Forecasting Renminbi Exchange Rate Volatility Using CARR-MIDAS Model

Table 3

Out-of-sample forecast evaluation results.

Horizon	GARCH	GARCH-MIDAS	CARR	CARR-MIDAS
Panel A: MSE loss function
1d	1.8812 E − 06	1.6093 E − 06	1.0439 E − 06	1.0100 E − 06
2d	2.0191 E − 06	1.6917 E − 06	1.2202 E − 06	1.1935 E − 06
3d	2.1171 E − 06	1.7454 E − 06	1.2792 E − 06	1.2428 E − 06
4d	2.1787 E − 06	1.7707 E − 06	1.3163 E − 06	1.2705E − 06
1w	2.2375 E − 06	1.7879 E − 06	1.3601 E − 06	1.2956 E − 06
2w	2.4510 E − 06	1.8444 E − 06	1.6051 E − 06	1.4181 E − 06
1m	2.9237 E − 06	1.8923 E − 06	2.0200 E − 06	1.4109 E − 06
2m	4.3222 E − 06	2.2110 E − 06	2.4252 E − 06	1.3921 E − 06
3m	5.5743 E − 06	2.1918 E − 06	2.5807 E − 06	1.3845 E − 06
Panel B: QLIKE loss function
1d	−5.1629	−5.1733	−5.2063	−5.2171
2d	−5.1539	−5.1672	−5.1782	−5.1961
3d	−5.1485	−5.1637	−5.1687	−5.1920
4d	−5.1457	−5.1628	−5.1617	−5.1909
1w	−5.1440	−5.1629	−5.1510	−5.1880
2w	−5.1362	−5.1611	−5.1023	−5.1728
1m	−5.1270	−5.1677	−4.9900	−5.1788
2m	−5.0712	−5.1431	−4.8115	−5.1863
3m	−5.0353	−5.1448	−4.7389	−5.1908

Note: MSE is the mean squared error, and QLIKE is the quasi-likelihood. Bold entries indicate the model with the lowest loss value per horizon (in each row). Shaded entries indicate the model includes the MCS at a 10% significance level. For the forecast horizons, d = day, = week, and m = month.