Consider the time series ->
$X(t) = 2 + 3t + Z(t) $
where Z(t) are gaussian white noises from $\mathcal{N}(0,1)$.
- is $X(t)$ stationary - why or why not?
- is $Y(t) = X(t) - X(t-1)$ stationary, why or why not?
- let $V(t)= \frac{1}{2q+1}\sum_{j=-q}^q X(t-j)$.
What is the mean and auto-covariance function of $V(t)$.
My approach is that: I know a stationary process is on in which the statistical properties of a given series is constant, such as constant mean, auto co variance etc. I know that the expected or mean of the noise component is zero. How do i compute the expectation of X(t). How do i show the statastical properties are constant or not constant?