# What number of lags for multivariate Portmanteau, Breusch-Godfrey, and Ljung-Box tests?

There are 3 types of tests for the residual autocorrelations here (I have a relatively small sample(58 obs):

# Asymptotic  Portmanteau test  for serially correlated errors
# Portmanteau Test (adjusted) for small samples

serial.test(var1, lags.pt = 16, type = "PT.adjusted")#serial correlation
serial.test(var2, lags.pt = 16, type = "PT.adjusted")#no serial correlation on 10%
serial.test(var3, lags.pt = 16, type = "PT.adjusted")#serial correlation
serial.test(var4, lags.pt = 16, type = "PT.adjusted")#serial correlation

# Breusch-Godfrey LM test for small samples (Edgerton-Shukur F test)
serial.test(var1, lags.bg = 5, type = "ES")# no serial correlation
serial.test(var2, lags.bg = 5, type = "ES")# no serial correlation
serial.test(var3, lags.bg = 5, type = "ES")# no serial correlation
serial.test(var4, lags.bg = 5, type = "ES")# no serial correlation

##Test for Autocorrelations
#H0=No autocorrelation
Box.test(resid1[,1],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid1[,2],lag=3,type="Ljung-Box")# Autocorrelation on 5%
Box.test(resid1[,3],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid1[,4],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid1[,5],lag=3,type="Ljung-Box")# Autocorrelation on 5%

Box.test(resid2[,1],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid2[,2],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid2[,3],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid2[,4],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid2[,5],lag=3,type="Ljung-Box")# No Autocorrelation

Box.test(resid3[,1],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid3[,2],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid3[,3],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid3[,4],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid3[,5],lag=3,type="Ljung-Box")# No Autocorrelation

Box.test(resid4[,1],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid4[,2],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid4[,3],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid4[,4],lag=3,type="Ljung-Box")# No Autocorrelation
Box.test(resid4[,5],lag=3,type="Ljung-Box")# No Autocorrelation


How do I know that I can rely on the results based on this lag (h=3)? Do I need to specify fitdf and how? Can I leave the default lags.pt = 16 and lags.bg = 5? Given that the selection criteria show:

VARselect(DATA[5:58,], lag.max = 4, type = "none")

AIC(n)  HQ(n)  SC(n) FPE(n)
4      1      1      2  ,


do I have enough justification that the VAR(2) model is the best fit based on the tests results above (besides the normality tests favor VAR(2) as well)?

How do I know if to include a const or not (in this case not included type = "none")

Many thanks in advance for help and I would be really grateful if some references are available.