Multivariate Ljung-Box tests

[yli725]

Dear Tom,

I use a BEKK model in my research, after estimating, I want to make sure my model was proper specified, so I applied multivariate Ljung-Box tests for both residuals for mean equation and squared residuals for variance equation. My codes are

Code: Select all

dec vect[series] zu(%nvar)
do time=%regstart(),%regend()
   compute %pt(zu,time,%solve(%decomp(hh(time)),rd(time)))
end do time
set z1s = (zu(1))**2
set z2s = (zu(2))**2
set z3s = (zu(3))**2
@mvqstat(lags=6)
# z1s z2s z3s

Since the entire residual vector needs to be standardized, I want to make sure that I make it right.
Also, the user guide says that the results will be different if I choose a different facrorization. I want to know what other facrorizations I can choose.
I appreciate that your kindly help.

[TomDoan]

What you want is to do is @MVARCHTEST applied to the standardized residuals:

Code: Select all

dec vect[series] zu(%nvar)
do time=%regstart(),%regend()
   compute %pt(zu,time,%solve(%decomp(hh(time)),rd(time)))
end do time
@MVARCHTest(lags=6)
# zu

The two (Q test applied to the squares and the ARCH test) will do similar things to the diagonals, but the ARCH test treats the interactions correctly.

[yli725]

What you want is to do is @MVARCHTEST applied to the standardized residuals:

Code: Select all

dec vect[series] zu(%nvar)
do time=%regstart(),%regend()
   compute %pt(zu,time,%solve(%decomp(hh(time)),rd(time)))
end do time
@MVARCHTest(lags=6)
# zu

The two (Q test applied to the squares and the ARCH test) will do similar things to the diagonals, but the ARCH test treats the interactions correctly.

Thank you very much, Tom.
When I appiled @mvarchtest, I noticed the degrees is 864, if my subsample's observation is only 800, does this test still valid?

[TomDoan]

What you want is to do is @MVARCHTEST applied to the standardized residuals:

Code: Select all

dec vect[series] zu(%nvar)
do time=%regstart(),%regend()
   compute %pt(zu,time,%solve(%decomp(hh(time)),rd(time)))
end do time
@MVARCHTest(lags=6)
# zu

The two (Q test applied to the squares and the ARCH test) will do similar things to the diagonals, but the ARCH test treats the interactions correctly.

Thank you very much, Tom.
When I appiled @mvarchtest, I noticed the degrees is 864, if my subsample's observation is only 800, does this test still valid?

LAGS=6 may be a bit much, but it's still OK. It's a multiple regression on cross products of the residuals, so the potential degrees of freedom is 6 (=n(n+1)/2) x 800.

[yli725]

I still confused about how to choose the lag number for both arch test and LB test.
For LB test, I saw most literature choose 6, 12,24 and even 36.
How about the arch test, usually I choose 1 to 3 up to most.
Here is my arch test result:

Code: Select all

@mvarchtest(lags=1)
# zu

Test for Multivariate ARCH
Statistic Degrees Signif
    70.31      36 0.00054


@mvarchtest(lags=2)
# zu

Test for Multivariate ARCH
Statistic Degrees Signif
    90.24      72 0.07181

@mvarchtest(lags=3)
# zu

Test for Multivariate ARCH
Statistic Degrees Signif
   107.60     108 0.49270



When I choose Lags=1, still have arch effect, but choose lags=3, arch effect is no long exist.
Does it mean I much include q=3 in the multivariate garch model to avoid the arch effect?