Long Memory and Fractality in the Universe of Volatility Indices
Table 2
Hurst exponent and fractal dimension values for the nine CBOE volatility indices.
Year
HVIX
HVXN
HVXO
HVXD
HRVX
HVPD
HOVX
HVVIX
HSKEW
Hurst
Fractal
Hurst
Fractal
Hurst
Fractal
Hurst
Fractal
Hurst
Fractal
Hurst
Fractal
Hurst
Fractal
Hurst
Fractal
Hurst
Fractal
2007
0.9913
1.0087
0.9015
1.0985
0.8794
1.1206
0.8998
1.1002
0.9049
1.0951
0.5643
1.4357
0.8516
1.1484
0.9549
1.0451
0.9073
1.0927
0.0002
0.0550
0.0539
0.0545
0.0554
0.0796
0.0688
0.0437
0.0543
2008
0.9992
1.0008
0.9873
1.0127
0.9868
1.0132
0.9888
1.0112
0.9883
1.0117
0.9732
1.0269
0.9883
1.0117
0.9472
1.0528
0.7949
1.2051
0.0000
0.0169
0.0175
0.0150
0.0157
0.0169
0.0155
0.0406
0.0492
2009
0.9949
1.0051
0.9946
1.0054
0.9937
1.0064
0.9990
1.0010
0.9951
1.0049
1.0000
1.0000
0.9906
1.0095
0.9221
1.0780
0.8438
1.1563
0.0069
0.0073
0.0086
0.0000
0.0065
0.0322
0.0128
0.0468
0.0475
2010
0.9709
1.0291
0.9486
1.0514
0.9159
1.0841
0.9415
1.0585
0.9669
1.0331
0.9930
1.0070
0.9315
1.0685
0.8604
1.1396
0.9289
1.0712
0.0329
0.0423
0.0473
0.0439
0.0355
0.0210
0.0446
0.0503
0.0471
2011
0.9920
1.0080
0.9995
1.0006
0.9872
1.0129
0.9892
1.0108
0.9889
1.0112
0.9847
1.0153
0.9240
1.0760
0.8340
1.1660
0.9053
1.0947
0.0110
0.0000
0.0172
0.0146
0.0151
0.0337
0.0464
0.0500
0.0494
2012
0.9617
1.0383
0.9676
1.0324
0.9138
1.0863
0.9148
1.0852
0.9764
1.0236
0.9892
1.0108
0.8144
1.1856
0.9695
1.0305
0.8768
1.1232
0.0378
0.0344
0.0481
0.0477
0.0283
0.0342
0.0463
0.0347
0.0500
2013
0.8366
1.1634
0.8324
1.1676
0.8351
1.1649
0.8205
1.1795
0.9164
1.0836
0.9837
1.0163
0.9560
1.0440
0.8724
1.1276
0.9990
1.0010
0.0504
0.0533
0.0498
0.0528
0.0500
0.0891
0.0381
0.0471
0.0000
2014
0.9826
1.0174
0.9373
1.0627
0.8998
1.1002
0.9226
1.0774
0.8595
1.1405
0.9859
1.0142
0.9943
1.0057
0.9567
1.0433
0.7994
1.2006
0.0221
0.0445
0.0485
0.0477
0.0494
0.0097
0.0077
0.0401
0.0500
2015
0.9301
1.0700
0.9781
1.0219
0.9526
1.0475
0.9648
1.0352
0.9805
1.0195
0.9677
1.0323
0.9788
1.0212
0.9315
1.0685
0.8607
1.1393
0.0468
0.0268
0.0411
0.0362
0.0245
0.0396
0.0261
0.0472
0.0513
2016
0.9840
1.0160
0.9793
1.0207
0.9632
1.0368
0.9667
1.0333
0.9529
1.0471
0.9854
1.0146
0.9912
1.0088
0.9304
1.0696
0.8348
1.1652
0.0208
0.0258
0.0379
0.0357
0.0423
0.0100
0.0119
0.0461
0.0468
2017
0.9581
1.0419
0.8817
1.1184
0.9490
1.0510
0.8560
1.1440
0.9816
1.0184
0.9954
1.0047
0.9625
1.0376
0.9292
1.0709
0.9526
1.0474
0.0412
0.0535
0.0446
0.0526
0.0233
0.0068
0.0358
0.0470
0.0439
2018
0.8875
1.1125
0.8635
1.1365
0.8702
1.1298
0.8532
1.1468
0.9352
1.0649
0.9345
1.0655
0.9995
1.0006
0.7307
1.2693
0.9547
1.0453
0.0443
0.0442
0.0451
0.0451
0.0430
0.0231
0.0000
0.0549
0.0420
2019
0.8075
1.1925
0.8242
1.1758
0.8032
1.1968
0.8395
1.1605
0.8432
1.1568
0.9899
1.0101
0.8208
1.1792
0.8956
1.1044
0.9995
1.0005
0.0484
0.0443
0.0445
0.0436
0.0441
0.0233
0.0464
0.0458
0.0000
2020
0.9538
1.0462
0.8941
1.1059
0.9008
1.0993
0.9133
1.0867
0.9463
1.0537
0.9811
1.0189
0.9825
1.0175
0.9515
1.0485
0.9501
1.0499
0.0447
0.0540
0.0550
0.0548
0.0482
0.0162
0.0229
0.0448
0.0489
Notes: the overall sample period is from October 5, 2007, to October 5, 2020. This table presents the Hurst exponent and fractal dimension for the nine volatility indices, with a fixed window (one calendar year: 1 January to 31 December) using the ARFIMA model and classical box-count estimator of D. Numbers in bold are standard error of the Hurst value.
