Witold Orzeszko
ARTICLE

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ABSTRACT

A presence of a noise is typical for real-world data. In order to avoid its negative impact on methods of time series analysis, noise reduction procedures may be used. The achieved results of an application of such procedures in identification of chaos or nonlinearity seem to be encouraging. One of the noise reduction methods is the Schreiber method, which, as it has been shown, is able to effectively reduce a noise added to time series generated by deterministic systems with chaotic dynamics. However, while analyzing real-world data, a researcher usually cannot be sure if the generating system is deterministic. Therefore, there is a risk that a noise reduction method will be applied to random data. In this paper, it has been shown that in situations where there in no clear evidence that investigated data are generated by a deterministic system, the Schreiber noise reduction method may negatively affect identification of time series. In the simulation carried out in this paper, the BDS test, the mutual information measure and the Pearson autocorrelation coefficient were used. The research has shown that an application of the Schreiber method may introduce spurious nonlinear dependencies to investigated data. As a result, random series may be misidentified as nonlinear.

KEYWORDS

nonlinear time series, noise reduction, Schreiber method, NRL quantity, BDS test, mutual information, bootstrap

REFERENCES

[1] Brock W.A., Dechert W.D., Scheinkman J.A. [1987], A test for independence based on the correlation dimension, SSRI Working Paper no. 8702, Department of Economics, University of Wisconsin, Madison.

[2] Brock W.A., Hsieh D.A., LeBaron B. [1991], Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence, The MIT Press, Cambridge, Massachusetts, London.

[3] Castagli M., Eubank S., Farmer J.D., Gibson J. [1991], State space reconstruction in the presence of noise, Physica D, 51, 52-98.

[4] Dionisio A., Menezes R., Mendes D.A. [2003], Mutual Information: a dependence measure for nonlinear time series, working paper.

[5] Fraser A.M., Swinney H.L. [1986], Independent coordinates for strange attractors from mutual information, Physical Review A, 33.2, 1134-1140.

[6] Granger C. W. J., Terasvirta T. [1993], Modelling nonlinear economic relationship, Oxford University Press.

[7] Granger C. W. J., Lin J-L. [1994], Using the mutual information coefficient to identify lags in nonlinear models, Journal of Time Series Analysis, 15, 371-384.

[8] Harrison R.G., Yua D., Oxleyb L., Lua W., Georgec D. [1999], Non-linear noise reduction and detecting chaos: some evidence from the S&P Composite Price Index, Mathematics and Computers in Simulation, 48, 497-502.

[9] Hassani H., Dionisio A., Ghodsi M. [2009a], The effect of noise reduction in measuring the linear and nonlinear dependency of financial markets, Nonlinear Analysis: Real World Applications, doi:10.1016/j.nonrwa.2009.01.004.

[10] Hassani H., Zokaeib M., Rosenc D., Amiric S., Ghodsi M. [2009b], Does noise reduction matter for curve fitting in growth curve models?, Computer methods and programs in biomedicine, 96, 173-181.

[11] Kantz H., Schreiber T., Hoffman I. [1993], Nonlinear noise reduction: A case study on experimental data, Physical Review E, 48.2, 1529-1538.

[12] Kantz H., Schreiber T. [1997], Nonlinear time series analysis, Cambridge University Press

[13] Kanzler L. [1999], Very Fast and Correctly Sized Estimation of the BDS Statistic, Department of Economics, Oxford University.

[14] Leontitsis A., Bountis T., Pagge J. [2004], An adaptive way for improving noise reduction using local geometric projection, Chaos 14, 106-110.

[15] Liang H., Lin Z., Yin F., [2005], Removal of ECG contamination from diaphragmatic EMG by nonlinear filtering, Nonlinear Analysis, 63, 745-753.

[16] Maasoumi E., Racine J. [2002], Entropy and predictability of stock market returns, Journal of Econometrics, 107, 291-312.

[17] Mees A. I., Judd K. [1993], Dangers of geometric filtering, Physica D, 68, 427-436.

[18] Orzeszko W. [2008], The New Method of Measuring the Effects of Noise Reduction in Chaotic Data, Chaos Solitons and Fractals, 38, 1355-1368.

[19] Perc M., [2005], Nonlinear time series analysis of the human electrocardiogram, European Journal of Physics, 26, 757-768.

[20] Schreiber T. [1993], Extremely simple nonlinear noise-reduction method, Physical Review E, 47.4, 2401-2404.

[21] Schreiber T. [1999], Interdisciplinary application of nonlinear time series methods, Physics Reports, 308, 1-64.

[22] Shintani M., Linton O. [2001], Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors, working paper, Vanderbilt University Nashville.

[23] Sivakumar B., Phoon K.-K., Liong S.-Y., Liaw C.-Y. [1999], A systematic approach to noise reduction in chaotic hydrological time series, Journal of Hydrology, 219, 103-135.

[24] Takens F. [1981], Detecting Strange Attractors in Turbulence, in: Dynamical Systems and Turbulence, Rand D., Young L., eds., Springer-Verlag, 366-381.

[25] Zeng X., Pielke R.A., Eykholt R. [1992], Extracting Lyapunov exponents from short time series of low precision, Modern Physics Letters B, 6, 55-75.

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