Statistical tests for power-law cross-correlated processes (CROSBI ID 190744)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Podobnik, Boris ; Jiang, Z.-Q ; Zhou, Wei-X ; Stanley, Eugene H.
engleski
Statistical tests for power-law cross-correlated processes
For stationary time series, the cross-covariance and the cross-correlation as functions of time lag n serve to quantify the similarity of two time series. The latter measure is also used to assess whether the cross-correlations are statistically significant. For nonstationary time series, the analogous measures are detrended cross-correlations analysis (DCCA) and the recently proposed detrended cross-correlation coefficient, ρDCCA(T, n), where T is the total length of the time series and n the window size. For ρDCCA(T, n), we numerically calculated the Cauchy inequality −1≤ρDCCA(T, n)≤1. Here we derive −1≤ρDCCA(T, n)≤1 for a standard variance-covariance approach and for a detrending approach. For overlapping windows, we find the range of ρDCCA within which the cross-correlations become statistically significant. For overlapping windows we numerically determine—and for nonoverlapping windows we derive—that the standard deviation of ρDCCA(T, n) tends with increasing T to 1/T. Using ρDCCA(T, n) we show that the Chinese financial market's tendency to follow the U.S. market is extremely weak. We also propose an additional statistical test that can be used to quantify the existence of cross-correlations between two power-law correlated time series.
cross-correlations; test
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Podaci o izdanju
84 (1)
2011.
066118-1-066118-7
objavljeno
1539-3755
10.1103/PhysRevE.84.066118