Suppose the stochastic process ${X_t}$ satisfies the equation
$$X_t=\phi X_{t-1} + Z_t \tag{A}$$
where $\phi>1$ and $Z_t$ is a white noise. Then iterating forward we get that the only stationary solution of the equation above can be written as:
$$X_t=-\sum_{j=1}^{\infty}Z_{t+j} {\phi}^{-j}$$
Therefore, we can write
$$X_t-\phi^{-1} X_{t-1} = -\sum_{j=1}^{\infty}Z_{t+j} {\phi}^{-j} +\sum_{j=1}^{\infty}Z_{t-1+j} {\phi}^{-j-1}=\phi^{-2}Z_t$$
And thus, defining $\tilde{Z}_t=\phi^{-2}Z_t$, we have that $X_t$ also satisfies the following AR equation:
$$X_t=\phi^{-1}X_{t-1}+\tilde{Z}_t\tag{B}$$
My question is simple. Suppose I have some data on $X_t$ and I run an OLS regression with one lag and no intercept on it. What solution will I estimate, (A) or (B)? Why?