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Velocity

Published onNov 23, 2020
Velocity
·

To this end, we first review the most common proxies in , then implement the proposed estimators to calculate velocity measures for Bitcoin in , and finally run tests in to evaluate the goodness of fit of the proxies w.r.t. the measures.

McircWba0{M_{\mathtt{circWba}}}\gets {0} return McircWba{M_{\mathtt{circWba}}}

McircMca0{M_{\mathtt{circMca}}}\gets {0} McircMca(t)0{M_{\mathtt{circMca}}}(t) \gets {0} valOutbreak(t)0{\mathtt{valOut}}^\mathtt{break}(t) \gets {0} OtOtOselfchurn{\mathbb{O}}'_{t} \gets{{\mathbb{O}}_{t}\setminus{}O^{{\mathtt{selfchurn}}}} valOuttoOthers(t)oOtvalOut(o){\mathtt{valOut}}^{\mathtt{toOthers}}(t) \gets{\sum_{o\in{}{\mathbb{O}}'_{t}} {\mathtt{valOut}}(o)} Itsort(type)It sorted ascending (\acs*fifo)/descending (\acs*lifo) according to type and thus generation time of inputs{\mathbb{I}^{\mathtt{sort}}_{t}}(\mathtt{type}) \gets{{\mathbb{I}_{\mathtt{t}}}\ \text{sorted ascending (\acs*{fifo})/descending (\acs*{lifo}) according to $\mathtt{type}$ and thus generation time of inputs}}
McircMcaMcircMca+McircMca(t){M_{\mathtt{circMca}}}\gets{{M_{\mathtt{circMca}}}+ {M_{\mathtt{circMca}}}(t)}[algo:code_mcirc_mc_break]

return McircMca{M_{\mathtt{circMca}}}

1 Mcirc <- 0

2 foreach t E Tp


The measure puts larger weight on the reactivation of long-dormant coins compared to ones frequently spun, a feature clearly differing from the concept of velocity.


Obs.

Mean

Med.

Min.

Max.

Std. Dev.

Kurtosis

VcddappV^{\mathtt{app}}_{\mathtt{cdd}}

2174.00

9.78

5.72

0.87

361.99

16.22

137.39

VturnappV^{\mathtt{app}}_{\mathtt{turn}}

2174.00

98.66

80.74

1.63

2635.37

93.81

255.22

VcircMcaFifomsrV^{\mathtt{msr}}_{\mathtt{circMcaFifo}}

2174.00

6.78

6.09

1.52

57.10

3.49

41.05

VcircMcaLifomsrV^{\mathtt{msr}}_{\mathtt{circMcaLifo}}

2174.00

6.78

6.09

1.52

57.10

3.49

41.05

VcircWbamsrV^{\mathtt{msr}}_{\mathtt{circWba}}

2174.00

5.83

5.22

1.49

48.99

3.05

40.44

VtrivmsrV^{\mathtt{msr}}_{\mathtt{triv}}

2174.00

0.11

0.08

0.02

4.46

0.13

577.05

VtotalmsrV^{\mathtt{msr}}_{\mathtt{total}}

2174.00

0.09

0.07

0.02

1.03

0.07

33.66

Table 1: Descriptives for velocity proxies and measures with p==1p = \ell = 1 day for 2013-06-01 to 2019-06-01.


The mz regressions are in line with the evidence in prior sections. Again, the trivial measure approximates the more sophisticated velocity measures better than the two commonly used proxy variables.

