Advances in Risk Management

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Table 17.6Continued

ε^2 1,t− 1 I(ε2,t− 1 <0) 0.68327 0.02167 0.30698 0.83677
ε^2 2,t− 1 I(ε1,t− 1 <0) 1.28405 0.01642 1.04079 0.93523
ε^2 2,t− 1 I(ε2,t− 1 <0) 1.29078 0.65406 0.30436 0.98573

Robust Conditional Moment Test in the British Market

Panel (E): applied on original returns

υ12,t=r1,tr2,t−σ 12 υ1,t=r^2 1,t−σ^21 υ2,t=r^2 2,t−σ^22 υbetat=r1,tr2,t/r^2 1,t

−σ 12 /σ^21

I(r1,t− 1 <0) 90.99919∗∗∗ 3.13913∗ 0.31223 274.00000∗∗∗
I(r2,t− 1 <0) 66.41886∗∗∗ 4.32508∗∗ 2.61077 254.99999∗∗∗
I(r1,t− 1 <0;r2,t− 1 <0) 35.15208∗∗∗ 5.16067∗∗ 1.20278 146.00000∗∗∗
I(r1,t− 1 <0;r2,t− 1 >0) 71.82084∗∗∗ 3.13945∗ 1.38575 128.00000∗∗∗
I(r1,t− 1 >0;r2,t− 1 <0) 31.81919∗∗∗ 0.19653 1.61586 109.00000∗∗∗
I(r1,t− 1 >0;r2,t− 1 >0) 156.81439∗∗∗ 24.13232∗∗∗ 10.78132∗∗∗ 208.00000∗∗∗
r^2 1,t− 1 I(r1,t− 1 <0) 0.93860 3.34471∗ 2.58045 56.42158∗∗∗
r^2 1,t− 1 I(r2,t− 1 <0) 0.84860 3.14928∗ 2.82037∗ 49.64218∗∗∗
r^2 2,t− 1 I(r1,t− 1 <0) 4.56553∗∗ 5.69538∗∗ 1.83772 33.92826∗∗∗
r^2 2,t− 1 I(r2,t− 1 <0) 4.89998∗∗ 6.07446∗∗ 2.87220∗ 33.51451∗∗∗

Panel (F): applied on the residuals of the model estimates

υ12,t=ε1,tε2,t−σ12,tυ1,t=ε^2 1,t−σ^2 1,tυ2,t=ε^2 2,t−σ^2 2,tυbetat=ε1,tε2,t/ε^2 1,t

−σ12,t/σ^2 1,t

I(ε1,t− 1 <0) 0.04181 1.49114 0.05898 0.27055
I(ε2,t− 1 <0) 1.87779 0.02587 0.81170 0.75620
I(ε1,t− 1 <0;ε2,t− 1 <0) 0.11286 1.21553 0.32800 1.30884
I(ε1,t− 1 <0;ε2,t− 1 >0) 0.86349 0.32819 0.16350 0.70133
I(ε1,t− 1 >0;ε2,t− 1 <0) 1.93700 1.25880 0.07043 0.02128
I(ε1,t− 1 >0;ε2,t− 1 >0) 1.40476 0.21308 0.39134 0.28494
ε^2 1,t− 1 I(ε1,t− 1 <0) 0.36570 0.00452 0.15896 0.93864
ε^2 1,t− 1 I(ε2,t− 1 <0) 0.60704 0.84934 0.85204 0.92168
ε^2 2,t− 1 I(ε1,t− 1 <0) 0.25875 0.49954 0.16039 0.03524
ε^2 2,t− 1 I(ε2,t− 1 <0) 0.31650 0.00452 0.15896 1.10559

Notes: Panels (A), (C) and (E) give the robust conditional moment test statistic applied on unconditional moment
estimates, whereσ^21 ,σ^22 ,σ 12 and beta coefficient are unconditional estimates of the large stock index variance,
small stock index variance, its covariance and beta, respectively. Panels (B), (D) and (F) give the robust conditional
moment test on the conditional estimates, whereσ^21 ,t,σ^22 ,t,σ 12 ,tand betatcoefficient are conditional estimates of
the large stock index variance, small stock index variance, its covariance and beta, respectively, obtained from the
asymmetric GARCH model. The misspecification indicators are listed in the first column and the remaining columns
in each panel give the test statistic computed for the generalized residual calculated as shown in the first row in
each panel.r 1 ,t− 1 andr 2 ,t− 1 are the return series of the large stock and small stock indexes respectively.ε 1 ,t− 1 is the
return shock to the large index andε 2 ,t− 1 is the return shock to the small index. The indicator functionI() takes the
value one if the expression inside the parentheses is satisfied and zero otherwise. All the statistics are distributed as
χ^2 (1). Test values highlighted with one (∗), two (∗∗) and three (∗∗∗) asterisks are significant at 90%, 95% and 99%,
respectively.