25
Figure 1: Kernel estimates of the distribution of weekly returns.
and
Table 3 presents the results of the maximum likelihood estimation of the parameters
of the marginals. In the table we present also the values of the averaged Ioglikelihood
function at maximum. Then, we have obtained the following maximum likelihood esti-
mates of the parameters ɑ in the three cases considered:
|
^0.0000 |
0.0702 0.0476 |
0.0000 0.0000 |
0.1072∖ 0.0357 | |
|
«SST = |
0.0491 |
0.0342 0.0000/ | ||
|
/0.0000 |
0.0730 |
0.0000 |
0.1095∖ | |
|
«SGSH = |
∖ |
0.0467 |
0.0000 0.0419 |
0.0363 0.0338 0.0000/ |
|
<0.0000 |
0.0728 |
0.0000 |
0.1086∖ | |
|
<*SEP = |
0.0473 |
0.0000 0.0385 |
0.0358 0.0332 0.0000/ |
with the values of the averaged Ioglikelihood function at maximum, respectively, equal
to 12.9449, 12.9496 and 12.94153.
Note that the three marginals have a similar behaviour, also if the shape parameter
of the skew Student-t for the NASCOMP index is lower than 4 and, as a consequence,
it has not kurtosis index. Also the structure of ɑ is very similar in the three cases
considered, confirming what we have writtem in the previous section.
3We have used a quasi-Newton algorithm to obtain the maximum of Ioglikelihood functions.