/publicaciones/download/documentos/197.pdf

  • Kapopoulos P, Siokis G (2005) Stock market crashes and dynamics of aftershocks. Econ Lett 89(1):48–54

    Article  Google Scholar 

  • Kettell B (2001) Financial economics: making sense of information in financial markets. Prentice-Hall, London

    Google Scholar 

  • Kindleberger CP (2000) Manias, panics and crashes: a history of financial crises, 4th edn. Wiley, New York

    Google Scholar 

  • Mandelbrot BB (1963) New methods in statistical economics. J Polit. Econ. 71:421–440

    Article  Google Scholar 

  • Mandelbrot BB, Hudson RL (2004) The (mis)behaviour of markets. Profile Books, London

    Google Scholar 

  • Mills TC (1999) The econometric modelling of financial time series, 2nd edn. Cambridge University Press, Cambridge, UK

    Google Scholar 

  • Mills TC (2004) Exploring the relationship between gold and the dollar. Significance 1(3):113–115

    Article  Google Scholar 

  • Rahman S, Lee C-F, Ang KP (2002) Intraday return volatility prcoess: evidence from NASDAQ stocks. Rev Quant Finance Account 19:155–180

    Article  Google Scholar 

  • Ratti RA, Seo J (2003) Multiple equilibria and currency crisis: evidence for Korea. J Int Money Finance 22:681–696

    Article  Google Scholar 

  • Reed WJ, Hughes BD (2002) From gene families and genera to incomes and internet file sizes: Why power laws are so common in nature. Phys Rev E 66:067103

    Article  Google Scholar 

  • Sampson M (2003) New eras and stock market bubbles. Struct Change Econ Dyn 14:297–315

    Article  Google Scholar 

  • Voit J (2001, 2003) The statistical mechanics of financial markets. Springer, Berlin

  • Wang K-L, Fawson C, Barrett CB (2002) An assessment of empirical model performance when financial market transactions are observed at different data frequencies: an application of East Asian data rates. Rev Quant Finance Account 19:113–129

    Google Scholar 

  • Xu Zhaoxaia, Gençay Ramazan (2003) Scaling, self-similarity ans multifractality in FGX markets. Physica A 323:578–590

    Article  Google Scholar 

  • Zeeman EC (1974) On the unstable behaviour of stock exchanges. Journal of Mathematical Economics 1:39–49

    Article  Google Scholar 

Download references

Acknowledgement

The authors thank a referee for some valuable criticism.

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Correspondence to B. D. Craven.

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Craven, B.D., Islam, S.M.N. A model for stock market returns: non-Gaussian fluctuations and financial factors. Rev Quant Finan Acc 30, 355–370 (2008). https://doi.org/10.1007/s11156-007-0066-3

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