Naslov
Quantifying cross-correlations using local and global detrending approaches

Autori
Podobnik, Boris ; Grosse, Ivo ; Horvatić, Davor ; Ilić, Suzana ; Ivanov, Plamen Ch ; Stanley, H. Eugene

Izvornik
European Physical Journal B (1434-6028) 71 (2009); 243-250

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
time series analysis; fluctuation phenomena; random processes

Sažetak
In order to quantify the long-range cross-correlations between two time series qualitatively, we introduce a new cross-correlations test $Q_{; ; \rm CC}; ; (m)$, where m is the number of degrees of freedom. If there are no cross-correlations between two time series, the cross-correlation test agrees well with the $\chi^2(m)$ distribution. If the cross-correlations test exceeds the critical value of the $\chi^2(m)$ distribution, then we say that the cross-correlations are significant. We show that if a Fourier phase-randomization procedure is carried out on a power-law cross-correlated time series, the cross-correlations test is substantially reduced compared to the case before Fourier phase randomization. We also study the effect of periodic trends on systems with power-law cross-correlations. We find that periodic trends can severely affect the quantitative analysis of long-range correlations, leading to crossovers and other spurious deviations from power laws, implying both local and global detrending approaches should be applied to properly uncover long-range power-law auto-correlations and cross-correlations in the random part of the underlying stochastic process.

Izvorni jezik
Engleski

Znanstvena područja
Fizika

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