Approximation

Estimator

MAE

MSE

MAE

MSE

MAE

MSE

MAE

MSE

VcddappV^{\mathtt{app}}_{\mathtt{cdd}}

VtotalmsrV^{\mathtt{msr}}_{\mathtt{total}}

1405.30

1405.30

152.42

30.15

1356.97

1356.97

116.79

28.06

VcddappV^{\mathtt{app}}_{\mathtt{cdd}}

VcircWbamsrV^{\mathtt{msr}}_{\mathtt{circWba}}

1611.26

1611.26

210.77

41.95

1600.15

1600.15

135.49

33.55

VcddappV^{\mathtt{app}}_{\mathtt{cdd}}

VcircMcaLifomsrV^{\mathtt{msr}}_{\mathtt{circMcaLifo}}

1607.60

1607.60

221.03

43.47

1623.72

1623.72

136.76

33.48

VcddappV^{\mathtt{app}}_{\mathtt{cdd}}

VcircMcaFifomsrV^{\mathtt{msr}}_{\mathtt{circMcaFifo}}

1607.61

1607.61

221.03

43.47

1623.72

1623.72

136.76

33.48

VturnappV^{\mathtt{app}}_{\mathtt{turn}}

VtotalmsrV^{\mathtt{msr}}_{\mathtt{total}}

1570.56

1570.56

129.35

16.85

1470.08

1470.08

116.05

14.50

VturnappV^{\mathtt{app}}_{\mathtt{turn}}

VcircWbamsrV^{\mathtt{msr}}_{\mathtt{circWba}}

1328.73

1328.73

^{\dag} 120.34

^{\dag} 14.95

1542.02

1542.02

121.99

16.33

VturnappV^{\mathtt{app}}_{\mathtt{turn}}

VcircMcaLifomsrV^{\mathtt{msr}}_{\mathtt{circMcaLifo}}

1373.43

1373.43

^{\dag} 129.71

^{\dag} 16.09

1549.60

1549.60

122.28

16.01

VturnappV^{\mathtt{app}}_{\mathtt{turn}}

VcircMcaFifomsrV^{\mathtt{msr}}_{\mathtt{circMcaFifo}}

1373.40

1373.40

^{\dag} 129.71

^{\dag} 16.09

1549.61

1549.61

122.28

16.01

VtrivappV^{\mathtt{app}}_{\mathtt{triv}}

VtotalmsrV^{\mathtt{msr}}_{\mathtt{total}}

^{\dag} 381.20

^{\dag} 381.20

^{\dag} 85.24

^{\dag} 7.32

^{\dag} 306.69

^{\dag} 306.69

^{\dag} 35.09

^{\dag} 4.60

VtrivappV^{\mathtt{app}}_{\mathtt{triv}}

VcircWbamsrV^{\mathtt{msr}}_{\mathtt{circWba}}

^{\dag} 892.30

^{\dag} 892.30

143.68

15.71

^{\dag} 838.69

^{\dag} 838.69

^{\dag} 69.11

^{\dag} 8.65

VtrivappV^{\mathtt{app}}_{\mathtt{triv}}

VcircMcaLifomsrV^{\mathtt{msr}}_{\mathtt{circMcaLifo}}

^{\dag} 912.54

^{\dag} 912.54

156.52

17.52

^{\dag} 864.98

^{\dag} 864.98

^{\dag} 70.60

^{\dag} 8.55

VtrivappV^{\mathtt{app}}_{\mathtt{triv}}

VcircMcaFifomsrV^{\mathtt{msr}}_{\mathtt{circMcaFifo}}

^{\dag} 912.55

^{\dag} 912.55

156.52

17.52

^{\dag} 864.99

^{\dag} 864.99

^{\dag} 70.60

^{\dag} 8.55

Table 2: Mean absolute error for normalized data of approximation methods compared to measurement methods with p==1p = \ell = 1 day. Proxy-variables in 1 % Model Confidence Set marked by †.

