Forecasting Renminbi Exchange Rate Volatility Using CARR-MIDAS Model

Table 7

Out-of-sample forecast evaluation results for forecast window of 1,500.

Horizon	GARCH	GARCH-MIDAS	CARR	CARR-MIDAS
Panel A: MSE loss function
1d	1.5384 E − 06	1.3723 E − 06	8.2349 E − 07	7.8460 E − 07
2d	1.6969 E − 06	1.4975 E − 06	9.5137 E − 07	9.6109 E − 07
3d	1.7951 E − 06	1.5689 E − 06	9.9754 E − 07	1.0141 E − 06
4d	1.8409 E − 06	1.5924 E − 06	1.0223 E − 06	1.0430 E − 06
1w	1.8853 E − 06	1.6136 E − 06	1.0535 E − 06	1.0800 E − 06
2w	2.0442 E − 06	1.6625 E − 06	1.1651 E − 06	1.1862 E − 06
1m	2.4191 E − 06	1.7385 E − 06	1.3695 E − 06	1.2373 E − 06
2m	3.1551 E − 06	1.8347 E − 06	1.6240 E − 06	1.2379 E − 06
3m	3.7905 E − 06	1.7622 E − 06	1.8127 E − 06	1.2149 E − 06
Panel B: QLIKE loss function
1d	−5.4350	−5.4477	−5.4963	−5.5060
2d	−5.4027	−5.4197	−5.4507	−5.4637
3d	−5.3801	−5.4004	−5.4282	−5.4471
4d	−5.3742	−5.3955	−5.4241	−5.4434
1w	−5.3721	−5.3938	−5.4168	−5.4353
2w	−5.3579	−5.3873	−5.3856	−5.4156
1m	−5.3368	−5.3762	−5.3529	−5.4052
2m	−5.3158	−5.3780	−5.2787	−5.4077
3m	−5.2903	−5.3790	−5.1855	−5.4140

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.