The monthly normalized information flow

Estimate tau21, the normalized information transfer from X2 to X1 with monthly data

Estimate tau21, the normalized information transfer from X2 to X1 with monthly data based on Bai et al.(2019)(https://ww2.mathworks.cn/matlabcentral/fileexchange/62471-the-normalized-information-flow).

On input:

X1, X2: the time series

xx1,xx2: the time series of target month

xn1,xn2: the time series of next month (Ye and tozuka)

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.

Slevel: the confidence level of the result.(warning: IF the length of the time series is not sufficient enough to be considered as following normal distribution, please use Bootstrap Test (Liang, 2015))

On output:

tau21b: relative info flow from X2 to X1 (Bai et al., 2017)

tau21l: relative info flow from X2 to X1 (Liang, 2015)

T21: information flow from X2 to X1 without normlization

YesorNot: The result of the significant test