This is probably a long shot, but I might as well try: does anyone know anything about time series? I would like to show that $\text{AR}(p)$ is a linear filter. Let $\tilde{z}_t = z_t - \mu$, for some constant $\mu$. Then the $\text{AR}(p)$ process is given by
$$\tilde{z}_t = \phi_1 \tilde{z}_{t-1} + \phi_2 \tilde{z}_{t-2}+ \cdots + \phi_p \tilde{z}_{t-p-1} + a_t$$ where $a_t \sim \mathcal{N}(0, \sigma^2_a)$. A linear filter is just a linear combination of the $a_i$ (plus, if applicable, a constant).