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5. Consider the following AR(p) process, with wr being iid N(0, 1) random variables: (a) Simulate this process in R using the function arima.sim) for T 500 observations, after burning in for 1000 observations (i.e. create 1500 observations then delete the first 1000) (b) Compute and plot the sample autocorrelation function for the simulated process using acf O. Compare the sample autocorrelation function to the theoretical autocorrelation function, which you can compute and plot using ARMAacf). (c) Why is X a causal process? Since it is, it can be written in the form k -0 Use the R function ARMAtoMA) to compute the first 25 values of the k and plot them