Approximation

Estimator

Radj2R^{2}_{adj}

α\alpha

pαp^{\alpha}

β\beta

pβp^{\beta}

pFTestp^{F-Test}

Radj2R^{2}_{adj}

α\alpha

pαp^{\alpha}

β\beta

pβp^{\beta}

pFTestp^{F-Test}

Δ\Delta VcddappV^{\mathtt{app}}_{\mathtt{cdd}}

Δ\Delta VtotalmsrV^{\mathtt{msr}}_{\mathtt{total}}

0.00

0.00

0.99

0.05

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

0.00

0.00

0.99

0.05

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

Δ\Delta VcddappV^{\mathtt{app}}_{\mathtt{cdd}}

Δ\Delta VcircWbamsrV^{\mathtt{msr}}_{\mathtt{circWba}}

0.00

0.00

0.99

0.00

0.97

0.00^{\ast}^{\ast}^{\ast}

0.00

0.00

0.99

0.00

0.97

0.00^{\ast}^{\ast}^{\ast}

Δ\Delta VcddappV^{\mathtt{app}}_{\mathtt{cdd}}

Δ\Delta VcircMcaLifomsrV^{\mathtt{msr}}_{\mathtt{circMcaLifo}}

0.00

0.00

0.99

-0.01

0.67

0.00^{\ast}^{\ast}^{\ast}

0.00

0.00

0.99

-0.01

0.67

0.00^{\ast}^{\ast}^{\ast}

Δ\Delta VcddappV^{\mathtt{app}}_{\mathtt{cdd}}

Δ\Delta VcircMcaFifomsrV^{\mathtt{msr}}_{\mathtt{circMcaFifo}}

0.00

0.00

0.99

-0.01

0.67

0.00^{\ast}^{\ast}^{\ast}

0.00

0.00

0.99

-0.01

0.67

0.00^{\ast}^{\ast}^{\ast}

Δ\Delta VturnappV^{\mathtt{app}}_{\mathtt{turn}}

Δ\Delta VtotalmsrV^{\mathtt{msr}}_{\mathtt{total}}

0.11

0.00

0.99

0.30

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

0.11

0.00

0.99

0.26

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

Δ\Delta VturnappV^{\mathtt{app}}_{\mathtt{turn}}

Δ\Delta VcircWbamsrV^{\mathtt{msr}}_{\mathtt{circWba}}

0.13

0.00

0.99

0.37

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

0.13

0.00

0.99

0.34

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

Δ\Delta VturnappV^{\mathtt{app}}_{\mathtt{turn}}

Δ\Delta VcircMcaLifomsrV^{\mathtt{msr}}_{\mathtt{circMcaLifo}}

0.13

0.00

0.99

0.37

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

0.13

0.00

0.99

0.34

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

Δ\Delta VturnappV^{\mathtt{app}}_{\mathtt{turn}}

Δ\Delta VcircMcaFifomsrV^{\mathtt{msr}}_{\mathtt{circMcaFifo}}

0.13

0.00

0.99

0.37

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

0.13

0.00

0.99

0.34

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

Δ\Delta VtrivappV^{\mathtt{app}}_{\mathtt{triv}}

Δ\Delta VtotalmsrV^{\mathtt{msr}}_{\mathtt{total}}

0.53

0.00

1.00

1.07

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

0.53

0.00

1.00

0.80

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

Δ\Delta VtrivappV^{\mathtt{app}}_{\mathtt{triv}}

Δ\Delta VcircWbamsrV^{\mathtt{msr}}_{\mathtt{circWba}}

0.35

0.00

1.00

1.01

0.00^{\ast}^{\ast}^{\ast}

0.90

0.35

0.00

1.00

0.79

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

Δ\Delta VtrivappV^{\mathtt{app}}_{\mathtt{triv}}

Δ\Delta VcircMcaLifomsrV^{\mathtt{msr}}_{\mathtt{circMcaLifo}}

0.34

0.00

1.00

0.99

0.00^{\ast}^{\ast}^{\ast}

0.89

0.34

0.00

1.00

0.78

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

Δ\Delta VtrivappV^{\mathtt{app}}_{\mathtt{triv}}

Δ\Delta VcircMcaFifomsrV^{\mathtt{msr}}_{\mathtt{circMcaFifo}}

0.34

0.00

1.00

0.99

0.00^{\ast}^{\ast}^{\ast}

0.89

0.34

0.00

1.00

0.78

0.00^{\ast}^{\ast}^{\ast}

0.00^{\ast}^{\ast}^{\ast}

Table 3: Model Confidence Set regressions for standardized and normalized approximation and measurement data with p==1p = \ell = 1 day.


