LK-Info-Flow 3.0.0

Liang Information Flow Package

Created on Mon Sep 7 16:26:22 2020

@author: Yinengrong @ [e-mail]

Created on Wed Jul 12 10:45:37 2023

@author: Yinen

Rong Yineng ([e-mail]) see https://github.com/YinengRong/LKIF for details and examples

On input: X: matrix storing the M time series (each as Nx1 column vectors) max_lag: time order of lags (default 1) >=1 lag time step -1 Determine the lag order of the data based on the AIC criterion. -2 Determine the lag order of the data based on the BIC criterion. np: integer >=1, time advance in performing Euler forward differencing, e.g., 1, 2. Unless the series are generated with a highly chaotic deterministic system, np=1 should be used. (default 1) dt: frequency of sampling (default 1) series_teporal_order: Nx1 column vector that records the timestamps of each sample, with a minimum sampling interval of dt. This option is used for panel data or datasets with missing measurements.. (default []) significance_test: 1 do the significance test (default) 0 not (to save the computation time) On output: IF: information flow nIF: normalized information flow max_lag: time order of lags (in IF) SEIF: standard error of information flow err_e90/e95/e99: standard error at 90/95/99# significance level p: p-value of information flow

Citations: X.S. Liang, 2016: Information flow and causality as rigorous notions ab initio. Phys. Rev. E, 94, 052201. X.S. Liang, 2014: Unraveling the cause-effect relation between time series. Phys. Rev. E 90, 052150. X.S. Liang, 2015: Normalizing the causality between time series. Phys. Rev. E 92, 022126. X.S. Liang, 2021: Normalized multivariate time series causality analysis and causal graph reconstruction. Entropy. 23. 679. X.S. Liang, Chen, D. K., Zhang, R. H. 2023: Quantitative causality, causality-aided discovery, and causal machine learning. Ocean-Land-Atmos Res.