For the AR(2) process ????̃???? − 1.0????̃????−1 + 0.5????̃????−2 = ????????:

(a) Calculate ????1.

(b) Using ????0 and ????1 as starting values and the difference equation form for the autocorrelation function, calculate the values of ???????? for ???? = 2, … , 15.

(c) Use the plotted autocorrelation function to estimate the period and damping factor of the autocorrelation function.

(d) Check the values in

(c) by direct calculation using the parameter values and the related roots ????−1 1 and ????−1 2 of ????(????)=1−1.0???? + 0.5????2.