Table 1 MSGARCH models
Label | Equation | Author |
|---|---|---|
“sARCH” | \(\sigma ^{2}_{k,t} = \omega _{k} + \alpha _{k}\epsilon ^{2}_{t-1}\) | Engle [39] |
“sGARCH” | \(\sigma ^{2}_{k,t} = \omega _{k} + \alpha _{k}\epsilon ^{2}_{t-1} + \beta _{k}\sigma ^{2}_{k,t-1}\) | Bollerslev [40] |
“eGARCH” | \(\ln \left (\sigma ^{2}_{k,t}\right) = \omega _{k} + \alpha _{1,k}\left (\left |\eta _{k,t-1}\right | - E\left [\left |\eta _{k,t-1}\right | \right ]\right) + \) | Nelson [41] |
\(+ \alpha _{2,k}\eta _{k,t-1}+\beta _{k}\ln \left (\sigma ^{2}_{k,t-1}\right)\) | ||
“gjrGARCH” | \(\sigma ^{2}_{k,t} = \omega _{k} + \left (\alpha _{1,k}+\alpha _{2,k}I \left \{\epsilon _{t-1}<0\right \} \right)\epsilon ^{2}_{t-1} + \) | GJR [42] |
\(+\beta _{k}\sigma ^{2}_{k,t-1}\) | ||
“tGARCH” | \(\sigma _{k,t} = \omega _{k} + \left (\alpha _{1,k}I \left \{\epsilon _{t-1}\geqq 0\right \} - \alpha _{1,k}I \left \{\epsilon _{t-1}\geqq 0\right \}\right) \epsilon _{t-1}+\) | Zakoian [43] |
+βkσk,t−1 |