Jess - 1 year ago 132
R Question

# Simulating time series random variable in R?

I have to admit that I'm completely new to R. Thus, my question may be very simple.

For an assignment, I need to simulate a random walk series. The initial position is a fixed point a on the real line. The first step is then taken with length X1 and the current position of the random walk process is changed to S(1)=a+X1. This process continues until n=1000.

After generating the random variable X~N(1,10^2) 1000 times, I need to report the value of S(n) and show the plot of this random walk series. I also need to report the mean and variance of the series.

This is what I have so far:

``````set.seed(1234)
x<-rnorm(1000,mean=1,sd=10)
a<--2
``````

How do I generate an S so that I can have an S(n) for every n up to 1000? (I'm sorry if this is a very rudimentary question.)

Each element of `x` is a step, therefore, the total distance traveled, i.e. the value of S(N) is the sum of the elements. In addition, the distance traveled at each `S(p)` equals the sum of the random walk vector `x` up to index `p`.
Using `plot` and `cumsum` you can generate the graph that shows the function of S(n) over time: