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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.

Christoph Hanck
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r_hudson
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1 Answers1

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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.

Christoph Hanck
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  • 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? – David M. Mar 24 '23 at 13:33
  • 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 $w_t=a_t$. – Christoph Hanck Mar 24 '23 at 14:12