[R-SIG-Finance] Rugarch package - Reasoning for the choice of lags in the Ljung-Box and ARCH LM tests

[alexios galanos]

The tests on the (squared) standardized residuals must be adjusted for 
the degrees of freedom: df (which must be >no.lags used in test) which 
is model dependent. For a GARCH(1,1) model this is equal to 2. For 
Weighted Ljung-Box Test and lag=1 the package sets the df=0 (perhaps 
badly), otherwise:

1. For Weighted Ljung-Box : lags = max(2, 2 * df + df - 1) and max(5, 4 
* df + df - 1)

2. For Weighted ARCH LM: lags = df+c(1,3,5)

You are of course free to choose any other lags and run the tests 
separately using the WeightedPortTest package.

Regards,

Alexios

On 6/4/18 2:41 PM, Andreas Bregiannis wrote:
> Dear all,
>
>
> I implemented some AR-t-EGARCH models using the Rugarch package and in the output I also received the results of the two Ljung-Box tests and the ARCH LM test. In the Ljung-Box tests, the chosen lags for testing is Lag[1], Lag[2*(p+q)+(p+q)-1],  Lag[4*(p+q)+(p+q)-1] while for the ARCH LM I think that the chosen lags are Lag[p+q+1], Lag[p+q+3] and Lag[p+q+5] . For those of the ARCH LM test I am not sure that these are the chosen lags because they are not mentioned analytically.
>
> My question is why these specific formulas for the lags are chosen?
>
> I understand that we want to test for the first lag and for further lags. But could you please tell me why e.g. the 4*(p+q)+(p+q)-1 lag or the p+q+5 lag are chosen? So, is there any specific explanation for these choices?
>
> Thank you in advance.
>
> Kind regards,
> Andreas
>
>
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