Assuming that the time series follows the models shown below and that vn follows a white noise with mean 0 and variance σ 2 , obtain the autocovariance function Ck . (1) AR model of order 1: yn =...

Assuming that the time series follows the models shown below and that vn follows a white noise with mean 0 and variance σ 2 , obtain the autocovariance function Ck .

(1) AR model of order 1: yn = −0.9yn−1 +vn.

(2) AR model of order 2: yn = 1.2yn−1 −0.6yn−2 +vn.

(3) MA model of order 1: yn = vn −bvn−1

(4) ARMA model of order (1,1): yn = ayn−1 +vn −bvn−1.