A time series was generated by first drawing the white noise series wt from a normal distribution with mean zero and variance one. The observed series xt was generated from xt = wt − θwt−1, t = 0, ±1, ±2, . . . , where θ is a parameter.

(a) Derive the theoretical mean value and autocovariance functions for the series xt and wt. Are the series xt and wt stationary? Give your reasons.

(b) Give a formula for the power spectrum of xt, expressed in terms of θ and

ω.