[R] question about the results given by the Box.test?

[Patrick Burns]

Hopefully the test is the same no matter what software
you are using.  A small p-value is an indication that there
is structure in the data.  So in your case there is no
indication of autocorrelation up to lag 5, but it appears
that there might be something going on at around lags 6
to 9.

"How small is too small?" is not a reasonable question
to ask in general.  It depends on how likely it is that
there is structure near that lag, how much data you have,
how important it is to capture all of the structure in your
model versus the harm of overfitting, ...

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

oliver wee wrote:

>Hello, I am using the Ljung Box test in R to compute
>if the resiudals of my fitted model is random or not.
>
>I am not sure though what the results mean, I have
>looked at various sources on the internet and have
>come up with contrasting explanations (mainly because
>these info deal with different program languages, like
>SAS, SPSS, etc).
>
>I know that my residuals should appropriate white
>noise( is random) since a check of its ACF shows it to
>be so (signifant correlation only at lag 1, decays
>very quickly to zero).
>
>But I am not sure how to interpret the ljung-box
>result given by R.
>
>To check for randomness of residuals, should the
>p-value be small or large? How small and how large?
>And at what lags should I check for the randomness of
>the residuals? Is a p-value > 0.05 (or < 0.05) enough?
>What if I have a very large p-value of 0.9796 at lag
>1, but its value is 0.0139 at lag 8? 
>
>For example, here's what I got for the first 10 lags
>of the residuals I'm testing:
>-------------------
> Box.test(SP500DataSetFitMA2$residuals, type =
>"Ljung", lag =1)
>
>        Box-Ljung test
>
>data:  SP500DataSetFitMA2$residuals 
>X-squared = 7e-04, df = 1, p-value = 0.9796
>
>  
>
>>Box.test(SP500DataSetFitMA2$residuals, type =
>>    
>>
>"Ljung", lag =2)
>
>        Box-Ljung test
>
>data:  SP500DataSetFitMA2$residuals 
>X-squared = 0.1088, df = 2, p-value = 0.947
>
>  
>
>>Box.test(SP500DataSetFitMA2$residuals, type =
>>    
>>
>"Ljung", lag =3)
>
>        Box-Ljung test
>
>data:  SP500DataSetFitMA2$residuals 
>X-squared = 1.4179, df = 3, p-value = 0.7014
>
>  
>
>>Box.test(SP500DataSetFitMA2$residuals, type =
>>    
>>
>"Ljung", lag =4)
>
>        Box-Ljung test
>
>data:  SP500DataSetFitMA2$residuals 
>X-squared = 3.866, df = 4, p-value = 0.4244
>
>  
>
>>Box.test(SP500DataSetFitMA2$residuals, type =
>>    
>>
>"Ljung", lag =5)
>
>        Box-Ljung test
>
>data:  SP500DataSetFitMA2$residuals 
>X-squared = 6.0251, df = 5, p-value = 0.3038
>
>  
>
>>Box.test(SP500DataSetFitMA2$residuals, type =
>>    
>>
>"Ljung", lag =6)
>
>        Box-Ljung test
>
>data:  SP500DataSetFitMA2$residuals 
>X-squared = 12.11, df = 6, p-value = 0.05956
>
>  
>
>>Box.test(SP500DataSetFitMA2$residuals, type =
>>    
>>
>"Ljung", lag =7)
>
>        Box-Ljung test
>
>data:  SP500DataSetFitMA2$residuals 
>X-squared = 13.0307, df = 7, p-value = 0.07137
>
>  
>
>>Box.test(SP500DataSetFitMA2$residuals, type =
>>    
>>
>"Ljung", lag =8)
>
>        Box-Ljung test
>
>data:  SP500DataSetFitMA2$residuals 
>X-squared = 19.1766, df = 8, p-value = 0.01394
>
>  
>
>>Box.test(SP500DataSetFitMA2$residuals, type =
>>    
>>
>"Ljung", lag =9)
>
>        Box-Ljung test
>
>data:  SP500DataSetFitMA2$residuals 
>X-squared = 19.6753, df = 9, p-value = 0.02003
>
>  
>
>>Box.test(SP500DataSetFitMA2$residuals, type =
>>    
>>
>"Ljung", lag =10)
>
>        Box-Ljung test
>
>data:  SP500DataSetFitMA2$residuals 
>X-squared = 19.7124, df = 10, p-value = 0.03209
>
>--------------
>
>I know this is not really a programming question, so I
>apologize if it is inappropriate or if the question is
>too elementary.
>
>Thank you very much for your help.
>
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>
>
>
>  
>