Statistical test for ΔρDCCA : Methods and data.

In this paper the algorithm for ΔρDCCA statistical test (Guedes et al., 2018) [1] is presented. Our test begins with the simulation of four time series pairs, by an ARFIMA process. These time series has N=250 , 500, 1000, and 2000 points, see Guedes et al. (2018) [1]. The probability distribution function (PDF) is made available for all 10,000 samples, that start from the original time series, in supplementary material.

Specifications Table

Value of the data

A robust test to analysis cross-correlation is important.

However, for , there is not a statistical test.

Here, we presented the algorithm to test the significance of .

Finally, the probability distribution function (PDF) for this test is found, as a supplementary material (Deltarhodata.zip), and this PDF allows that other researchers extend yours analyses.

Data

The test starts with four time series pairs with , , , and points, produced by an autoregressive integrated moving average process (ARFIMA) [2], [3], see Fig. 1. These time series initially are useful in modeling time series with long memory, and are found in the supplementary material as ASCII file: {(af2501.txt; af2502.txt), (af5001.txt;af5002.txt), (af10001.txt;af10002.txt), (af20001.txt;af20002.txt)}. After this time series simulation the algorithm for statistical test is presented below in the Section 4.

Fig. 1

Original time series (pairs) produced by an ARFIMA process, with: (a) , (b) , (c) , and (d) .

Experimental design, materials, and methods

Initially, in the sense to verify the cross-correlation between these original time series (raw data), we applied the Detrended cross-correlation coefficient, [4], see Fig. 2.

Fig. 2

as a function of n.

Thereafter, from the original signal we:

Split these time series into two (before/after) and we shuffle randomly these pairs (see Fig. 3);

Fig. 3

The algorithm procedure.

Estimate (each part) and their difference [1];

Repeat this procedure many (10,000) times from Step (a);

And, finally obtain the PDF function of .

See the supplementary material (Deltarhodata.zip).

Subject area	Physics and Astronomy
More specific subject area	General physics and methods
Method name	Δρ_DCCA Statistical test
Reference of the original paper	〈https://doi.org/10.1016/j.physa.2018.02.148〉
Type of data	Zip File (Deltarhodata.zip)
Data format	ASCII (Raw and analyzed)
Data Accessibility	Data are accessible within the article