Table 13.
DM Test statistics and p values for JCI Index
| Forecast 1 vs Forecast 2 | DM(A) | < > p value | > p value | < p value | DM(S) | < > p value | > p value | < p value | DM(A) | < > p value | > p value | < p value | DM(S) | < > p value | > p value | < p value |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Recursive daily | Rolling window daily | |||||||||||||||
| GARCH vs EGARCH | 4.6370 | 0.0000 | 1.0000 | 0.0000 | 2.6396 | 0.0083 | 0.9958 | 0.0042 | 3.4684 | 0.0005 | 0.9997 | 0.0003 | 2.8227 | 0.0048 | 0.9976 | 0.0024 |
| GARCH vs TGARCH | 0.5832 | 0.5598 | 0.7201 | 0.2799 | 0.7078 | 0.4791 | 0.7604 | 0.2396 | − 0.4036 | 0.6865 | 0.3433 | 0.6567 | 0.6048 | 0.5453 | 0.7273 | 0.2727 |
| GARCH vs MGARCH | 0.9560 | 0.3392 | 0.8304 | 0.1696 | 0.9949 | 0.3199 | 0.8401 | 0.1599 | − 2.2341 | 0.0256 | 0.0128 | 0.9872 | − 2.1377 | 0.0326 | 0.0163 | 0.9837 |
| GARCH vs PGARCH | 0.2000 | 0.8415 | 0.5792 | 0.4208 | 1.1065 | 0.2686 | 0.8657 | 0.1343 | 0.9110 | 0.3624 | 0.8188 | 0.1812 | 1.0952 | 0.2735 | 0.8632 | 0.1368 |
| EGARCH vs TGARCH | − 3.0237 | 0.0025 | 0.0013 | 0.9987 | − 0.6463 | 0.5181 | 0.2591 | 0.7409 | − 3.0742 | 0.0021 | 0.0011 | 0.9989 | − 0.6270 | 0.5307 | 0.2654 | 0.7346 |
| EGARCH vs MGARCH | − 4.5683 | 0.0000 | 0.0000 | 1.0000 | − 2.4357 | 0.0149 | 0.0075 | 0.9925 | – 3.7418 | 0.0002 | 0.0001 | 0.9999 | − 2.9682 | 0.0030 | 0.0015 | 0.9985 |
| EGARCH vs PGARCH | − 3.8168 | 0.0001 | 0.0001 | 0.9999 | − 1.2144 | 0.2247 | 0.1124 | 0.8876 | − 2.3661 | 0.0180 | 0.0090 | 0.9910 | − 0.5570 | 0.5775 | 0.2888 | 0.7112 |
| TGARCH vs MGARCH | − 0.5485 | 0.5834 | 0.2917 | 0.7083 | − 0.6874 | 0.4919 | 0.2460 | 0.7540 | 0.1339 | 0.8935 | 0.5533 | 0.4467 | -0.6670 | 0.5048 | 0.2524 | 0.7476 |
| TGARCH vs PGARCH | − 0.4343 | 0.6641 | 0.3320 | 0.6680 | -0.1352 | 0.8925 | 0.4462 | 0.5538 | 2.2327 | 0.0256 | 0.9872 | 0.0128 | 0.6630 | 0.5074 | 0.7463 | 0.2537 |
| MGARCH vs PGARCH | 0.1428 | 0.8864 | 0.5568 | 0.4432 | 1.0901 | 0.2758 | 0.8621 | 0.1379 | 1.1724 | 0.2411 | 0.8794 | 0.1206 | 1.1589 | 0.2466 | 0.8767 | 0.1233 |
| Recursive weekly | Rolling window weekly | |||||||||||||||
| GARCH vs EGARCH | 0.5757 | 0.5650 | 0.7175 | 0.2825 | 1.1574 | 0.2476 | 0.8762 | 0.1238 | 0.4608 | 0.6451 | 0.6775 | 0.3225 | 1.4358 | 0.1516 | 0.9242 | 0.0758 |
| GARCH vs TGARCH | − 3.3100 | 0.0010 | 0.0005 | 0.9995 | − 1.1492 | 0.2509 | 0.1255 | 0.8745 | − 3.5921 | 0.0004 | 0.0002 | 0.9998 | − 0.5874 | 0.5571 | 0.2786 | 0.7214 |
| GARCH vs MGARCH | 2.2249 | 0.0265 | 0.9868 | 0.0132 | 0.9873 | 0.3239 | 0.8380 | 0.1620 | − 0.9667 | 0.3341 | 0.1671 | 0.8329 | 0.1195 | 0.9049 | 0.5476 | 0.4524 |
| GARCH vs PGARCH | − 3.8382 | 0.0001 | 0.0001 | 0.9999 | − 1.3643 | 0.1730 | 0.0865 | 0.9135 | − 5.0858 | 0.0000 | 0.0000 | 1.0000 | − 1.2250 | 0.2210 | 0.1105 | 0.8895 |
| EGARCH vs TGARCH | − 3.8979 | 0.0001 | 0.0001 | 0.9999 | − 2.1643 | 0.0308 | 0.0154 | 0.9846 | − 4.2839 | 0.0000 | 0.0000 | 1.0000 | − 2.7713 | 0.0058 | 0.0029 | 0.9971 |
