Consider the following AR(2) model: yt=2+0.2yt1+0.4yt2+et where 1=0.2,2=0.4 and etN(0,12). (a) Setting a seed value as the last 3 digits of your student ID number, simulate the above AR(2) data generating process. Set a sample size of T=1000. For example, if your student number is 1234567 , your code should start with: set.seed (567) [2 marks] (b) Using appropriate time series graph(s), explain if the simulated process is stationary. [4 marks] (c)(i) Based on your simulated data, report the sample autocorrelation value at lag 1. [ 1 mark] (c)(ii) Derive the theoretical value of the autocorrelation at lag 1. Show your workings. [4 marks] (d) Apart from being told that the data is being simulated from an AR(2) time series model, what other evidence is there to show that the simulated data is indeed from an AR(2) model? Consider the following AR(2) model: yt=2+0.2yt1+0.4yt2+et where 1=0.2,2=0.4 and etN(0,12). (a) Setting a seed value as the last 3 digits of your student ID number, simulate the above AR(2) data generating process. Set a sample size of T=1000. For example, if your student number is 1234567 , your code should start with: set.seed (567) [2 marks] (b) Using appropriate time series graph(s), explain if the simulated process is stationary. [4 marks] (c)(i) Based on your simulated data, report the sample autocorrelation value at lag 1. [ 1 mark] (c)(ii) Derive the theoretical value of the autocorrelation at lag 1. Show your workings. [4 marks] (d) Apart from being told that the data is being simulated from an AR(2) time series model, what other evidence is there to show that the simulated data is indeed from an AR(2) model