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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Physica A: Statistical Mechanics and its Applications, Volume 344, Issues 1–2, 1 December 2004, Pages 284–288
Using a recently developed method of noise level estimation that makes use of properties of the coarse-grained entropy, we have analyzed the noise level for the Dow Jones index and a few stocks from the New York Stock Exchange. We have found that the noise level ranges from 40% to 80% of the signal variance. The condition of a minimal noise level has been applied to construct optimal portfolios from selected shares. We show that the implementation of a corresponding threshold investment strategy leads to positive returns for historical data.
Although it is a common belief that the stock market behaviour is driven by stochastic processes ,  and , it is difficult to separate stochastic and deterministic components of market dynamics. In fact, the deterministic fraction follows usually from nonlinear effects and can possess a non-periodic or even chaotic characteristic  and . The aim of this paper is to study the level of determinism in time series coming from stock market. We will show that our noise level analysis can be useful for portfolio optimization. We employ here a method of noise-level estimation that has been described in details in Ref. . The method is quite universal and it is valid even for high noise levels. It makes use of the functional dependence of coarse-grained correlation entropy K2(ɛ) on the threshold parameter ɛ. Since the function K2(ɛ) depends in a characteristic way on the noise standard deviation σ, thus one can estimate the noise level σ by observing the dependence K2(ɛ). The validity of our method has been verified by applying it for the noise level estimation in several chaotic models  and for the Chua electronic circuit contaminated by noise. The method distinguishes a noise appearing due to the presence of a stochastic process from a non-periodic deterministic behaviour (including the deterministic chaos). Analytic calculations justifying our method have been developed for the Gaussian noise added to the observed deterministic variable. It has been also checked in numerical experiments that the method works properly for a uniform noise distribution and at least for some models with dynamical noise corresponding to the Langevine equation .
نتیجه گیری انگلیسی
This work has been partially supported by the KBN Grant 2 P03B 032 24 (KU) and by a special Grant Dynamics of Complex Systems of the Warsaw University of Technology (JAH).