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

Financial Innovation

Table 5 Comparison results of using volatile 1-year stock data

	GE-NoVaS	GA-NoVaS	P-GA-NoVaS	GARCH-direct
NKE-1step	0.63568	0.63209	0.65594	1.00000
NKE-5steps	0.20171	0.19089	0.22226	1.00000
NKE-30steps	0.00411	0.00278*	0.00340	1.00000
AMZN-1step	0.97099	0.96719	0.90487	1.00000
AMZN-5steps	0.88705	0.88274	0.72850	1.00000
AMZN-30steps	0.58124	0.62863	0.53310	1.00000
IBM-1step	0.80222	0.79823	0.79509	1.00000
IBM-5steps	0.38933	0.37346	0.38413	1.00000
IBM-30steps	0.01143	0.00996*	0.00879	1.00000
MSFT-1step	0.80133	0.79528	0.81582	1.00000
MSFT-5steps	0.35567	0.33419	0.38022	1.00000
MSFT-30steps	0.01342	0.01031*	0.00784	1.00000
SBUX-1step	0.68206	0.67067	0.66743	1.00000
SBUX-5steps	0.24255	0.23072	0.26856	1.00000
SBUX-30steps	0.00499	0.00337*	0.00236	1.00000
KO-1step	0.77906	0.75389	0.77035	1.00000
KO-5steps	0.34941	0.32459	0.33405	1.00000
KO-30steps	0.01820	0.01848	0.01582	1.00000
MCD-1step	0.51755	0.51351	0.56414	1.00000
MCD-5steps	0.10725	0.09714	0.17439	1.00000
MCD-30steps	3.32E−05	2.97E−05*	7.62E−06	1.00000
Tesla-1step	0.90712	0.90250	0.88782	1.00000
Tesla-5steps	0.68450	0.67935	0.66937	1.00000
Tesla-30steps	0.21643	0.21718	0.22395	1.00000
Bitcoin-1step	0.36323	0.36260	0.36326	1.00000
Bitcoin-5steps	0.01319	0.01321	0.01322	1.00000
Bitcoin-30steps	7.75E−17	7.65E−17	7.75E−17	1.00000

As the benchmark is the GARCH-direct method, 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 means that the corresponding method is the optimal choice for this data case. Cell with \(*\) means 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