Forecasting Renminbi Exchange Rate Volatility Using CARR-MIDAS Model

Table 6

Out-of-sample forecast evaluation results for forecast window of 1,000.

Horizon	GARCH	GARCH-MIDAS	CARR	CARR-MIDAS
Panel A: MSE loss function
1d	1.6488 E − 06	1.4435 E − 06	9.3247 E − 07	8.9878 E − 07
2d	1.7634 E − 06	1.5265 E − 06	1.1026 E − 06	1.0841 E − 06
3d	1.8302 E − 06	1.5694 E − 06	1.1623 E − 06	1.1379 E − 06
4d	1.8754 E − 06	1.5939 E − 06	1.2060 E − 06	1.1746 E − 06
1w	1.9301 E − 06	1.6259E − 06	1.2743 E − 06	1.2281 E − 06
2w	2.0993 E − 06	1.6973 E − 06	1.5302 E − 06	1.3638 E − 06
1m	2.4848 E − 06	1.8318 E − 06	2.0408 E − 06	1.4434 E − 06
2m	3.3213 E − 06	2.0724 E − 06	2.3934 E − 06	1.4053 E − 06
3m	3.8112 E − 06	1.9729 E − 06	2.5319 E − 06	1.4155 E − 06
Panel B: QLIKE loss function
1d	−5.2591	−5.2696	−5.3043	−5.3150
2d	−5.2495	−5.2615	−5.2714	−5.2880
3d	−5.2431	−5.2564	−5.2571	−5.2801
4d	−5.2391	−5.2535	−5.2470	−5.2754
1w	−5.2345	−5.2499	−5.2314	−5.2660
2w	−5.2238	−5.2431	−5.1694	−5.2402
1m	−5.1942	−5.2218	−5.0010	−5.2156
2m	−5.1519	−5.1964	−4.8021	−5.2212
3m	−5.1284	−5.1926	−4.7188	−5.2122

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.