Table 9.

Out-of-sample $R^2$results.

Forecasting models	h = 1			h = 5			h = 20
	$R_{OOS}^2$(%)	MSPE-Adj.	p-value	$R_{OOS}^2$(%)	MSPE-Adj.	p-value	$R_{OOS}^2$(%)	MSPE-Adj.	p-value
MIDAS-RV-OVX	2.9621	1.4513	0.0733	0.2385	1.6354	0.0510	3.8737	2.2304	0.0129
MS-MIDAS-RV	−7.7173	−1.2302	0.8907	8.6505	2.1747	0.0148	42.5511	4.3905	0.0000
MS-MIDAS-RV-OVX	1.3141	1.5069	0.0659	39.0853	3.2587	0.0006	44.2059	6.6704	0.0000

Notes: The value of $R_{OOS}^2$is calculated in Equation (19). This table shows out-of-sample performance of models’ evaluation by $R_{OOS}^2$and MSPE-adjusted statistic. If $R_{oos}^2>0$, implying that corresponding model outperform the benchmark model.