The predictive power of Bitcoin prices for the realized volatility of US stock sector returns

Bouri, Elie; Salisu, Afees A.; Gupta, Rangan

doi:10.1186/s40854-023-00464-8

Financial Innovation

Table 4 Predictability and forecast evaluation (75:25 data split with GARCH based realized volatility)

From: The predictive power of Bitcoin prices for the realized volatility of US stock sector returns

Sectors	PANEL A	PANEL B Relative RMSE				PANEL C Clark and West (2007)
	Parameter estimate	PANEL B Relative RMSE				PANEL C Clark and West (2007)
		In sample	Out-of-sample			In sample	Out-of-sample
			\(\varvec{h} = {\mathbf{30}}\)	\(\varvec{h} = {\mathbf{60}}\)	\(\varvec{h} = {\mathbf{120}}\)		\(\varvec{h} = {\mathbf{30}}\)	\(\varvec{h} = {\mathbf{60}}\)	\(\varvec{h} = {\mathbf{120}}\)
Composite	− 3.36E−05*** [3.51E−07]	9.67E−01	9.66E−01	9.65E−01	9.63E−01	3.71E−08*** [2.72E−09]	3.65E−08*** [2.63E−09]	3.57E−08*** [2.54E−09]	3.50E−08*** [2.38E−09]
Consumer discretionary	− 4.86E−05*** [8.47E−07]	9.79E−01	9.78E−01	9.79E−01	9.78E−01	2.19E−08*** [9.74E−10]	2.17E−08*** [9.41E−10]	2.09E−08*** [9.30E−10]	2.07E−08*** [8.77E−10]
Consumer staples	− 2.97E−05*** [4.33E−07]	9.65E−01	9.80E−01	1.02E+00	1.08E+00	1.34E−08*** [2.20E−09]	1.46E−08*** [2.14E−09]	1.57E−08*** [2.08E−09]	1.84E−08*** [1.98E−09]
Energy	− 1.41E−04*** [2.21E−07]	9.27E−01	9.30E−01	9.33E−01	9.41E−01	3.68E−07*** [1.48E−08]	3.51E−07*** [1.46E−08]	3.37E−07*** [1.43E−08]	3.05E−07*** [1.39E−08]
Financials	− 1.41E−04*** [3.71E−06]	1.01E+00	1.01E+00	1.01E+00	1.01E+00	2.21E−08*** [7.10E−09]	2.35E−08*** [6.85E−09]	2.45E−08*** [6.62E−09]	2.87E−08*** [6.21E−09]
Health Care	− 1.07E−04*** [9.80E−07]	9.79E−01	9.78E−01	9.77E−01	9.73E−01	9.63E−09*** [3.92E−10]	9.69E−09*** [3.79E−10]	9.72E−09*** [3.66E−10]	1.00E−08*** [3.45E−10]
Industrials	− 1.22E−05*** [5.91E−07]	9.97E−01	9.95E−01	9.95E−01	9.93E−01	1.81E−08*** [1.93E−09]	1.92E−08*** [1.87E−09]	2.00E−08*** [1.82E−09]	2.26E−08*** [1.74E−09]
Info. Technology	2.60E−06*** [1.40E−07]	9.97E−01	9.96E−01	9.96E−01	9.96E−01	4.03E−08*** [2.54E−09]	3.92E−08*** [2.46E−09]	3.79E−08*** [2.38E−09]	3.60E−08*** [2.24E−09]
Materials	− 4.26E−05*** [4.09E−07]	8.69E−01	8.71E−01	8.78E−01	8.89E−01	1.16E−07*** [1.85E−08]	1.13E−07*** [1.79E−08]	1.11E−07*** [1.72E−08]	1.09E−07*** [1.61E−08]
Real Estate	9.67E−06*** [1.86E−07]	1.01E+00	1.01E+00	1.01E+00	1.01E+00	8.24E−08*** [1.31E−08]	8.13E−08*** [1.26E−08]	8.23E−08*** [1.22E−08]	1.38E−08*** [3.46E−09]
Telecommunications	− 5.80E−05*** [8.16E−07]	9.86E−01	9.87E−01	9.87E−01	9.87E−01	1.08E−08*** [5.67E−10]	1.04E−08*** [5.52E−10]	9.98E−09*** [5.37E−10]	9.28E−09*** [5.09E−10]
Utilities	− 4.27E−05*** [1.21E−08]	9.67E−01	9.68E−01	9.72E−01	9.77E−01	1.72E−08*** [9.53E−10]	3.23E−08*** [2.94E−09]	3.31E−08*** [2.84E−09]	3.58E−08*** [2.68E−09]

The results presented on the table are from the estimation of the WN-Type distributed lag predictive model for Bitcoin prices using realized volatilities of US sectoral stock returns singly as predictors, while simultaneously accounting for inherent persistence, endogeneity, conditional heteroscedasticity and structural breaks. The table comprises three panels: PANEL A presents the in-sample predictability of the realized volatility of US sectoral stock returns for log-transformed Bitcoin price; PANEL B presents the relative root mean square error that compares our WN-Type distributed lag model with the historical average model; while PANEL C presents the Clark and West (2007) test statistics that entails a pairwise comparison of our predictive model with the benchmark historical average model. Under Panels A and C, each cell contain the estimates and the corresponding standard errors in square brackets; while the *** indicates statistical significance at 1% level. Under the PANEL B, values less than unity indicate preference of our predictive model over the benchmark Historical average model; while under PANEL C, our predictive model is adjudged the preferred when the CW statistic is positive and statistically significant

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