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| ARIFMA |
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| ARIFMA-FIGARCH |
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| Normal-distribution | t-distribution | Skew-t-distribution | ||||||||
| Estimate | Std. Error | Pr(>|t|) | Coefficient | Std. Error | t-prob | Coefficient | Std. Error | t-prob | Coefficient | Std. Error | t-prob | ||
| Cst(M) | 0.000464 | 0.000466 | 0.3199 | 0.001209 | 0.000711 | 0.0895 | 0.001957 | 0.000774 | 0.0115 | 0.001131 | 0.000696 | 0.1043 | |
| d-ARFIMA | 0.083774 | 0.003865 | 0 | 0.148646 | 0.071422 | 0.0376 | 0.184906 | 0.070633 | 0.0089 | 0.179491 | 0.075805 | 0.018 | |
| AR (1) | 1.295357 | 0.000191 | 0 | −0.19058 | 0.16611 | 0.2514 | −0.49701 | 0.16767 | 0.0031 | −0.53517 | 0.12657 | 0 | |
| AR (2) | −0.8637 | 0.000349 | 0 | −0.00794 | 0.19776 | 0.968 | 0.052938 | 0.12123 | 0.6624 | 0.009362 | 0.09944 | 0.925 | |
| AR (3) | −0.09521 | 0.00017 | 0 | 0.595891 | 0.11948 | 0 | 0.600178 | 0.083673 | 0 | 0.581247 | 0.064572 | 0 | |
| MA (1) | −1.34154 | 0.000016 | 0 | 0.143369 | 0.14627 | 0.3272 | 0.392524 | 0.1664 | 0.0185 | 0.414539 | 0.1244 | 0.0009 | |
| MA (2) | 0.934703 | 0.000008 | 0 | −0.05671 | 0.18801 | 0.763 | −0.18711 | 0.106 | 0.0777 | −0.17244 | 0.080884 | 0.0332 | |
| MA (3) | 0.051143 | 0.000008 | 0 | −0.68492 | 0.12286 | 0 | −0.7098 | 0.090325 | 0 | −0.71193 | 0.068807 | 0 | |
| Cst(V) × 10^4 | 0.016657 | 0.00008 | 0 | 0.043271 | 0.026916 | 0.1081 | 0.056419 | 0.02778 | 0.0424 | 0.04334 | 0.023721 | 0.0679 | |
| d-FIGARCH |
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| 0.613892 | 0.1202 | 0 | 0.657075 | 0.10225 | 0 | 0.667657 | 0.10798 | 0 | |
| ARCH (Phi1) |
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| 0.164956 | 0.085968 | 0.0552 | 0.03289 | 0.072874 | 0.6518 | 0.046961 | 0.066469 | 0.48 | |
| GARCH (Beta1) |
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| 0.654849 | 0.13198 | 0 | 0.642636 | 0.094668 | 0 | 0.669853 | 0.095867 | 0 | |
| Asymmetry |
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| 5.993905 | 0.87547 | 0 | −0.14588 | 0.042802 | 0.0007 | |
| Tail |
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| 6.322875 | 0.9999 | 0 | |
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| LogLikelihood | 4131.557 |
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| 4385.51 |
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| 4429.85 |
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| 4436.96 | 4131.557 |
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| Akaike | −5.3401 |
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| −5.6652 |
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| −5.7213 |
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| −5.7292 |
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| Bayes | −5.309 |
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| −5.6237 |
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| −5.6763 |
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| −5.6808 |
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| Shibata | −5.3402 |
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| −5.6653 |
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| −5.7215 |
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| −5.7294 |
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| Hannan-Quinn | −5.3285 |
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| −5.6497 |
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| −5.7046 |
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| −5.7112 |
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| Q (17) | 17.597 | 0 |
| 23.0005 | [0.0176724]* |
| 23.347 | [0.0157853]* |
| 30.017 | [0.0015749]** |
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| Q (29) | 26.104 | 0.000619 |
| 32.5941 | [0.0884055] |
| 35.1294 | [0.0504973] |
| 42.0471 | [0.0089643]** |
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| Q2 (17) | 59.87 | 1.11E−16 |
| 8.87072 | [0.8841796] |
| 10.1489 | [0.8102684] |
| 11.3267 | [0.7291133] |
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| Q2 (29) | 115.12 | 0.00E+00 |
| 20.9427 | [0.7889642] |
| 22.1955 | [0.7273764] |
| 23.5133 | [0.6571527] |
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| ARCH LM Tests | |||||||||||||
| ARCH Lag [2] | 79.35 | 0 |
| 0.34833 | [0.7059] |
| 1.6044 | [0.2014] |
| 1.9743 | [0.1392] |
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| ARCH Lag [5] | 116.87 | 0 |
| 0.91195 | [0.4722] |
| 1.1656 | [0.3239] |
| 1.3504 | [0.2404] |
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| ARCH Lag [10] | 149.56 | 0 |
| 0.59509 | [0.8190] |
| 0.7576 | [0.6701] |
| 0.88077 | [0.5507] |
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