Summary of on-chain velocity measures and proxy-variables

L0.1C0.15C0.15C0.12C0.12C0.12C0.12C0.12 & &
Type & & &
Notation & Vcddapp ⁣p{{V^{{\mathtt{app}}}_{\mathtt{cdd}}}_{\!{p}}}& Vturnappp{{V^{{\mathtt{app}}}_{\mathtt{turn}}}_{{p}}}& Vtrivmsrp{{V_\mathtt{triv}^{\mathtt{msr}}}_{p}}& Vtotalmsr{V_\mathtt{total}^{\mathtt{msr}}}& VcircWbamsrp[]{{V_{\mathtt{circWba}}^{\mathtt{msr}}}_{{p}[{\ell}]}}& VcircMcaLifomsrp[]{{V_{\mathtt{circMcaLifo}}^{\mathtt{msr}}}_{{p}[{\ell}]}}& VcircMcaFifomsrp[]{{V_{\mathtt{circMcaFifo}}^{\mathtt{msr}}}_{{p}[{\ell}]}}
Description & Coin days destroyed& Turnover& Trivial velocity measure& Velocity measure based on total money supply& Based on money in effective circulation using the Whole Bill Approach& Based on money in effective circulation using the Moved Coin Approach (FIFO)& Based on money in effective circulation using the Moved Coin Approach (LIFO)
Formula & tTpcdd(t)\sum_{t\in{\mathbb{T}_{p}}} \mathtt{cdd}(t)& 1dormpδ\frac{1}{\mathtt{dorm}_{p}} \cdot \delta& Pp,TpMtotalp\frac{\langle{P_{p}}',{T_{p}}'\rangle}{{{M_\mathtt{total}}_{p}}}& Pp,TpMtotalp\frac{\langle{P_{p}},{T_{p}}\rangle}{{{M_\mathtt{total}}_{p}}}& Pp,TpMcircWbamsrp[]\frac{\langle{P_{p}},{T_{p}}\rangle}{{{M_{\mathtt{circWba}}^{\mathtt{msr}}}_{{p}[{\ell}]}}}& Pp,TpMcircMcaLifomsrp[]\frac{\langle{P_{p}},{T_{p}}\rangle}{{{M_{\mathtt{circMcaLifo}}^{\mathtt{msr}}}_{{p}[{\ell}]}}}& Pp,TpMcircMcaFifomsrp[]\frac{\langle{P_{p}},{T_{p}}\rangle}{{{M_{\mathtt{circMcaFifo}}^{\mathtt{msr}}}_{{p}[{\ell}]}}}
Related Section& 9.1.1& 9.1.2& 6& 6& 8.2& 8.2& 8.2
Sources & Bitcointalk.org, 2011& [1]& [2]& [3][4]& novel& novel& novel
Considered in & [5][6][7][8][9][10][11]& [1]& [2]& [3][4]& & &




tt

\hdots\hdots{}

an individual transaction

Tp{\mathbb{T}_{p}}

\hdots\hdots{}

the set of all transactions in period p{p}

cdd(t)\mathtt{cdd}(t)

\hdots\hdots{}

coin days destroyed for transaction tt as defined in Section 9.1

dormp\mathtt{dorm}_{p}

\hdots\hdots{}

dormancy in period p{p} as defined in Section 9.1.2

δ\delta

\hdots\hdots{}

the period for which an approximated turnover per coin in circulation is calculated

Pp,Tp\langle{P_{p}}',{T_{p}}'\rangle

\hdots\hdots{}

the inflated price-sum

Pp,Tp\langle{P_{p}},{T_{p}}\rangle

\hdots\hdots{}

the deflated price-sum

Mtotalp{{M_\mathtt{total}}_{p}}

\hdots\hdots{}

the complete, ever mined coin supply

McircWbamsrp[]{{M_{\mathtt{circWba}}^{\mathtt{msr}}}_{{p}[{\ell}]}}

\hdots\hdots{}

money in effective circulation using the Whole Bill Approach

McircMcaFifomsrp[]{{M_{\mathtt{circMcaFifo}}^{\mathtt{msr}}}_{{p}[{\ell}]}}

\hdots\hdots{}

money in effective circulation using the Moved Coin Approach adopting first-in-first-out assignment between inputs and outputs

McircMcaLifomsrp[]{{M_{\mathtt{circMcaLifo}}^{\mathtt{msr}}}_{{p}[{\ell}]}}

\hdots\hdots{}

money in effective circulation using the Moved Coin Approach adopting last-in-first-out assignment between inputs and outputs

Descriptives of the entirety of raw data


Obs.

