dcca {fractalRegression}

Detrended Cross-Correlation Analysis

Description

Fast function for computing detrended cross-correlation analysis (DCCA) on long time series, which is a bivariate extension of detrended fluctuation analysis (DFA).

Usage

dcca(x, y, order, scales)

Arguments

x

A real valued vector (i.e., time series data) to be analyzed.

y

A real valued vector (i.e., time series data) to be analyzed.

order

is an integer indicating the polynomial order used for detrending the local windows (e.g, 1 = linear, 2 = quadratic, etc.). There is not a pre-determined limit on the order of the polynomial order but the user should avoid using a large polynomial on small windows. This can result in overfitting and non-meaningful estimates.

scales

An integer vector of scales over which to compute correlation. Unlike univariate DFA, MRA does not require that scales be in log units. Scale intervals can be sequential, for example, when the analysis is exploratory and no a priori hypotheses have been made about the scale of correlation. A small subset of targeted scales may also be investigated where scale-specific research questions exist. We have found that windows smaller than say 8 observations create stability problems due to overfitting. This is espcially when the order of the fitting polynomial is large.

Details

Details of the algorithm are specified in Podobnik and Stanley (2008) and in Zebende (2011). In general, the output of the algorithm are estimates of \rhoDCCA, which range from -1 to 1 and can generally be interpreted as follows:

• \rho DCCA = -1.0 -> perfect anti-cross-correlation

• \rho DCCA = 0.0 -> no cross-correlation

• \rho DCCA = 1.0 -> perfect cross-correlation

Value

The object returned from the function is a list including the following:

• scales indicates the values of the scales used for estimates \rhoDCCA

• rho includes the scale-wise estimates of \rhoDCCA

References

Podobnik, B., & Stanley, H. E. (2008). Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series. Physical review letters, 100(8), 084102.

Zebende, G. F. (2011). DCCA cross-correlation coefficient: Quantifying level of cross-correlation. Physica A: Statistical Mechanics and its Applications, 390(4), 614-618.

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Examples

# Here is a simple example for running DCCA using a white noise and pink noise time series.
# For more detailed examples, see the vignette. 

noise <- rnorm(5000)

pink.noise <- fgn_sim(n = 5000, H = 0.9)

scales <- logscale(scale_min = 10, scale_max = 1250, scale_ratio = 1.1)

dcca.out <- dcca(noise, pink.noise, order = 1, scales = scales)