# A Plot of 250 Random Walks

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For some reason I feel like plotting some random walks. Nothing groundbreaking, but hopefully this post will be useful to someone. Here’s my R code:**mickeymousemodels**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

# Generate k random walks across time {0, 1, ... , T} T <- 100 k <- 250 initial.value <- 10 GetRandomWalk <- function() { # Add a standard normal at each step initial.value + c(0, cumsum(rnorm(T))) } # Matrix of random walks values <- replicate(k, GetRandomWalk()) # Create an empty plot dev.new(height=8, width=12) plot(0:T, rep(NA, T + 1), main=sprintf("%s Random Walks", k), xlab="time", ylab="value", ylim=10 + 4.5 * c(-1, 1) * sqrt(T)) mtext(sprintf("%s%s} with initial value of %s", "Across time {0, 1, ... , ", T, initial.value)) for (i in 1:k) { lines(0:T, values[ , i], lwd=0.25) } for (sign in c(-1, 1)) { curve(initial.value + sign * 1.96 * sqrt(x), from=0, to=T, n=2*T, col="darkred", lty=2, lwd=1.5, add=TRUE) } legend("topright", "1.96 * sqrt(t)", bty="n", lwd=1.5, lty=2, col="darkred") savePlot("random_walks.png")

Just to be clear, these are one-dimensional random walks, in discreet time, and all I'm doing is taking cumulative sums of standard normals. The goal is to end up with a nice plot:

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