| EGARCH vs MGARCH | − 0.4096 | 0.6822 | 0.3411 | 0.6589 | − 1.0785 | 0.2812 | 0.1406 | 0.8594 | − 0.6169 | 0.5376 | 0.2688 | 0.7312 | − 1.3753 | 0.1695 | 0.0848 | 0.9152 |
| EGARCH vs PGARCH | − 4.2608 | 0.0000 | 0.0000 | 1.0000 | − 2.2708 | 0.0235 | 0.0118 | 0.9882 | − 5.3594 | 0.0000 | 0.0000 | 1.0000 | − 3.2480 | 0.0012 | 0.0006 | 0.9994 |
| TGARCH vs MGARCH | 3.3459 | 0.0009 | 0.9996 | 0.0004 | 1.1734 | 0.2411 | 0.8794 | 0.1206 | 3.2812 | 0.0011 | 0.9995 | 0.0005 | 0.5715 | 0.5679 | 0.7161 | 0.2839 |
| TGARCH vs PGARCH | − 2.0985 | 0.0363 | 0.0181 | 0.9819 | − 1.5081 | 0.1321 | 0.0660 | 0.9340 | − 2.4205 | 0.0158 | 0.0079 | 0.9921 | − 1.7576 | 0.0793 | 0.0397 | 0.9603 |
| MGARCH vs PGARCH | 0.5757 | 0.5650 | 0.7175 | 0.2825 | 1.1574 | 0.2476 | 0.8762 | 0.1238 | − 4.7785 | 0.0000 | 0.0000 | 1.0000 | − 1.1632 | 0.2452 | 0.1226 | 0.8774 |
| Recursive monthly | Rolling window monthly | |||||||||||||||
| GARCH vs EGARCH | − 3.9896 | 0.0001 | 0.0001 | 0.9999 | − 2.9315 | 0.0039 | 0.0020 | 0.9980 | 0.5628 | 0.5744 | 0.7128 | 0.2872 | 1.3262 | 0.1869 | 0.9065 | 0.0935 |
| GARCH vs TGARCH | − 3.8280 | 0.0002 | 0.0001 | 0.9999 | − 2.5648 | 0.0113 | 0.0057 | 0.9943 | − 1.5331 | 0.1274 | 0.0637 | 0.9363 | − 1.0423 | 0.2990 | 0.1495 | 0.8505 |
| GARCH vs MGARCH | 1.5076 | 0.1338 | 0.9331 | 0.0669 | − 0.2530 | 0.8006 | 0.4003 | 0.5997 | − 4.0777 | 0.0001 | 0.0000 | 1.0000 | − 3.7775 | 0.0002 | 0.0001 | 0.9999 |
| GARCH vs PGARCH | − 2.2652 | 0.0250 | 0.0125 | 0.9875 | − 2.1852 | 0.0305 | 0.0152 | 0.9848 | − 2.0589 | 0.0413 | 0.0206 | 0.9794 | − 2.0946 | 0.0379 | 0.0190 | 0.9810 |
| EGARCH vs TGARCH | 2.0662 | 0.0406 | 0.9797 | 0.0203 | 1.5945 | 0.1130 | 0.9435 | 0.0565 | − 1.2940 | 0.1978 | 0.0989 | 0.9011 | − 1.8435 | 0.0674 | 0.0337 | 0.9663 |
| EGARCH vs MGARCH | 4.0244 | 0.0001 | 1.0000 | 0.0000 | 2.9349 | 0.0039 | 0.9981 | 0.0019 | − 0.9810 | 0.3283 | 0.1642 | 0.8358 | − 1.4297 | 0.1550 | 0.0775 | 0.9225 |
| EGARCH vs PGARCH | 1.4036 | 0.1626 | 0.9187 | 0.0813 | − 0.4481 | 0.6548 | 0.3274 | 0.6726 | − 1.4909 | 0.1382 | 0.0691 | 0.9309 | − 1.9045 | 0.0589 | 0.0294 | 0.9706 |
| TGARCH vs MGARCH | 3.9616 | 0.0001 | 0.9999 | 0.0001 | 2.6077 | 0.0101 | 0.9950 | 0.0050 | 1.1712 | 0.2434 | 0.8783 | 0.1217 | 0.9461 | 0.3457 | 0.8272 | 0.1728 |
| TGARCH vs PGARCH | − 0.5048 | 0.6144 | 0.3072 | 0.6928 | − 1.9459 | 0.0536 | 0.0268 | 0.9732 | − 1.8788 | 0.0623 | 0.0311 | 0.9689 | − 2.2280 | 0.0274 | 0.0137 | 0.9863 |
| MGARCH vs PGARCH | − 2.3181 | 0.0218 | 0.0109 | 0.9891 | − 2.1936 | 0.0298 | 0.0149 | 0.9851 | − 1.8281 | 0.0696 | 0.0348 | 0.9652 | − 2.0594 | 0.0412 | 0.0206 | 0.9794 |
1. The columns labelled DM(A) and DM(S) contain t-statistic based on absolute and squared prediction errors, respectively. 2. The null hypothesis of DM-test is that of equal predictive ability of the two models; a significantly positive (negative) t-statistics indicates the benchmark model is dominated by (dominates) the corresponding model