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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?

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marked as duplicate by Richard Hardy, Peter Flom Apr 14 at 12:25

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  • $\begingroup$ the proof for what? $\endgroup$ – Lucas Farias Apr 13 at 23:20
  • $\begingroup$ When you compare this formula to asymptotic case where n goes infinity, formula becomes just $n \sum_{n=0}^h p_k^2$. As you can see, for finite sample there are some adjustments. I would like to know how to derive those adjustments? $\endgroup$ – mertcan Apr 14 at 10:00