Forecasting Stock Market Volatility: A Combination Approach

Table 6

Out-of-sample forecasting results with different lag lengths.

	WTI	BRT	VIX	WTI + VIX	BRT + VIX	CC ()	CC ()
Out-of-sample forecasting results with lag length 2
	1.41	1.32	10.25	11.18	10.67	10.28	10.18
value	0.0765	0.0821	0.0006	0.0001	0.0002	0.0003	0.0003
Out-of-sample forecasting results with lag length 4
	1.48	1.41	10.36	11.20	10.70	10.33	10.20
value	0.0574	0.0654	0.0004	0.0001	0.0002	0.0003	0.0003
Out-of-sample forecasting results with lag length 6
	1.53	1.44	10.41	11.21	10.73	10.38	10.24
value	0.0574	0.0654	0.0003	0.0001	0.0002	0.0003	0.0003
Out-of-sample forecasting results with lag length 8
	1.50	1.40	10.37	11.17	10.67	10.31	10.21
value	0.0786	0.0766	0.0005	0.0003	0.0003	0.0005	0.0005

Note. This table reports the forecasting results for the predictive regression models for monthly stock volatility with the alternative lag orders: 2, 4, 6, and 8 where the out-of-sample period is 2003 : 01–2018 : 12. The table reports the out-of-sample , defined in the percent reduction of the mean-squared predictive error (MSPE) of the interest models relative to that of the benchmark of AR (). 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.