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

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  • $\begingroup$ It might be worth providing the index of the first summation (t or j?) in order to make the question clearer. $\endgroup$ – boomkin Jul 3 at 15:58
  • $\begingroup$ 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. $\endgroup$ – mertcan Jul 3 at 17:36
  • $\begingroup$ Please could you help me about my question? mybe @Richard Hardy? $\endgroup$ – mertcan Jul 4 at 12:21

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