Dynamic Time Warping (DTW) monotonicity constraint - r

Question

How to specify a monotonicity constraint (that one time series should not come before the other) when using dynamic time warping?
For example, I have cost and revenue data; one should impact the other but not vice versa. I am using the basic dtw package but I know that there are many others that could be better. Below is my current alignment.
(I would like to save the corresponding revenue point into a separate column, would that be possible?)
library(dtw)
asy<-dtw(df$cost,
df$revenue,
keep=TRUE,
window.size = 7, # max 7 days shift
step=asymmetric # gives best results for this problem (other: symmetric1 & symmetric2)
);
plot(asy, type="two", off=1);
Thank you for your help!

Answer 1

I think you can enforce this by defining your own window function.
For example, take these series:
library(dtw)
set.seed(310L)
idx <- seq(0, 6.28, len = 100L)
reference <- sin(idx)
query <- cos(idx) + runif(100L) / 10
foo <- dtw(query, reference, keep = TRUE, step.pattern = symmetric2, window.type = sakoeChibaWindow, window.size = 30L)
plot(foo, type = "two", off = 2)
The red line is the reference,
and you want the query's values to only match values from the past or the same day.
win_fun <- function(i, j, ...) { i >= j }
bar <- dtw(query, reference, keep = TRUE, step.pattern = symmetric2, window.type = win_fun)
plot(bar, type = "two", off = 2)
If you want to match past values strictly excluding values from the same time,
change the condition to i > j.
Check the documentation of dtwWindowingFunctions for more options.
You might want to add a window size constraint.