HELENA CHULIÁ AND HIPÒLIT TORRÓ 339Table 17.3Continued
Estimates of the conditional CAPM ADC-in-mean model in the British market
Panel (E): model estimatesY=2.75
(0.00)C=
0.0048
(0.88)
0.0016
(0.00)
−0.0002
(0.07)
B=
0.7199
(0.00)
0.0355
(0.00)
−0.2777
(0.00)0.7935
(0.00)
A=
0.4118
(0.00)
0.1649
(0.00)
−0.2244
(0.00)−0.4323
(0.00)
G=
0.1216
(0.00)0.3958
(0.00)
0.6651
(0.00)
0.1287
(0.00)
φ 12 =1.0142
ρ 12 =−0.0632Panel (F): testing restrictions for nested modelsBEKK 2.75× 105 (0.00)
VECH 4.25× 106 (0.00)
CCORR 4.37× 106 (0.00)
Notes: Panels (A), (C) and (E) of this table display the quasi-maximum likelihood estimates of the
conditional CAPM ADC-M model defined in equations (1) and (2).P-values appear in brackets. In
the three cases, the necessary conditions for the stationarity of the process are satisfied.
Panels (B), (D) and (F) display the Wald test for the restrictions imposed on the ADC model to obtain
the encompassed models.p-values appear in brackets. The specification test proposed by Kroner
and Ng (1998) is as follows: (1) Ifρ 12 =b 12 =b 21 =a 12 =a 21 =g 12 =g 21 =0, a restricted asymmet-
ric VECH is obtained; (2) ifφ 12 =b 12 =b 21 =a 12 =a 21 =g 12 =g 21 =0, the asymmetric CCORR is
derived; (3) ifφ 12 =1 andρ 12 =0 the asymmetric BEKK model is obtained.
significantly below zero) reveal that the estimated ADC model has similar
properties to the BEKK model, although the encompassing restrictions are
clearly rejected.
Table 17.4 displays an analysis of the standardized residuals. It can be
observed that, in the large firm index, autocorrelation and heteroskedas-
ticity problems have been successfully amended. Regarding the small cap
index, heteroskedasticity disappears but autocorrelation remains. However,
itmustbehighlightedthatourmainfocusisonconditionalsecondmoments,
and Nelson (1992) shows that misspecification in the conditional mean does
not affect the key properties of the second moments.
Figure 17.2 displays the annualized conditional volatility of both indices
over the studied period for the three countries. Both volatility series have
similar patterns but large stock index volatility is almost always higher than
small stock index volatility.