Mean

Med.

Min.

Max.

Std. Dev.

Kurtosis

McircMcaFifo^{\ast} M_{\mathtt{circMcaFifo}}

2174.00

0.20

0.18

0.05

0.60

0.08

1.35

McircMcaLifo^{\ast} M_{\mathtt{circMcaLifo}}

2174.00

0.20

0.18

0.05

0.60

0.08

1.35

McircWba^{\ast} M_{\mathtt{circWba}}

2174.00

0.23

0.21

0.06

0.66

0.09

0.77

Mtotal^{\ast} M_{\mathtt{total}}

2174.00

15.12

15.63

11.23

17.73

1.88

-1.04

PUSD/BTCP^{\mathtt{USD}/\mathtt{BTC}}

2174.00

2525.95

645.16

67.81

19535.70

3387.80

3.17

Vol.(deflated)^{\ast} \mathtt{Vol.(deflated)}

2174.00

1.37

1.10

0.21

12.03

1.05

20.32

Vol.(inflated)^{\ast} \mathtt{Vol.(inflated)}

2174.00

1.64

1.28

0.26

21.84

1.45

60.21

VcddappV^{\mathtt{app}}_{\mathtt{cdd}}

2174.00

9.67

5.72

0.87

171.96

14.48

52.80

VturnappV^{\mathtt{app}}_{\mathtt{turn}}

2174.00

97.92

80.74

1.63

1036.72

78.87

29.82

VcircMcaFifomsrV^{\mathtt{msr}}_{\mathtt{circMcaFifo}}

2174.00

6.76

6.09

1.52

41.67

3.36

24.24

VcircMcaLifomsrV^{\mathtt{msr}}_{\mathtt{circMcaLifo}}

2174.00

6.77

6.09

1.52

41.67

3.36

24.24

VcircWbamsrV^{\mathtt{msr}}_{\mathtt{circWba}}

2174.00

5.82

5.22

1.49

36.34

2.95

26.05

VtrivmsrV^{\mathtt{msr}}_{\mathtt{triv}}

2174.00

0.11

0.08

0.02

1.42

0.09

66.46

VtotalmsrV^{\mathtt{msr}}_{\mathtt{total}}

2174.00

0.09

0.07

0.02

0.76

0.07

22.90

[tbl:appendix_desc_other]

Descriptives of the normalized proxy-variables and measurements


Obs.

Mean

Med.

Min.

Max.

Std. Dev.

Kurtosis

VcddappV^{\mathtt{app}}_{\mathtt{cdd}}

2174.00

0.02

0.01

0.00

1.00

0.04

137.39

VturnappV^{\mathtt{app}}_{\mathtt{turn}}

2174.00

0.04

0.03

0.00

1.00

0.04

255.22

VcircMcaFifomsrV^{\mathtt{msr}}_{\mathtt{circMcaFifo}}

2174.00

0.09

0.08

0.00

1.00

0.06

41.05

VcircMcaLifomsrV^{\mathtt{msr}}_{\mathtt{circMcaLifo}}

2174.00

0.09

0.08

0.00

1.00

0.06

41.05

VcircWbamsrV^{\mathtt{msr}}_{\mathtt{circWba}}

2174.00

0.09

0.08

0.00

1.00

0.06

40.44

VtrivmsrV^{\mathtt{msr}}_{\mathtt{triv}}

2174.00

0.02

0.01

0.00

1.00

0.03

577.05

VtotalmsrV^{\mathtt{msr}}_{\mathtt{total}}

2174.00

0.07

0.06

0.00

1.00

0.07

33.66

[tbl:appendix_desc_other_norm]

Descriptives of the standardized proxy-variables and measurements


Obs.

Mean

Med.

Min.

Max.

Std. Dev.

