The MA(q)-process where is a white innovation process with unit variance, has covariance function Determine the order of the process, the MA-coefficients, and the spectral density. Let et,t ∈ Z,...

The MA(q)-process

where

is a white innovation process with unit variance, has covariance function

Determine the order of the process, the MA-coefficients, and the spectral density.

Let e_t,t ∈ Z, be independent random variables with expectation m and variance σ₂. Define, for a constant M,

(a) Choose M, such that {Z_t} is an MA(3)-process. Determine the expectation, covariance function, and spectral density of {Z_t}.

(b) Find expectation, covariance function, and spectral density of {X_t}.