An AR(2) process is described by the difference equation x(n) = 0.81x(n 2) + (n) Where (n) is a white noise process with variance

An AR(2) process is described by the difference equation

x(n) = 0.81x(n – 2) + ω(n)

Where ω(n) is a white noise process with variance σ²_ω.

(a) Determine the parameters of the MA(2), MA(4), and MA(8) models which provide a minimum mean-square error fit to the data x(n).

(b) Plot the true spectrum and those of the MA(q), q = 2, 4, 8, spectra and compare the results. Comment on how well the MA(q) models approximate the AR(2) process.