Simulating a Random Walk

Question

Xn can take values of -1 or 1 each with a probability of 0.5. And Sn= Sn-1 + Xn How can I compute the partial sum observed at time n given by Sn = X1 + X2 + : : : + Xn. I'm trying to simulate a random walk here. I did the following but I'm not exactly sure it's right:

rw <- function(n){
    x=numeric(n)
    xdir=c(TRUE, FALSE)
    step=c(1,-1)
    for (i in 2:n)
    if (sample(xdir,1)) {
        x[i]=x[i-1]+sample(step,1)
    } else {
        x[i]=x[i-1]
    }
    list(x=x)
}

Please Help!

Answer 1

You can also do this really concisely and efficiently with cumsum

set.seed(1)

n <- 1000
x <- cumsum(sample(c(-1, 1), n, TRUE))