TimeSeriesCausality.jl

psi_est(data, seglen ; segshift, eplen, freqlist, method,
        nboot, segave, subave, detrend)

calculates phase slope index (PSI)

Arguments

• data::AbstractArray: NxM array for N data points in M channels
• seglen::Integer: segment length (determines the frequency resolution). If defining freqlist, seglen must be the same as sampling frequency.

optional arguments

• segshift::Integer: number of bins by which neighboring segments are shifted (default is seglen / 2)
• eplen::Integer: length of epochs (default is number of samples)
• freqlist::AbstractArray: a UnitRange or 2D-Array where each column is a frequency band (default is full range). Note that the DC component (0th frequency of FFT) is discarded, and freqlist shall only include integer values.
• method::String: standard deviation estimation method (default is "jackknife")
• subave::Bool: if true, subtract average across Cross Spectra segments (default is false)
• segave::Bool: if true, average across Cross Spectra segments (default is true)
• nboot::Integer: number of bootstrap resampling iterations (default is 100)
• detrend::Bool: if true, performs a 0th-order detrend across raw segments (default is false)
• window::Function: window function with interval length as sole necessary argument (default is Hanning)
• verbose::Bool: if true, warnings and info logs would be echoed. (default is false)

Returns

• psi::AbstractArray: Phase Slope Index with shape (channel, channel, frequency bands)
• psi_std::AbstractArray: PSI estimated standard deviation with shape (channel, channel, frequency bands)

granger_est(data, seglen; order, method, verbose)

Granger's method of causal relation approximation

Arguments

• data::AbstractArray: Nx2 array for N data points in 2 channels.
• seglen::Integer: segment length.

optional arguments

• method::String: standard deviation estimation method (default is "jackknife")
• order::Int: Model order. Assumed time delay order of interest (default is n_samples / 2)
• verbose::Bool: if true, warnings and info logs would be echoed.

Returns

• Grind::Float64: Granger causality index
• Grind_std::Float64: estimated standard deviation of error

Internal variables:

• Covs: Concatenated covariance mats of different orders
• Acoef: Design (A) matrix coefficients
• Perr: Prediction Error
• Σ: Measures the accuracy of the autoregressive prediction

References:

• C. W. J. Granger (1969). Investigating causal relations by econometric models and cross-spectral methods, Econometrica, 37, 424-438.
• M. Ding et al. (2006). Granger Causality: Basic Theory and Application to Neuroscience available online: https://arxiv.org/abs/q-bio/0608035