Table 2.
Estimation results of GARCH-MIDAS+RV+EMV-ID model.
| Stock index | ω | α | β | m | θ1 | θ2 | w1 | w2 | BIC |
|---|---|---|---|---|---|---|---|---|---|
| Panel A: lag K = 3 months | |||||||||
| S&P 500 | 0.0678*** | 0.1254*** | 0.8588*** | 0.4291** | −0.0045** | 0.0078*** | 1.7390** | 1.5683*** | 9814.57 |
| (0.0128) | (0.0083) | (0.0086) | (0.2110) | (0.0019) | (0.0022) | (0.8591) | (0.4051) | ||
| CSI 300 | 0.0495*** | 0.0628*** | 0.9353*** | 1.8367*** | −0.0062*** | 0.0021** | 1.0010*** | 3.8105* | 13,370.90 |
| (0.0190) | (0.0035) | (0.0034) | (0.2821) | (0.0011) | (0.0010) | (0.1459) | (2.1773) | ||
| FTSE 100 | 0.0397*** | 0.1166*** | 0.8629*** | 0.3162** | −0.0024* | 0.0061*** | 7.5366 | 1.3510*** | 10,127.60 |
| (0.0127) | (0.0091) | (0.0102) | (0.1510) | (0.0014) | (0.0021) | (7.1834) | (0.4060) | ||
| NIKKEI 225 | 0.0632*** | 0.1027*** | 0.8839*** | 1.0761*** | −0.0032** | 0.0106*** | 2.5909** | 1.4990*** | 12,290.10 |
| (0.0186) | (0.0064) | (0.0073) | (0.1837) | (0.0013) | (0.0023) | (1.1527) | (0.2534) | ||
| Panel B: lag K = 6 months | |||||||||
| S&P 500 | 0.0679*** | 0.1240*** | 0.8574*** | 0.3165* | −0.0045* | 0.0148*** | 3.8744 | 1.4503*** | 9685.68 |
| (0.0130) | (0.0083) | (0.0090) | (0.1826) | (0.0027) | (0.0033) | (2.5416) | (0.3106) | ||
| CSI 300 | 0.0491** | 0.0640*** | 0.9335*** | 1.5921*** | −0.0073*** | 0.0028** | 2.3788*** | 7.2521* | 13,115.00 |
| (0.0192) | (0.0037) | (0.0035) | (0.4309) | (0.0019) | (0.0014) | (0.6923) | (4.2782) | ||
| FTSE 100 | 0.0375*** | 0.1305*** | 0.8174*** | −0.2271*** | 0.0106*** | 0.0123*** | 1.0058*** | 1.0349*** | 9984.41 |
| (0.0133) | (0.0106) | (0.0146) | (0.0836) | (0.0014) | (0.0032) | (0.1939) | (0.1849) | ||
| NIKKEI 225 | 0.0606*** | 0.1021*** | 0.8801*** | 0.9427*** | −0.0029* | 0.0090** | 5.4749 | 3.3293** | 12,147.50 |
| (0.0192) | (0.0066) | (0.0078) | (0.1606) | (0.0017) | (0.0036) | (3.5115) | (1.3636) | ||
| Panel C: lag K = 12 months | |||||||||
| S&P 500 | 0.0708*** | 0.1301*** | 0.8515*** | 0.3418* | −0.0040 | 0.0223*** | 8.7063 | 1.7036*** | 9400.41 |
| (0.0134) | (0.0088) | (0.0094) | (0.1993) | (0.0031) | (0.0062) | (7.6282) | (0.4907) | ||
| CSI 300 | 0.0447** | 0.0630*** | 0.9337*** | 1.2773*** | −0.0061** | 0.0029** | 5.5741** | 14.5700 | 12,735.10 |
| (0.0195) | (0.0038) | (0.0036) | (0.3361) | (0.0023) | (0.0015) | (2.6346) | (9.1368) | ||
| FTSE 100 | 0.0341** | 0.1328*** | 0.8121*** | −0.2543*** | 0.0124*** | 0.0130** | 2.0656*** | 1.7320** | 9733.75 |
| (0.0139) | (0.0111) | (0.0153) | (0.0873) | (0.0017) | (0.0052) | (0.5824) | (0.8542) | ||
| NIKKEI 225 | 0.0501** | 0.1011*** | 0.885*** | 1.1579*** | −0.0039* | 0.0082** | 8.6552 | 7.3802* | 11,732.50 |
| (0.0198) | (0.0065) | (0.0076) | (0.2389) | (0.0023) | (0.0041) | (5.3192) | (3.8643) | ||
| Panel D: lag K = 24 months | |||||||||
| S&P 500 | 0.0734*** | 0.1449*** | 0.8260*** | −0.0569 | 0.0086*** | 0.0659*** | 1.7018*** | 1.0011*** | 8852.62 |
| (0.0140) | (0.0104) | (0.0115) | (0.1571) | (0.0022) | (0.0107) | (0.6161) | (0.0642) | ||
| CSI 300 | 0.0335 | 0.0582*** | 0.9398*** | 2.5874*** | −0.0204*** | 0.0018 | 1.1093*** | 36.6950 | 11,715.00 |
| (0.0208) | (0.0035) | (0.0033) | (0.5369) | (0.0058) | (0.0012) | (0.2240) | (32.7200) | ||
| FTSE 100 | −0.1126*** | 0.1191*** | 0.8808*** | −11.753 | −0.0530*** | 0.1584*** | 4.2737*** | 1.0113*** | 9416.54 |
| (0.0099) | (0.0055) | (0.0039) | (10.8020) | (0.0108) | (0.01654) | (0.8794) | (0.0322) | ||
| NIKKEI 225 | 0.0496** | 0.1032*** | 0.8805*** | 1.0262*** | −0.0028 | 0.0074** | 24.0030 | 18.2600* | 10,914.60 |
| (0.0207) | (0.0069) | (0.0082) | (0.1927) | (0.0019) | (0.0036) | (18.5720) | (9.5953) | ||
Note: 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.