Table 3 Extreme values of the states bins for the four discretization approaches with 5 states applied to the Bitcoin returns

Panel A: 1-min interval

quantile

[− 5.974,− 0.066)

[− 0.066,− 0.018)

[− 0.018,0.017)

[0.017,0.065)

[0.065,4.860]

sigma

[− 5.974,− 0.174)

[− 0.174,− 0.058)

[− 0.058,0.058)

[0.058,0.174)

[0.174,4.860]

k-means

[− 5.974,− 0.130)

[− 0.130,− 0.022)

[− 0.022,0.066)

[0.066,0.247)

[0.247,4.860]

GMM

[− 5.974,− 0.065)

[− 0.065, 0.076)

[ 0.076,0.261)

[0.261,0.325)

[0.325,4.860]

Panel B: 1-s interval

quantile

[− 0.4,− 0.005)

[− 0.005, 0.000)

[ 0.000,0.000)

[0.000,0.005)

[0.005,0.472]

sigma

[− 0.4,− 0.023)

[− 0.023,− 0.008)

[− 0.008,0.008)

[0.008,0.023)

[0.023,0.472]

k-means

[− 0.4,− 0.027)

[− 0.027,− 0.006)

[− 0.006,0.011)

[0.011,0.043)

[0.043,0.472]

GMM

[− 0.4,− 0.034)

[− 0.034,− 0.003)

[− 0.003,0.003)

[0.003,0.036)

[0.036,0.472]