Let Z_t = \mu + \psi (B) a_t where \psi (B) = \Sigma^{\infty}_0 \psi_j B^j , \psi_0 = 1 , \Sigma^{\infty}_0 |\psi_j|<\infty and the a_t are white noise with mean 0 and variance \sigma^2_a.Let \gamma_j be the jth autocovariance of the process Zt.

Prove that \Sigma^{\infty}_{-\infty}|\gamma_j|< \infty

I know that |\gamma_j| = E[(Z_t - \mu)(Z_{t+k} - \mu)] <= \sqrt{Var(Z_t)Var(Z_{t+k})} = \sigma^2_a \Sigma \psi^2_j < \infty

Don't know where to go from there.