Consider the process given by X t = Z t + θZ t −1Z t −2, where {Z t , t ∈ Z} is a sequence of i.i.d. Gaussian variables with zero mean and variance σ 2. (a) Show that {X t , t ∈ Z} is strict-sense and...

Consider the process given by X_t
= Z_t
+ θZ_t−1Z_t−2, where {Z_t
, t ∈ Z} is a sequence of i.i.d. Gaussian variables with zero mean and variance σ 2.

(a) Show that {X_t
, t ∈ Z} is strict-sense and weak-sense stationary.

(b) Show that {X_t
, t ∈ Z} is a (weak) white-noise.

(c) Compute the bispectrum of {X_t
, t ∈ Z}.