Forecasting Renminbi Exchange Rate Volatility Using CARR-MIDAS Model

Table 5

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

Horizon	GARCH	GARCH-MIDAS	CARR	CARR-MIDAS
Panel A: MSE loss function
1d	2.0068 E − 06	1.6990 E − 06	9.0186 E − 07	8.6854 E − 07
2d	2.1629 E − 06	1.7962 E − 06	1.0384 E − 06	9.9931 E − 07
3d	2.2868 E − 06	1.8680 E − 06	1.0871 E − 06	1.0256 E − 06
4d	2.3687 E − 06	1.9056 E − 06	1.1331 E − 06	1.0539 E − 06
1w	2.4308 E − 06	1.9265 E − 06	1.1882 E − 06	1.0895 E − 06
2w	2.6363 E − 06	1.9515 E − 06	1.3307 E − 06	1.1545 E − 06
1m	3.0896 E − 06	1.9259 E − 06	1.5823 E − 06	1.1650 E − 06
2m	4.3618 E − 06	2.1107 E − 06	1.8549 E − 06	1.1911 E − 06
3m	5.5636 E − 06	2.0560 E − 06	2.0134 E − 06	1.2128 E − 06
Panel B: QLIKE loss function
1d	−5.2147	−5.2273	−5.2764	−5.2867
2d	−5.2055	−5.2205	−5.2535	−5.2707
3d	−5.1996	−5.2167	−5.2467	−5.2695
4d	−5.1950	−5.2143	−5.2391	−5.2680
1w	−5.1906	−5.2117	−5.2279	−5.2625
2w	−5.1804	−5.2092	−5.1952	−5.2534
1m	−5.1659	−5.2144	−5.1322	−5.2532
2m	−5.1183	−5.2024	−5.0378	−5.2602
3m	-5.0770	−5.1996	−4.9712	−5.2538

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.