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Financial Innovation

Table 1 Summary statistics and preliminary analysis

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

 

Bitcoin

Composite

Consumer discretionary

Consumer staples

Energy

Financials

Health Care

Industrials

Info. Technology

Materials

Real Estate

Telecom. Services

Utilities

Summary statistics

Mean

9.43

0.71

0.83

0.61

1.32

0.96

0.71

0.87

0.98

0.89

0.81

0.86

0.76

Deviation

0.83

0.59

0.54

0.47

0.92

0.74

0.5

0.63

0.65

0.57

0.67

0.49

0.65

Skewness

0.65

3.9

3.24

4.52

3.26

3.87

3.83

3.83

3.5

3.85

4.37

3.51

4.69

Kurtosis

2.24

21.66

17.27

26.65

16.4

20.9

20.73

20.76

19.09

20.75

24.32

19.47

26.84

Conditional heteroscedasticity effects

\(ARCH\left( 1 \right)\)

13.88***

45.89***

3.33*

143.91***

0.05

51.71***

15.44***

8.84***

88.24***

2.58

6.05**

71.64***

99.52***

\(ARCH\left( 5 \right)\)

29.08***

25.21***

26.72***

43.06***

1.67

23.08***

10.13***

25.61***

21.96***

13.31***

5.60***

21.73***

63.52***

\(ARCH\left( {10} \right)\)

19.99***

13.99***

15.91***

29.09***

1.53

11.98***

7.58***

16.36***

11.85***

8.25***

2.96***

11.10***

40.67***

First and higher order autocorrelation

\(Q\left( 1 \right)\)

2.15

85.92***

24.35***

109.94***

7.59***

82.48***

49.02***

50.95***

87.94***

49.63***

71.94***

50.73***

94.94***

\(Q\left( 5 \right)\)

28.01***

385.58***

222.12***

478.94***

96.922***

312.26***

225.05***

274.15***

266.14***

195.50***

319.54***

183.19***

518.90***

\(Q\left( {10} \right)\)

47.00***

566.07***

324.58***

682.49***

170.96***

456.86***

381.44***

445.09***

379.3***

306.76***

441.44***

243.13***

791.43***

\(Q^{2} \left( 1 \right)\)

13.77***

44.25***

3.34*

127.53***

0.05

49.59***

15.31***

8.82***

81.96***

2.59

6.05**

67.51***

91.54***

\(Q^{2} \left( 5 \right)\)

204.07***

156.55***

120.86***

298.51***

8.74

172.29***

58.78***

164.59***

127.29***

80.12***

31.20***

131.32***

408.02***

\(Q^{2} \left( {10} \right)\)

419.33***

196.16***

139.09***

430.91***

16.81*

204.49***

106.18***

252.16***

147.59***

108.23***

35.41***

139.23***

563.21***

Persistence

0.999***

0.994***

0.992***

0.994***

0.992***

0.994***

0.993***

0.994***

0.993***

0.993***

0.994***

0.991***

0.995***

Significant break dates (Bai and Perron 2003)

Break_1

–

02/01/2019

02/01/2019

07/05/2018

01/23/2019

01/31/2019

02/01/2019

02/01/2019

02/01/2019

02/01/2019

01/23/2019

07/11/2018

02/11/2019

Break_2

–

02/27/2020

02/27/2020

02/21/2019

03/06/2020

03/02/2020

02/25/2020

03/03/2020

02/25/2020

02/27/2020

02/28/2020

02/28/2019

03/02/2020

Break_3

–

10/08/2020

10/08/2020

02/27/2020

10/21/2020

10/12/2020

10/08/2020

10/13/2020

10/08/2020

10/08/2020

10/23/2020

03/02/2020

10/12/2020

Break_4

–

05/21/2021

05/21/2021

10/08/2020

–

–

05/21/2021

–

05/21/2021

05/20/2021

–

10/12/2020

–

  1. The summaries are done for 1,072 observation points, where ARCH(#), Q(#) and Q2(#) represent the tests for presence of conditional heteroscedasticity, first and higher-order serial correlations, respectively; and statistical significance implying that the tested feature is present in the series, up to the specified lag #. The ***, ** and * denote statistical significance at 1%, 5% and 10% levels, respectively. The break dates are determined using the Bai and Perron (2003) multiple break point test allowing for a maximum of five lags in a regression of each sector stock returns’ volatility on a one period lag of log-transformed Bitcoin prices
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