# Interpretation of Ljung-Box tests for GARCH models from the 'rugarch' package in R

I have used the 'rugarch' R package to fit a GARCH model, as:

model.garch = ugarchspec(mean.model=list(armaOrder=c(1,1)),variance.model=list(model = "sGARCH"),distribution.model = "norm")
ugarchfit(model.garch, data=my_data)


However, I am confused about the right interpretation of the Ljung-Box tests associated with my results. Specifically, this is what I have:

Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic   p-value
Lag[1]                       1.304 2.535e-01
Lag[2*(p+q)+(p+q)-1][14]    10.501 3.392e-06
Lag[4*(p+q)+(p+q)-1][24]    17.820 3.235e-02
d.o.f=5
H0 : No serial correlation

Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1]                     0.1355  0.7128
Lag[2*(p+q)+(p+q)-1][5]    0.3466  0.9786
Lag[4*(p+q)+(p+q)-1][9]    0.4837  0.9986
d.o.f=2

Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[3]   0.00900 0.500 2.000  0.9244
ARCH Lag[5]   0.03188 1.440 1.667  0.9974
ARCH Lag[7]   0.14606 2.315 1.543  0.9985


Given that some of the p-values from the "Weighted Ljung-Box Test on Standardized Residuals" are significant (with the exemption of Lag[1]), should I conclude that my GARCH model failed to correct for the temporal auto-correlation in my data?

Perhaps more importantly, how those results influence the overall assessment of the model given that the p-values from the "Weighted Ljung-Box Test on Standardized Squared Residuals" and the "Weighted ARCH LM Tests" are NOT significant? Thank you in advance!

A problem with applying any of these tests to standardized (squared) residuals from a GARCH model is that the test statistics have nonstandard distributions under the null. (They have their standard null distributions when applied to raw data, but not when applied to residuals of a GARCH model.)* As far as I know, this is not accounted for in the rugarch package. Hence, you should take the test results with a grain of salt.