Summary
Financial time series, in general, exhibit average behaviour at “long” time scales and stochastic behaviour at ‘short” time scales. As in statistical physics, the two have to be modelled using different approaches — deterministic for trends and probabilistic for fluctuations about the trend. In this talk, we will describe a new wavelet based approach to separate the trend from the fluctuations in a time series. A deterministic (non-linear regression) model is then constructed for the trend using genetic algorithm. We thereby obtain an explicit analytic model to describe dynamics of the trend. Further the model is used to make predictions of the trend. We also study statistical and scaling properties of the fluctuations. The fluctuations have non-Gaussian probability distribution function and show multi-scaling behaviour. Thus, our work results in a comprehensive model of trends and fluctuations of a financial time series.
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References
Mandelboot BB (1997) Fractals and Scaling in Finance, Springer-Verlag, New York; Bouchaud JP, Potters M (2000) Theory of Financial Risk, Cambridge University Press, Cambridge; Mantegna RN, Stanley HE (2000) An Introduction to Econophysics, Cambridge University Press, Cambridge
Parikh JC (2003) Stochastic Processes and Financial Markets, Narosa, New Delhi
Manimaran P, Panigrahi PK, Parikh JC (2005) Phys. Rev. E72: 046120-
Daubechies I (1992) Ten Lectures on Wavelets, SIAM, Philadelphia
Kantelhardt JW, Zschiegner SA, Koscielny-Bunde E, Havlin S, Bunde A, Stanley HE (2002) Physica A 316:87
Szpiro GG (1997) Phys. Rev. E 55:2557
Feder J (1998) Fractals, Plenum Press, New York
Abarbanel H, Brown R, Sidorovich J, Tsimring L (1993) Rev. Mod. Phys. 65:1331.
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© 2006 Springer-Verlag Italia
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Manimaran, P., Parikh, J.C., Panigrahi, P.K., Basu, S., Kishtawal, C.M., Porecha, M.B. (2006). Modelling Financial Time Series. In: Chatterjee, A., Chakrabarti, B.K. (eds) Econophysics of Stock and other Markets. New Economic Windows. Springer, Milano. https://doi.org/10.1007/978-88-470-0502-0_19
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DOI: https://doi.org/10.1007/978-88-470-0502-0_19
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-0501-3
Online ISBN: 978-88-470-0502-0
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