Consider the stationary ARMA(2,1) process Yt + Yt-1 + 0.6Yt-2 = et - 0.5et-1.
a. Show that its autocorrelation function (acf) satisfies the equation: ' greek letter rho'k + 'greek letter rho'k-1+0.6'greek letter rho'k-2=0, k greater or equel 2
b. Verify that the acf display a damped sine wave behavior. Find the frequence and period of the acf.
c. Given a realization of size 200 from the preceding ARMA(2,1) model, how many "cycles" do you expect to see in the series?Explain your answer.
d. Simulate a realization of size 200 from the preceding ARMA(2,1)model, compare your answer for part c with realization. Does your realization confirm your answer in part c?