The autoregressive process $\phi(B)X_t = Z_t$ is called causal if the autoregressive characteristic function $1 - \phi_1z - \cdot \cdot \cdot - \phi_pz ^ {p}$ has no zeroes inside of the unit circle, and it is called purely non-causal if all the zeros of the characteristic function are inside of the unit circle. The causal autoregressive model depends on past and present values of $Z_t$ and the non-causal autoregressive model depends on future values of $Z_t$.
I tried to simulate non-causal $AR(1)$ and $AR(2)$ and perceived that the plots were completely different from the regular time series plot. How could these models be used for real data? Basically, are these models appropriate to use for such a purpose? This is my first question and I am not sure if I am asking this question correctly, so please let me know if I need to clarify anything. Thanks in advance for any help you can provide.