Portmanteau test results R When reading a VAR model tutorial I was confused by the below excerpt on the Portmanteau test for autocorrelation.
My questions are:
1) How does one interpret the results of the below demonstration?
2) How does the author come to the conclusion that the VAR(3) model is more suitable, and based on what criteria?
3) Assuming (I don't know if it is the right assumption) that autocorrelation is a desired trait in terms of VAR($p$) predictions, why does the author move on to VAR(3) after rejecting the null hypothesis for VAR(1)?
> #vector autoregression with lag1
> var = VAR(climate2.ts, p=1)

#It is important now to test for serial autocorrelation in the model      
#residuals and below is for the Portmanteau test (several options in the vars 
#package are available).

> serial.test(var, lags.pt=10, type=”PT.asymptotic”)

Portmanteau Test (asymptotic)

data:  Residuals of VAR object var
Chi-squared = 55.4989, df = 36, p-value = 0.01996

#The null hypothesis is no serial correlation, so we can reject it with extreme 
#prejudice…on to var3
> var3 = VAR(climate2.ts, p=3)
> serial.test(var3, lags.pt=10, type=”PT.asymptotic”)

Portmanteau Test (asymptotic)
data:  Residuals of VAR object var3
Chi-squared = 36.1256, df = 28, p-value = 0.1394

#That is more like it.  
#You can review the details of the var model, in this case temperature, if you so choose:
> summary(var3, equation=”d.temp”)

 A: Let me use the term "autocorrelation" as a synonym for "serial correlation".

1) How does one interpret the results of the below demonstration?

Most of the interpretation is already in the comments to the code. First, a VAR(1) model is estimated. It is tested for autocorrelation in errors using a portmanteau test. The null hypothesis of no autocorrelation is rejected since the $p$-value of 0.01996 is lower than the significance level of 0.05. Since autocorrelation is an undesirable feature of the model, the author moves on to look for another model that does not have autocorrelation. He/She estimates a VAR(3) model, tests for autocorrelation, and finds that the null of no autocorrelation cannot be rejected because the $p$-value of 0.1394 is greater than the significance level of 0.05. Since there is not enough evidence of presence of autocorrelation, the author is satisfied and sticks to the VAR(3) model.

2) How does the author come to the conclusion that the VAR3 model is more suitable, and based on what criteria?

Lack of autocorrelation makes VAR(3) more suitable than VAR(1); see also my answer to question (1).

3) Assuming (I don't know if it the right assumption) that serial autocorrelation is a desired trait in terms of VAR(p) predictions, why does the author move on to var3 after rejecting the null hypothesis for var?

Autocorrelation is not a desired trait. It biases the estimators and makes them less efficient. Meanwhile, the estimators do have their nice properties (unbiasedness, efficiency) when there is no autocorrelation (assuming the other standard assumptions are satisfied, too).
