Calculate the lagged mutual information fucntion within (auto-mif) or between (cross-mif) time series, or, conditional on another time series (conditional-cross-mif). Alternatively, calculate the total information of a multivariate dataset for different lags.
A Nx1 matrix for auto-mif, a Nx2 matrix or data frame for cross-mif, a Nx3 matrix or data frame for mif between col 1 and 2 conditional on col 3; or a NxM matrix or data frame for the multi-information function. Mutual information for each lag will be calculated using functions in package infotheo::infotheo() for lags lagged versions of the time series.
The lags to evaluate mutual information.
The number of bins passed to infotheo::discretize() if y is a matrix or ts_discrete()
Produce a plot of the symbolic time series by calling plotRED_mif() (default = FALSE)
If TRUE, a surrogate will be conducted using simple surrogates. The surrogates will be created from the transition probabilities of the discretised time series, i.e. the probability of observing bin j when the current value is in bin j. The number of surrogates needed will be computed based on the value of the alpha parameter, conceived as a one-sided test: mi > 0.
The alpha level for the surrogate test (default = 0.05)
The auto- or cross-mi function
Other Redundancy measures (mutual information):
mi_interlayer(),
mi_mat()
# Lags to evaluate mututal information
lags <- -10:30
# Auto-mutual information
y1 <- sin(seq(0, 100, by = 1/8)*pi)
(mif(data.frame(y1),lags = lags))
#> -10 -9 -8 -7 -6 -5 -4 -3
#> 1.656295 1.929039 1.645481 1.571829 1.567038 1.680948 1.460478 1.497499
#> -2 -1 0 1 2 3 4 5
#> 1.476553 2.868931 2.868931 2.868931 1.476553 1.497499 1.460478 1.680948
#> 6 7 8 9 10 11 12 13
#> 1.567038 1.571829 1.645481 1.929039 1.656295 1.550729 1.924130 1.563809
#> 14 15 16 17 18 19 20 21
#> 1.607910 1.621651 1.560486 1.859941 1.474408 1.626296 1.476240 1.515003
#> 22 23 24 25 26 27 28 29
#> 1.453358 1.745546 1.566279 1.964918 1.604698 1.666703 1.567914 1.564823
#> 30
#> 1.734763
#> attr(,"miType")
#> [1] "I(X;X)"
#> attr(,"lags")
#> [1] -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
#> [20] 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
#> [39] 28 29 30
#> attr(,"nbins")
#> [1] 19
# Cross-mututal information, y2 is a lagged version y1
y2 <- y1[10:801]
y <- data.frame(ts_trimfill(y1, y2, action = "trim.cut"))
(mif(y,lags = lags))
#> -10 -9 -8 -7 -6 -5 -4 -3
#> 1.626296 1.474408 1.859941 1.560486 1.621651 1.607910 1.563809 1.924130
#> -2 -1 0 1 2 3 4 5
#> 1.550729 1.656295 1.656295 1.656295 1.921974 1.687149 1.582642 1.610835
#> 6 7 8 9 10 11 12 13
#> 1.694766 1.457975 1.479514 1.467038 2.868171 1.483081 1.499478 1.474411
#> 14 15 16 17 18 19 20 21
#> 1.605462 1.578502 1.572016 1.660324 1.906882 1.644848 1.561052 1.923715
#> 22 23 24 25 26 27 28 29
#> 1.566571 1.604723 1.613996 1.696857 1.861352 1.475690 1.653503 1.467068
#> 30
#> 1.511635
#> attr(,"miType")
#> [1] "I(X;Y)"
#> attr(,"lags")
#> [1] -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
#> [20] 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
#> [39] 28 29 30
#> attr(,"nbins")
#> [1] 19
# Conditional mutual information, add some noise to y2 and add it as a 3rd column
y$s <- y2+rnorm(NROW(y2))
(mif(y,lags = lags))
#> -10 -9 -8 -7 -6 -5 -4 -3
#> 1.834929 1.736090 1.970503 1.833393 1.955936 1.964817 1.937624 2.039731
#> -2 -1 0 1 2 3 4 5
#> 1.826218 1.881377 1.881377 1.881377 2.003972 1.933971 1.925013 1.982503
#> 6 7 8 9 10 11 12 13
#> 1.972004 1.826775 1.756128 1.733573 2.485812 1.819047 1.866779 1.838623
#> 14 15 16 17 18 19 20 21
#> 1.886196 1.910751 1.887256 1.857787 2.008641 1.966172 1.943974 2.106459
#> 22 23 24 25 26 27 28 29
#> 1.953648 1.914736 1.856459 1.881538 1.949608 1.809318 1.935573 1.857520
#> 30
#> 1.871952
#> attr(,"miType")
#> [1] "I(X;Y|Z)"
#> attr(,"lags")
#> [1] -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
#> [20] 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
#> [39] 28 29 30
#> attr(,"nbins")
#> [1] 19
# Multi-information, the information of the entire multivariate series at each lag
y$y3 <- cumsum(rnorm(NROW(y)))
(mif(y,lags = lags))
#> -10 -9 -8 -7 -6 -5 -4 -3
#> 4.993314 4.988131 4.985059 4.985194 5.130505 5.133889 5.125356 5.120978
#> -2 -1 0 1 2 3 4 5
#> 5.120084 5.119594 5.119594 5.119594 5.120177 5.121040 5.125480 5.130071
#> 6 7 8 9 10 11 12 13
#> 5.131867 4.980106 4.981731 4.988115 4.991903 4.998527 4.996337 5.004096
#> 14 15 16 17 18 19 20 21
#> 5.007288 5.126603 5.125768 5.132465 5.135320 5.139722 5.140392 5.142012
#> 22 23 24 25 26 27 28 29
#> 5.146356 5.147014 5.146989 5.151418 4.997510 4.998788 5.009308 5.015651
#> 30
#> 5.011882
#> attr(,"miType")
#> [1] "I(X;Y;Z;...;N)"
#> attr(,"lags")
#> [1] -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
#> [20] 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
#> [39] 28 29 30
#> attr(,"nbins")
#> [1] 19