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How to interpret white noise test from Stata? Have a white noise means that a variable does not have autocorrelation.

Can I say here that all of my variables has a white noise (does not have autocorrelation)? How can I see it?

 wntestq a

 Portmanteau test for white noise
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  Portmanteau (Q) statistic =    28.0682
  Prob > chi2(40)           =     0.9221

  wntestq b

 Portmanteau test for white noise
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  Portmanteau (Q) statistic =   162.3201
  Prob > chi2(40)           =     0.0000


 wntestq  c

 Portmanteau test for white noise
 ---------------------------------------
  Portmanteau (Q) statistic =   162.6615
  Prob > chi2(40)           =     0.0000


 wntestq  d

 Portmanteau test for white noise
 ---------------------------------------
  Portmanteau (Q) statistic =   192.8795
  Prob > chi2(40)           =     0.0000


 wntestq  e

 Portmanteau test for white noise
 ---------------------------------------
  Portmanteau (Q) statistic =   182.2451
  Prob > chi2(40)           =     0.0000


 wntestq  f

 Portmanteau test for white noise
 ---------------------------------------
  Portmanteau (Q) statistic =   126.0059
  Prob > chi2(40)           =     0.0000
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    $\begingroup$ If a P-value reported as 0.9221 has the same interpretation as one reported as 0.0000, then anything goes. $\endgroup$
    – Nick Cox
    Commented Nov 17, 2014 at 9:40
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    $\begingroup$ Note that a White test is not the same as a white noise test. $\endgroup$
    – Nick Cox
    Commented Nov 17, 2014 at 9:40
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    $\begingroup$ Well documented at stata.com/manuals13/tswntestq.pdf $\endgroup$
    – Nick Cox
    Commented Nov 17, 2014 at 9:43

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In the Portmanteau test, the null hypothesis is that the variable follows a white noise process. And just like in any other statistical inference, a p-value that is smaller than the significance level, α (the probability of rejecting a true null hypothesis, usually set at α=0.05) means that you reject the null and conclude that the variable is not a white noise. On the other hand, if the p-value is larger than α, then you cannot reject the null, implying that the variable is indeed a white noise process. In your case, the results of the test show that the variable a is the only variable that follows a white noise process.

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