I am modelling the volatility spillover between SP500 and the USD/CNY from 2008 to 2018 with a DCC-GARCH(1,1) model as follows:
# univariate normal GARCH(1,1) for each series
garch11.spec = ugarchspec(mean.model = list(armaOrder = c(0,0)),
variance.model = list(garchOrder = c(1,1),
model = "sGARCH"),
distribution.model = "norm")
# dcc specification - GARCH(1,1) for conditional correlations
dcc.garch11.spec = dccspec(uspec = multispec( replicate(2, garch11.spec) ),
dccOrder = c(1,1),
distribution = "mvnorm")
dcc.garch11.spec
dcc.fit = dccfit(dcc.garch11.spec, data = SP_FX)
dcc.fit
I obtain the residuals:
resid = residuals(dcc.fit)/sd(residuals(dcc.fit))
And test with Ljung-Box:
> Box.test(resid[,1],lag=1,type="Ljung-Box")
Box-Ljung test
data: resid[, 1]
X-squared = 2469.8, df = 1, p-value < 2.2e-16
> Box.test(resid[,2],lag=1,type="Ljung-Box")
Box-Ljung test
data: resid[, 2]
X-squared = 11.298, df = 1, p-value = 0.000776
These results are not that encouraging, the null hypothesis is rejected in both cases at a 1% significance level. The results of the DCC-GARCH(1,1) are:
Optimal Parameters
-----------------------------------
Estimate Std. Error t value Pr(>|t|)
[usdollar].mu -6.550942 0.008495 -771.16107 0.000000
[usdollar].omega 0.000171 0.000067 2.55112 0.010738
[usdollar].alpha1 0.646702 0.093376 6.92579 0.000000
[usdollar].beta1 0.352295 0.095610 3.68469 0.000229
[sp500].mu -0.000795 0.000144 -5.52138 0.000000
[sp500].omega 0.000002 0.000001 1.74663 0.080702
[sp500].alpha1 0.159949 0.020985 7.62191 0.000000
[sp500].beta1 0.827351 0.020548 40.26497 0.000000
[Joint]dcca1 0.001306 0.001895 0.68899 0.490827
[Joint]dccb1 0.994451 0.002769 359.07387 0.000000
Information Criteria
---------------------
Akaike -5.7121
Bayes -5.6863
Shibata -5.7122
Hannan-Quinn -5.7027
My question consists of two parts.
- If I understand correctly, the Li-Mak test should be used in multivariate cases (see for example: Difference between Ljung Box and McLeod Li Test?).
Is there a function within the
rmgarchpackage in R that could run these tests? - As for the test itself, is it (based on the results at hand now) safe to presume that the DCC model fails at modelling the volatility spillovers?
