I have an autocovariance function $\gamma_x(k)$ for a process $x_t$ which is stationary.
Now, I have another process $y_t = x_t - x_{t-1}$. I'd like to express the autocovariance function $\gamma_y(k)$ in terms of $\gamma_x(k)$.
I assume that it'd just be a linear combination like so: $\gamma_y(k) = \gamma_x(k) - \gamma_x(k-1)$ and since x is stationary, these are the same and cancel out, leaving me with $\gamma_y(k) = 0$. Is this the correct approach or am I missing something?
Thank you