Multifractal Background Noise of Monofractal Signals

• Authors: D. Grech , G. Pamuła
• Languages of publication: EN

Abstracts

EN

We investigate the presence of multifractal residual background effect for monofractal signals which appears due to the finite length of the signals and (or) due to the constant long memory the signals reveal. This phenomenon is investigated numerically within the multifractal detrended fluctuation analysis (MF-DFA) for artificially generated time series. Next, the analytical formulas enabling to describe the multifractal content in such signals are provided. Final results are shown in the frequently used generalized Hurst exponent h(q) multifractal scenario as a function of time series length L and the autocorrelation scaling exponent value γ. The obtained results may be significant in any practical application of multifractality, including financial data analysis, because the "true" multifractal effect should be clearly separated from the so called "multifractal noise" resulting from the finite data length. Examples from finance in this context are given. The provided formulas may help to decide whether one deals with the signal of real multifractal origin or not and make further step in analysis of the so called spurious or corrupted multifractality discussed in literature.

Keywords

EN

05.45.Tp; 89.75.Da; 05.40.-a; 89.75.-k; 89.65.Gh

Discipline

• 89.75.-k: Complex systems(for complex chemical systems, see 82.40.Qt; for biological complexity, see 87.18.-h)
• 05.45.Tp: Time series analysis
• 89.65.Gh: Economics; econophysics, financial markets, business and management(for economic issues regarding production and use of renewable energy, see 88.05.Lg)
• 89.75.Da: Systems obeying scaling laws
• 05.40.-a: Fluctuation phenomena, random processes, noise, and Brownian motion(for fluctuations in superconductivity, see 74.40.-n; for statistical theory and fluctuations in nuclear reactions, see 24.60.-k; for fluctuations in plasma, see 52.25.Gj; for nonlinear dynamics and chaos, see 05.45.-a)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2012
• Volume: 121
• Issue: 2B
• Pages: B-34-B-39

Dates

published

2012-02

Contributors

author

D. Grech

• Institute of Theoretical Physics, University of Wrocław, PL-50-204 Wrocław, Poland

author

G. Pamuła

• Institute of Theoretical Physics, University of Wrocław, PL-50-204 Wrocław, Poland

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Identifiers

DOI

10.12693/APhysPolA.121.B-34