Findings of the marginal estimation of models for USDX returns
| AIC | WLB test | WLM test | KS test | |
|---|---|---|---|---|
| Skewed t distribution | ||||
| GARCH (1,1) | −7.418 | 0.853 | 0.452 | 1.000 |
| EGARCH (1,1) | −7.710 | 0.862 | 0.252 | 1.000 |
| IGARCH (1,1) | −7.507 | 0.818 | 0.472 | 1.000 |
| GJR-GARCH (1,1) | −7.829 | 0.873 | 0.495 | 1.000 |
| APARCH (1,1) | −7.528 | 0.862 | 0.590 | 1.000 |
| Skewed normal distribution | ||||
| GARCH (1,1) | −7.097 | 0.881 | 0.422 | 1.000 |
| EGARCH (1,1) | −7.404 | 0.875 | 0.289 | 1.000 |
| IGARCH (1,1) | −7.655 | 0.886 | 0.483 | 1.000 |
| GJR-GARCH (1,1) | −7.379 | 0.885 | 0.479 | 1.000 |
| APARCH (1,1) | −7.527 | 0.896 | 0.552 | 1.000 |
| Student’s t distribution | ||||
| GARCH (1,1) | −7.188 | 0.873 | 0.485 | 1.000 |
| EGARCH (1,1) | −7.793 | 0.862 | 0.206 | 1.000 |
| IGARCH (1,1) | −7.670 | 0.894 | 0.383 | 1.000 |
| GJR-GARCH (1,1) | −7.626 | 0.879 | 0.432 | 1.000 |
| APARCH (1,1) | −7.226 | 0.887 | 0.789 | 1.000 |
| −7.418 | 0.853 | 0.452 | 1.000 | |
| −7.710 | 0.862 | 0.252 | 1.000 | |
| −7.507 | 0.818 | 0.472 | 1.000 | |
| GJR-GARCH (1,1) | −7.829 | 0.873 | 0.495 | 1.000 |
| −7.528 | 0.862 | 0.590 | 1.000 | |
| −7.097 | 0.881 | 0.422 | 1.000 | |
| −7.404 | 0.875 | 0.289 | 1.000 | |
| −7.655 | 0.886 | 0.483 | 1.000 | |
| GJR-GARCH (1,1) | −7.379 | 0.885 | 0.479 | 1.000 |
| −7.527 | 0.896 | 0.552 | 1.000 | |
| −7.188 | 0.873 | 0.485 | 1.000 | |
| −7.793 | 0.862 | 0.206 | 1.000 | |
| −7.670 | 0.894 | 0.383 | 1.000 | |
| GJR-GARCH (1,1) | −7.626 | 0.879 | 0.432 | 1.000 |
| −7.226 | 0.887 | 0.789 | 1.000 | |
The weighted Ljung–Box test is known as the WLB test, while the weighted LM test is known as the WLM test
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