Best model for each group
| Groups | ||||
|---|---|---|---|---|
| (1) Without mean and variance | (2) With mean and variance | (3) With variance | (4) With mean | |
| Best model | E-GARCH | E-GARCH | GJR-GARCH | E-GARCH |
| Order AR | (2, 2) | (1, 1) | (2, 2) | (1, 1) |
| Order GARCH | (1, 1) | (1, 1) | (1, 1) | (1, 1) |
| Conditional mean equation | ||||
| mu | 0.000491* | 0.000539** | 0.000570** | 0.000551** |
| (0.000275) | (0.000302) | (0.000285) | (0.000267) | |
| AR (1) | 1.637082*** | 0.134748*** | 0.911344*** | 0.143856*** |
| (0.012455) | (0.025117) | (0.004585) | (0.032556) | |
| AR (2) | −0.702824*** | – | −0.966448*** | – |
| (0.012319) | – | (0.005013) | – | |
| MA (1) | −1.667640*** | −0.171693*** | −0.932336*** | −0.180836*** |
| (0.000025) | (0.024772) | (0.002338) | (0.032202) | |
| MA (2) | 0.739511*** | – | 0.976144*** | – |
| (0.002995) | – | (0.000445) | – | |
| mxreg (1) | – | −0.011138** | – | −0.011152** |
| – | (0.004754) | – | (0.005081) | |
| Conditional volatility equation | ||||
| omega | −0.228015*** | −0.214980*** | 0.000009*** | −0.219534*** |
| (0.012542) | (0.025563) | (0.000001) | (0.009533) | |
| alpha (1) | −0.071853*** | −0.067077*** | 0.031605*** | −0.065056*** |
| (0.014133) | (0.011045) | (0.007792) | (0.012713) | |
| beta (1) | 0.972910*** | 0.974459*** | 0.895930*** | 0.973923*** |
| (0.001574) | (0.003232) | (0.008909) | (0.001221) | |
| Vxreg (1) | – | −0.135982 | 0.000003 | – |
| – | (0.123927) | (0.000040) | – | |
| gamma | 0.124239*** | 0.119126*** | 0.071600*** | 0.121291*** |
| (0.026062) | (0.015682) | (0.020344) | (0.021329) | |
| Log-Lik | 6229.404 | 6229.847 | 6232.252 | 6229.313 |
| AIC | −5.5555 | −5.5559 | −5.5572 | −5.5563 |
| BIC | −5.5300 | −5.5304 | −5.5291 | −5.5334 |
| LM (Het.) | 0.3377 | 0.2437 | 0.8740 | 0.2597 |
| Ljung-Box | 0.6993 | 0.6493 | 0.9823 | 0.6127 |
| Groups | ||||
|---|---|---|---|---|
| (1) Without mean and variance | (2) With mean and variance | (3) With variance | (4) With mean | |
| Best model | E-GARCH | E-GARCH | GJR-GARCH | E-GARCH |
| Order AR | (2, 2) | (1, 1) | (2, 2) | (1, 1) |
| Order GARCH | (1, 1) | (1, 1) | (1, 1) | (1, 1) |
| mu | 0.000491* | 0.000539** | 0.000570** | 0.000551** |
| (0.000275) | (0.000302) | (0.000285) | (0.000267) | |
| AR (1) | 1.637082*** | 0.134748*** | 0.911344*** | 0.143856*** |
| (0.012455) | (0.025117) | (0.004585) | (0.032556) | |
| AR (2) | −0.702824*** | – | −0.966448*** | – |
| (0.012319) | – | (0.005013) | – | |
| MA (1) | −1.667640*** | −0.171693*** | −0.932336*** | −0.180836*** |
| (0.000025) | (0.024772) | (0.002338) | (0.032202) | |
| MA (2) | 0.739511*** | – | 0.976144*** | – |
| (0.002995) | – | (0.000445) | – | |
| mxreg (1) | – | −0.011138** | – | −0.011152** |
| – | (0.004754) | – | (0.005081) | |
| omega | −0.228015*** | −0.214980*** | 0.000009*** | −0.219534*** |
| (0.012542) | (0.025563) | (0.000001) | (0.009533) | |
| alpha (1) | −0.071853*** | −0.067077*** | 0.031605*** | −0.065056*** |
| (0.014133) | (0.011045) | (0.007792) | (0.012713) | |
| beta (1) | 0.972910*** | 0.974459*** | 0.895930*** | 0.973923*** |
| (0.001574) | (0.003232) | (0.008909) | (0.001221) | |
| Vxreg (1) | – | −0.135982 | 0.000003 | – |
| – | (0.123927) | (0.000040) | – | |
| gamma | 0.124239*** | 0.119126*** | 0.071600*** | 0.121291*** |
| (0.026062) | (0.015682) | (0.020344) | (0.021329) | |
| Log-Lik | 6229.404 | 6229.847 | 6232.252 | 6229.313 |
| AIC | −5.5555 | −5.5559 | −5.5572 | −5.5563 |
| BIC | −5.5300 | −5.5304 | −5.5291 | −5.5334 |
| LM (Het.) | 0.3377 | 0.2437 | 0.8740 | 0.2597 |
| Ljung-Box | 0.6993 | 0.6493 | 0.9823 | 0.6127 |
Note(s): ***p < 0.01; **p < 0.05; *p < 0.1
Source(s): Authors’ elaboration
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