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I know we use Ljung-Box test to determine if the residuals are white noise or not. Can we use same test to determine if the time-series in itself is white - noise? This is to by-pass acf-pacf plotting, as I need to forecast some hundred's of series.

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Yes, absolutely. In fact, this is the case for which the Box-Pierce test, and its later refinement, the Ljung-Box test were designed.

The application of the test to residuals - which, from a subject matter point of view, is often the more interesting hypothesis to test as there are not many time series which might conceivably be white noise - in turn is fraught with certain difficulties, which are described for example here.

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  • $\begingroup$ The Ljung-Box paper appears to mention the residuals, not the time series itself. Could you please point to a reference which describes how the test applies to a time series? $\endgroup$
    – David M.
    Mar 24, 2023 at 13:33
  • $\begingroup$ I think the paper spells it out - consider how they distinguish between $r_k$ and $\hat r_k$ and note that for the WN null, $\phi(B)=\theta(B)=1$, so that $w_t=a_t$. $\endgroup$ Mar 24, 2023 at 14:12

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