[R] Box-Ljung p-value -> Test for Independence

Patrick Burns pburns at pburns.seanet.com
Sat Apr 17 15:33:15 CEST 2004

1) A small p-value is evidence that there is dependence.
So you want to see large p-values.  But a large p-value
is not really evidence of independence -- merely a lack
of evidence of dependence.

You might be able to get a hint of the power of your test
(which is what you really care about) from the working
paper about Ljung-Box on the Burns Statistics website.

2) The statistic is really an average of the lags up to the
stated lag.  So if the dependence is all at lag 5, tests with
lags below 5 have no power, the lag 5 test has maximum
power, and the power decreases as the lag of the test
increases above 5.

Patrick Burns

Burns Statistics
patrick at burns-stat.com
+44 (0)20 8525 0696
(home of S Poetry and "A Guide for the Unwilling S User")

Aroon Nataraj wrote:

> Hi all
> I'm using the Box-Ljung test (from within R) to test if a time-series 
> in independently distributed.
> 2 questions:
> 1) p-value returned by Box-Ljung:
> IF I want to test if the time-series is independant at say 0.05 
> sig-level (it means that prob of erroneously accepting that the 
> time-series is independent is 0.05 right?)
> --> then do I consider time-series as "independant" when
>      --> p-value (from Box-Ljung) > 0.05
>      OR
>       --> p-value < 0.05
> Or should i be using (0.95) instead of (0.05) for this case. I'm 
> confused about this (this is a goodness-of-fit test?).
> 2) Box-Ljung takes a lag argument, say lag=k.
>     Does it check "all lags upto k"
>     OR
>     Does it check "only AT k" (i.e acf val is small at only k?)
> thank you in advance. I apologize if the questions are very basic.
> Aroon
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