A Ljung-Box Test in finite sample Proof

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Hi everyone, initially I have seen that in order to analyze residuals for finite sample, Ljung - Box is defined as $$n*(n+2)*\sum_{n=0}^h p_k^2/(n-k)$$ where n is the sample size, $$p_k$$ is the sample autocorrelation at lag k, and h is the number of lags being tested. Actually I know the proof of formula when sample size goes infinity but in finite sample case there is a little adjustment. Also no sufficient information exist for that adjustment. Could you provide me with the proof?

Regards;
 

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