# Martingale Difference Sequence CLT

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 $$\mathbb{E}(e_t)=0$$, $$Var(e_t)= \sigma^2$$

• It might be worth providing the index of the first summation (t or j?) in order to make the question clearer. – boomkin Jul 3 at 15:58
• I have edited as you wish. To be honest whatever I have asked so far here I can not get sufficient response. Please spare your time towards the aim of forum.@Richard Hardy, always will be waiting for your valuable return. – mertcan Jul 3 at 17:36
• Please could you help me about my question? mybe @Richard Hardy? – mertcan Jul 4 at 12:21