A model-free approach to do long-term volatility forecasting and its variants

Financial Innovation

Table 2 Comparison results of using 2-year data

Previous 2-year	GE	GA	P-GA	GARCH	More recent 2-year	GE	GA	P-GA	GARCH
AAPL-1step	0.99795	0.99236	0.97836	1.00000	AAPL-1step	0.80150	0.79899	0.79915	1.00000
AAPL-5steps	1.04919	1.04800	0.96999	1.00000	AAPL-5steps	0.41405	0.42338	0.40427	1.00000
AAPL-30steps	1.12563	1.21986	0.96174	1.00000	AAPL-30steps	0.13207	0.14046	0.14543	1.00000
BAC-1step	0.99889	1.00396	1.02780	1.00000	BAC-1step	0.98393	0.99164	0.96542	1.00000
BAC-5steps	1.04424	1.02185	0.99399	1.00000	BAC-5steps	0.98885	1.01480	0.91857	1.00000
BAC-30steps	1.32452	1.13887*	1.00363	1.00000	BAC-30steps	1.14111	1.03657	0.88596	1.00000
MSFT-1step	0.98785	0.98598	0.96185	1.00000	MSFT-1step	0.98405	0.98630	0.96374	1.00000
MSFT-5steps	1.00236	1.00096	0.95271	1.00000	MSFT-5steps	0.65027	0.67005	0.64278	1.00000
MSFT-30steps	1.25272	1.09881*	0.88515	1.00000	MSFT-30steps	0.19767	0.20060	0.21473	1.00000
MCD-1step	1.01845	1.00789	0.99005	1.00000	MCD-1step	0.99631	0.99539	0.98035	1.00000
MCD-5steps	1.11249	1.07748	0.97777	1.00000	MCD-5steps	0.95403	0.95327	0.91317	1.00000
MCD-30steps	1.76385	1.69757	0.99418	1.00000	MCD-30steps	0.75730	0.75361	0.74557	1.00000

Column names “GA” and “GE” represent GE-NoVaS and GA-NoVaS methods, respectively; “GARCH” means the GARCH-direct method; and “P-GA” means the P-GA-NoVaS method. The benchmark is the GARCH-direct method, so numerical values in the table corresponding to the GARCH-direct method are 1. Other numerical values are relative performance compared to the GARCH-direct method. The bold value indicates that the corresponding method is the optimal choice for this data case. A cell with \(*\) indicates that the GA-NoVaS method is at least 10\(\%\) better than the GE-NoVaS method, or inversely, the GE-NoVaS method is at least 10\(\%\) better