I have a question about deriving the asymptotic distribution of an explosive AR(1) process:
$$X_t=\rho X_{t-1}+\epsilon_t; X_0=0; \rho\gt1 $$
In particular, I have been given the following identity, but I do not understand how to derive it. Can anyone lend me a helping hand?
$$\sum_{t=1}^{n} X_{t-1}^2=\frac{1}{\rho^2-1} \left\{X_n^2-\sum_{t=1}^{n}\epsilon^2_t-2\rho\sum_{t=1}^{n}X_{t-1}\epsilon_t \right\} $$