Table 3.
Estimation results of GJR-GARCH-MIDAS+RV+EMV-ID model.
| Stock index | ω | α | β | λ | m | θ1 | θ2 | w1 | w2 | BIC |
|---|---|---|---|---|---|---|---|---|---|---|
| Panel A: lag K = 3 months | ||||||||||
| S&P 500 | 0.0281** | 1.437e-09 | 0.8675*** | 0.2213*** | 0.1538 | −0.0020** | 0.0039* | 8.2411 | 1.8210** | 9608.66 |
| (0.0129) | (0.0086) | (0.0089) | (0.0160) | (0.1691) | (0.0010) | (0.0020) | (8.7749) | (0.8480) | ||
| CSI 300 | 0.0478** | 0.0599*** | 0.9358*** | 0.0046 | 1.8045*** | −0.0060*** | 0.0019* | 1.0010*** | 3.5829 | 13,358.80 |
| (0.0200) | (0.0052) | (0.0036) | (0.0056) | (0.2907) | (0.0011) | (0.0011) | (0.1495) | (2.2578) | ||
| FTSE 100 | 0.0034 | 7.0088e-09 | 0.8939*** | 0.1679*** | 0.1210 | −0.0024** | −1.2083e-05 | 10.8450 | 6.0241 | 9944.88 |
| (0.0138) | (0.0072) | (0.0082) | (0.0125) | (0.1286) | (0.0009) | (0.0009) | (11.7470) | (635.6400) | ||
| NIKKEI 225 | 0.0292 | 0.0339*** | 0.8741*** | 0.1347*** | 0.7848*** | −0.0017* | 0.0080*** | 5.8402 | 1.4257*** | 12,179.30 |
| (0.0192) | (0.0051) | (0.0080) | (0.0104) | (0.1172) | (0.0010) | (0.0021) | (5.0035) | (0.2959) | ||
| Panel A: lag K = 6 months | ||||||||||
| S&P 500 | 0.0306** | 2.9086e-08 | 0.8673*** | 0.2179*** | 0.0896 | −0.0020* | 0.0068** | 15.1260 | 1.7108** | 9480.93 |
| (0.0130) | (0.0087) | (0.0089) | (0.0156) | (0.1514) | (0.0010) | (0.0032) | (16.6070) | (0.7591) | ||
| CSI 300 | 0.0484** | 0.0621*** | 0.9343*** | 0.0021 | 1.5726*** | −0.0069*** | 0.0028* | 2.4344*** | 6.6077 | 13,103.00 |
| (0.0202) | (0.0054) | (0.0036) | (0.0057) | (0.4269) | (0.0019) | (0.0015) | (0.7381) | (4.2943) | ||
| FTSE 100 | 0.0038 | 8.2399e-09 | 0.8938*** | 0.1644*** | 0.0720 | −0.0028*** | 0.0113*** | 18.7030 | 1.0010*** | 9823.46 |
| (0.0138) | (0.0070) | (0.0085) | (0.0125) | (0.1165) | (0.0010) | (0.0029) | (16.4300) | (0.1169) | ||
| NIKKEI 225 | 0.0289 | 0.0299*** | 0.8713*** | 0.1381*** | 0.7078*** | −0.0012 | 0.0092** | 15.4690 | 2.0924** | 12,032.20 |
| (0.0197) | (0.0054) | (0.0083) | (0.0110) | (0.1034) | (0.0010) | (0.0038) | (19.4170) | (0.9201) | ||
| Panel C: lag K = 12 months | ||||||||||
| S&P 500 | 0.0328** | 3.2348e-08 | 0.8643*** | 0.2250*** | 0.1157 | −0.0019* | 0.0094* | 34.047 | 1.8915* | 9197.42 |
| (0.0133) | (0.0090) | (0.0093) | (0.0160) | (0.1627) | (0.0010) | (0.0055) | (40.4390) | (1.1306) | ||
| CSI 300 | 0.0438** | 0.0605*** | 0.9342*** | 0.0037 | 1.2703*** | −0.0058** | 0.0029* | 5.7976** | 12.8240 | 12,722.70 |
| (0.0206) | (0.0055) | (0.0037) | (0.0056) | (0.3328) | (0.0022) | (0.0017) | (2.7957) | (9.0169) | ||
| FTSE 100 | −0.0009 | 5.0996e-09 | 0.8343*** | 0.2114*** | −0.3729*** | 0.0131*** | 0.0086** | 2.0324*** | 1.7397 | 9545.87 |
| (0.0146) | (0.0093) | (0.0140) | (0.0185) | (0.0794) | (0.0014) | (0.0040) | (0.4227) | (1.1550) | ||
| NIKKEI 225 | 0.0146 | 0.0306*** | 0.8778*** | 0.1344*** | 0.7908*** | −0.0016 | 0.0170** | 20.2320 | 1.5909** | 11,622.60 |
| (0.0202) | (0.0051) | (0.0083) | (0.0102) | (0.1313) | (0.0013) | (0.0073) | (21.7010) | (0.6556) | ||
| Panel D: lag K = 24 months | ||||||||||
| S&P 500 | 0.0309** | 5.0533e-09 | 0.8411*** | 0.2480*** | −0.2861** | 0.0106*** | 0.0479*** | 1.6094*** | 1.0010*** | 8649.12 |
| (0.0140) | (0.0110) | (0.0113) | (0.0188) | (0.1341) | (0.0016) | (0.0099) | (0.3122) | (0.0797) | ||
| CSI 300 | 0.0775*** | 0.1160*** | 0.8212*** | 0.1253*** | −8.2023 | −0.2617*** | 0.0997*** | 3.1162*** | 1.0620*** | 12,255.70 |
| (0.0147) | (0.0059) | (0.0046) | (0.0098) | (1.1905e+11) | (0.0111) | (0.0227) | (0.1106) | (0.1025) | ||
| FTSE 100 | −0.0022 | 2.6215e-10 | 0.8364*** | 0.2082*** | −0.3652*** | 0.0131*** | 0.0293*** | 4.1055*** | 1.2041*** | 8944.87 |
| (0.0155) | (0.0095) | (0.0147) | (0.0192) | (0.0877) | (0.0016) | (0.0073) | (0.9355) | (0.3193) | ||
| NIKKEI 225 | 0.0315** | 0.0695*** | 0.9013*** | 0.0582*** | 0.0002 | −0.0640*** | 0.0656*** | 4.9933*** | 4.9990*** | 11,059.10 |
| (0.0157) | (0.0050) | (0.0041) | (0.0060) | (0.5191) | (0.0059) | (0.0209) | (0.4640) | (1.5622) | ||
Note: λ is the volatility leverage coefficient in the GJR-GARCH model of Eq. (7). θ1 and θ2 indicate the impacts of lagged RV and EMV-ID on the permanent volatility of the four stock markets, respectively. The bracketed numbers are the standard errors of the estimations. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.