In the example, the residuals subtract a walk from a random walk. This could be used for evaluating a model to find the reference pattern.

random_walks.jl

using Plots

walk(n_steps; start=0.0, step_std=1.0) = cumsum([start; randn(n_steps) .* step_std])
residual(y) = walk(length(y) - 1) .- y
residuals(y, n) = [residual(y) for _ in 1:n]

#Example
reference = walk(100)
plot(reference, linewidth=4, label="Reference")
plot!(residuals(reference, 10), alpha=0.7, label=false)