Forecasting Stock Market Volatility: A Combination Approach

Table 4

Out-of-sample forecasting results, rolling window.

	WTI	BRT	VIX	WTI + VIX	BRT + VIX	CC ()	CC ()
Out-of-sample forecasting results for 1998–2018
	0.56	0.17	12.81	12.83	13.70	13.12	13.15
value	0.082	0.117	0.0005	0.0001	0.0001	0.0001	0.0001
Out-of-sample forecasting results for 2003–2018
	1.53	1.43	12.01	14.47	13.22	12.66	12.72
value	0.057	0.065	0.0001	0.0001	0.0001	0.0001	0.0001
Out-of-sample forecasting results for 2008–2018
	2.52	1.43	12.10	13.67	14.38	12.89	12.88
value	0.064	0.113	0.0009	0.0001	0.0001	0.0006	0.0007
Out-of-sample forecasting results for 2013–2018
	5.22	4.32	21.27	22.61	25.50	21.67	22.07
value	0.067	0.066	0.0026	0.0007	0.0002	0.0020	0.0019

Note. The forecasting results for the predictive regression models in (3), (4), and (5) for monthly stock volatility. The table reports the out-of-sample , defined in the percent reduction of mean-squared predictive error (MSPE) of the interest models relative to that of the benchmark of AR (6). The values of Clark and West [45] (CW) tests for the equivalence of MSPEs between the interest models and the benchmark model are given in the parentheses. The asterisks , , and indicate rejections of null hypothesis at 10%, 5%, and 1% significance levels, respectively.