Kurtosis

VcddappV^{\mathtt{app}}_{\mathtt{cdd}}

2174.00

0.00

-0.27

-0.61

11.20

1.00

52.80

VturnappV^{\mathtt{app}}_{\mathtt{turn}}

2174.00

0.00

-0.22

-1.22

11.90

1.00

29.82

VcircMcaFifomsrV^{\mathtt{msr}}_{\mathtt{circMcaFifo}}

2174.00

0.00

-0.20

-1.56

10.38

1.00

24.24

VcircMcaLifomsrV^{\mathtt{msr}}_{\mathtt{circMcaLifo}}

2174.00

0.00

-0.20

-1.56

10.38

1.00

24.24

VcircWbamsrV^{\mathtt{msr}}_{\mathtt{circWba}}

2174.00

0.00

-0.20

-1.47

10.34

1.00

26.05

VtrivmsrV^{\mathtt{msr}}_{\mathtt{triv}}

2174.00

0.00

-0.24

-0.94

14.24

1.00

66.46

VtotalmsrV^{\mathtt{msr}}_{\mathtt{total}}

2174.00

-0.00

-0.25

-1.11

10.23

1.00

22.90

[tbl:appendix_desc_other_stand]

Correlations of the entirety of raw data

















VtrivmsrV^{\mathtt{msr}}_{\mathtt{triv}}

1

0.86

0.73

0.72

0.72

0.19

0.54

1

0.15

0.52

0.52

0.52

0.99

0.85

-0.07

VtotalmsrV^{\mathtt{msr}}_{\mathtt{total}}

0.86

1

0.84

0.83

0.83

0.22

0.44

0.86

0.18

0.62

0.62

0.61

0.87

0.99

-0.05

VcircWbamsrV^{\mathtt{msr}}_{\mathtt{circWba}}

0.73

0.84

1

0.99

0.99

0.02

0.55

0.73

0.18

0.2

0.2

0.18

0.74

0.84

-0.07

VcircMcaLifomsrV^{\mathtt{msr}}_{\mathtt{circMcaLifo}}

0.72

0.83

0.99

1

1

0.03

0.53

0.72

0.24

0.19

0.19

0.2

0.74

0.84

0.01

VcircMcaFifomsrV^{\mathtt{msr}}_{\mathtt{circMcaFifo}}

0.72

0.83

0.99

1

1

0.03

0.54

0.72

0.24

0.19

0.19

0.2

0.74

0.84

0.01

VcddappV^{\mathtt{app}}_{\mathtt{cdd}}

0.19

0.22

0.02

0.03

0.03

1

-0.3

0.19

0.17

0.43

0.43

0.44

0.21

0.24

0.17

VturnappV^{\mathtt{app}}_{\mathtt{turn}}

0.54

0.44

0.55

0.53

0.54

-0.3

1

0.54

0

0.04

0.04

0.02

0.52

0.41

-0.24

VtrivappV^{\mathtt{app}}_{\mathtt{triv}}

1

0.86

0.73

0.72

0.72

0.19

0.54

1

0.15

0.52

0.52

0.52

0.99

0.85

-0.07

MtotalM_{\mathtt{total}}

0.15

0.18

0.18

0.24

0.24

0.17

0

0.15

1

0.3

0.3

0.38

0.24

0.29

0.64

McircMcaLifoM_{\mathtt{circMcaLifo}}

0.52

0.62

0.2

0.19

0.19

0.43

0.04

0.52

0.3

1

1

0.99

0.54

0.64

0.09

McircMcaFifoM_{\mathtt{circMcaFifo}}

0.52

0.62

0.2

0.19

0.19

0.43

0.04

0.52

0.3

1

1

0.99

0.54

0.64

0.09

McircWbaM_{\mathtt{circWba}}

0.52

0.61

0.18

0.2

0.2

0.44

0.02

0.52

0.38

0.99

0.99

1

0.54

0.63

0.18

Vol.(inflated)\mathtt{Vol.(inflated)}

0.99

0.87

0.74

0.74

0.74

0.21

0.52

0.99

0.24

0.54

0.54

0.54

1

0.87

0

Vol.(deflated)\mathtt{Vol.(deflated)}

0.85

0.99

0.84

0.84

0.84

0.24

0.41

0.85

0.29

0.64

0.64

0.63

0.87

1

0.03

PUSD/BTCP^{\mathtt{USD}/\mathtt{BTC}}

-0.07

-0.05

-0.07

0.01

0.01

0.17

-0.24

-0.07

0.64

0.09

0.09

0.18

0

0.03

1

[tbl:corrtable_all]

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