Could you provide me with the proof of the following:
$$n^{-1/2} \cdot\sum_t a_{t-j}e_t$$ converges to normal distribution as $n$ goes infinity by martingale difference sequence CLT where $a_t = \sum_{j=0}^\infty \psi_je_{t-j}$ with $\sum_{j=0}^\infty |\psi_j|< \infty$ and $e_t$ is i.i.d with $\mathbb{E}(e_t)=0$, $Var(e_t)= \sigma^2$
