I want to simulate a time series in R, following an ARMA(1,0) model in the form $Y_t = Y_{t-1} + \epsilon_t$, shocking it at time 20.
In a few words, I therefore have to input $\epsilon_{20} = 30$ (the shock magnitude).
Now, I am using the arima.sim
function as it is the one I'm familiar with for simulating a time series, but I am not sure on how to implement a shock into it.
Let's start with a standard simulation, based on 250 observations:
shocksim <- arima.sim(n=250, list(ar = c(0.5)))
How can I input the shock in such a simulation?
Best Answer
Plotting a trajectory yields
Note your code says you want an AR(1) process with coefficient 0.5 while the text specifies a random walk. I did the former.