Take EGARCH (1, 1) function to portray margin-The marginal distribution of S&P500 data which al distribution of each sequence, and the model is based on EGARCH (1, 1) model is: structure is as follows: (6) In order to make the model portrayed more accu-Assuming standardized residuals obey distribu-rate, we should test if there is still ARCH effect, and tion, that means obeys distribution. GARCH effect after the model has been portrayed. yk eus , e dn c d wo e cr a na y g tg h esti- Te h i pr a ea r si e Abu R Co H Lf M t0 . mal at dst r r su u lo ts To h lC ts u1 g e) s td h t th ARCH effect has

Chapter

Chapter

ABSTRACT

Take EGARCH (1, 1) function to portray marginal distribution of each sequence, and the model structure is as follows:

Parameters Parameters esti-

mation

P value

C -0.132454 0.0000

g -0.042156 0.0022

β 0.978897 0.0000

Parameters Parameters esti-

mation

P value

α 0.068466 0.0000

g -0.125256 0.0000

β 0.985738 0.0000

M-Copula

function

Parame-

ters

Parameter es-

timates

Likelihood

value

α 0.3812

0.9328

θ 0.0128

λ 0.0051

ω2 0.8730

(4)

By using preprocessed data, we can get the estimated results.