The normalized information flow

% [tau21b, tau21l, dH1_noise] = tau_est(xx1, xx2, np)
%
% Estimate tau21, the normalized information transfer from X2 to X1
% dt is taken to be 1.
%
% On input:
% X1, X2: the time series
% 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.
%
% On output:
% tau21b: relative info flow from X2 to X1 (Bai et al., 2017)
% tau21l: relative info flow from X2 to X1 (Liang, 2015)