340
Table 17.4 Summary statistics for the standardized residualsPanel A: summary statistics for the standardized residuals of France
ε1,t/
√
h11,t ε2,t/
√
h22,tMean −0.0146 0.0101
Variance 0.9866 1.0179
Skewness −0.1160 [0.221] −0.2340 [0.011]
Kurtosis −0.0311 [0.866] 1.3391 [0.000]
Normality 13.4101 [0.001] 59.6086 [0.000]
Q(20) 29.9128 [0.171] 147.223 [0.000]
Q^2 (20) 32.5969 [0.137] 20.8033 [0.408]
A(20) 14.7484 [0.790] 20.5445 [0.424]Panel B: summary statistics for the standardized residuals of Germanyε1,t/√
h11,t ε2,t/√
h22,t
Mean −0.0819 −0.0714
Variance 0.9861 0.9996
Skewness −1.7001 [0.000] −0.3606 [0.000]
Kurtosis 11.3915 [0.000] 1.3637 [0.000]
Normality 4192.75 [0.000] 70.5993 [0.000]
Q(20) 30.3931 [0.263] 105.185 [0.000]
Q^2 (20) 1.5671 [0.999] 13.4789 [0.855]
A(20) 2.2071 [0.999] 15.8992 [0.722]Panel C: summary statistics for the standardized residuals of Great Britainε1,t/
√
h11,t ε2,t/
√
h22,t
Mean −0.0547 0.0490
Variance 0.9709 0.9653
Skewness −0.2925 [0.003] −0.2296 [0.022]
Kurtosis 0.4162 [0.039] 0.6244 [0.002]
Normality 12.7144 [0.001] 14.8173 [0.000]
Q(20) 19.9705 [0.459] 163.784 [0.000]
Q^2 (20) 16.1603 [0.706] 19.4896 [0.490]
A(20) 21.9096 [0.345] 20.0035 [0.457]
Notes: Skewness refers to series skewness coefficient. The asymptotic distribution of the skewness
coefficient under the null hypothesis isN(0, 6/T), whereTis the sample size. The null hypothesis
tested is whether that coefficient is equal to zero. Kurtosis refers to the series kurtosis coefficient. The
null hypothesis tested is whether that coefficient is equal to zero. The asymptotic distribution of the
kurtosis coefficient under the null hypothesis isN(0,24/T), whereTis the sample size. Normality refers
to the Bera-Jarque statistic test. This statistic tests the normality or non-normality of the series. The Bera-
Jarque statistic is calculated as follows,T[S^2 /6+(K−3)^2 /24], whereSis the skewness coefficient andK
is the kurtosis coefficient. Under the null hypothesis of normal distribution, the Bera-Jarque statistic has
an asymptoticχ^2 (2) distribution. Q(20) and Q^2 (20) are Ljung Box tests. The null hypothesis tested is
the no existence of twentieth order serial correlation inε 1 ,t,ε 2 ,tandε^21 ,t,ε^22 ,trespectively. Finally, A(20)
is the Engle (1982) test. The null hypothesis tested is the non-existence of twentieth-order ARCH in
the residuals. Thep-values of these tests are displayed as [.].