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.
Arguments
- y
A
Nx1matrix for auto-mif, aNx2matrix or data frame for cross-mif, aNx3matrix or data frame for mif between col 1 and 2 conditional on col 3; or aNxMmatrix or data frame for the multi-information function. Mutual information for each lag will be calculated using functions in packageinfotheo::infotheo()forlagslagged versions of the time series.- lags
The lags to evaluate mutual information.
- nbins
The number of bins passed to
infotheo::discretize()if y is a matrix orts_discrete()- doPlot
Produce a plot of the symbolic time series by calling
plotRED_mif()(default =FALSE)- surTest
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 binjwhen the current value is in binj. The number of surrogates needed will be computed based on the value of thealphaparameter, conceived as a one-sided test:mi > 0.- alpha
The alpha level for the surrogate test (default =
0.05)
See also
Other Redundancy measures (mutual information):
mi_interlayer(),
mi_mat()
Examples
# 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$s <- y2+rnorm(NROW(y2))
(mif(y,lags = lags))
#> -10 -9 -8 -7 -6 -5 -4 -3
#> 1.856324 1.760333 1.972326 1.894520 2.037140 2.018302 1.954398 2.060624
#> -2 -1 0 1 2 3 4 5
#> 1.906130 1.928654 1.928654 1.928654 2.038830 2.000205 2.000832 2.005716
#> 6 7 8 9 10 11 12 13
#> 2.048216 1.819364 1.788236 1.757781 2.533057 1.860127 1.881443 1.885172
#> 14 15 16 17 18 19 20 21
#> 1.917186 1.949878 1.866049 1.886839 2.044955 2.026359 1.994301 2.138082
#> 22 23 24 25 26 27 28 29
#> 1.997720 1.975022 1.898101 1.912561 2.014143 1.856500 2.003992 1.897845
#> 30
#> 1.886449
#> attr(,"miType")
#> [1] "I(X;Y|Z)"
#> attr(,"lags")
#> [1] -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
#> [20] 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
#> [39] 28 29 30
#> attr(,"nbins")
#> [1] 19
# Multi-information, the information of the entire multivariate series at each lag
y$y3 <- cumsum(rnorm(NROW(y)))
(mif(y,lags = lags))
#> -10 -9 -8 -7 -6 -5 -4 -3
#> 4.999962 4.993003 4.995222 4.995344 5.147024 5.141590 5.140739 5.136341
#> -2 -1 0 1 2 3 4 5
#> 5.137842 5.135579 5.135579 5.135579 5.136183 5.136404 5.140863 5.143714
#> 6 7 8 9 10 11 12 13
#> 5.149050 4.999075 4.997191 4.992986 5.002092 5.001638 5.010102 5.010770
#> 14 15 16 17 18 19 20 21
#> 5.011519 5.146876 5.141826 5.146757 5.152094 5.152936 5.155416 5.158851
#> 22 23 24 25 26 27 28 29
#> 5.163217 5.165698 5.167500 5.166540 5.012652 5.010329 5.015428 5.019965
#> 30
#> 5.027103
#> 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