Table 3.
BDS test results, January 1, 2020–April 15, 2021.
| Cryptos | m | (1) | (2) | (3) | (4) |
|---|---|---|---|---|---|
| BTC | 2 | 2.9444 (0.0000) |
2.8544 (0.0000) |
2.6355 (0.0000) |
2.1587 (0.0000) |
| 3 | 3.1339 (0.0000) |
2.4114 (0.0000) |
2.1990 (0.0000) |
1.9987 (0.0000) |
|
| ETH | 2 | 2.4558 (0.0000) |
2.5094 (0.0000) |
2.5302 (0.0000) |
2.4289 (0.0000) |
| 3 | 2.7203 (0.0000) |
2.8894 (0.0000) |
2.7510 (0.0000) |
2.7279 (0.0000) |
|
| BNB | 2 | 5.4762 (0.0000) |
6.9610 (0.0000) |
7.2520 (0.0000) |
7.1507 (0.0000) |
| 3 | 6.6441 (0.0000) |
7.9203 (0.0000) |
7.4799 (0.0000) |
6.8558 (0.0000) |
|
| XRP | 2 | 7.9473 (0.0000) |
6.2280 (0.0000) |
6.1843 (0.0000) |
5.3456 (0.0000) |
| 3 | 10.3679 (0.0000) |
7.7647 (0.0000) |
7.1115 (0.0000) |
6.3731 (0.0000) |
|
| USDT | 2 | 11.1999 (0.0000) |
10.6716 (0.0000) |
10.6391 (0.0000) |
8.3295 (0.0000) |
| 3 | 11.6899 (0.0000) |
11.0857 (0.0000) |
11.0759 (0.0000) |
8.4664 (0.0000) |
|
| DOGE | 2 | 10.6368 (0.0000) |
9.0406 (0.0000) |
8.5708 (0.0000) |
7.8353 (0.0000) |
| 3 | 11.2474 (0.0000) |
9.2907 (0.0000) |
9.1241 (0.0000) |
8.2433 (0.0000) |
|
| ADA | 2 | 2.5430 (0.0001) |
3.3264 (0.0008) |
3.0314 (0.0024) |
2.4549 (0.0014) |
| 3 | 2.4869 (0.0002) |
3.2976 (0.0009) |
3.1062 (0.0018) |
2.6604 (0.0078) |
|
| BCH | 2 | 5.5857 (0.0000) |
4.4405 (0.0000) |
2.6581 (0.0000) |
1.3245 (0.0000) |
| 3 | 5.2543 (0.0000) |
4.3471 (0.0000) |
3.0287 (0.0000) |
1.7869 (0.0000) |
|
| LTC | 2 | 3.5150 (0.0004) |
3.9805 (0.0000) |
3.1962 (0.0013) |
2.0667 (0.0038) |
| 3 | 3.4456 (0.0005) |
3.4398 (0.0000) |
2.9187 (0.0035) |
1.7721 (0.0076) |
|
| LINK | 2 | 2.0084 (0.0004) |
2.5722 (0.0012) |
2.8375 (0.0045) |
2.5628 (0.0010) |
| 3 | 2.2614 (0.0002) |
2.9298 (0.0033) |
3.5832 (0.0030) |
3.2739 (0.0010) |
|
| VET | 2 | 3.0629 (0.0002) |
2.7179 (0.0065) |
3.2055 (0.0013) |
3.6333 (0.0002) |
| 3 | 3.8079 (0.0001) |
3.4912 (0.0004) |
3.8690 (0.0001) |
3.8415 (0.0001) |
|
| XLM | 2 | 4.8490 (0.0000) |
4.5723 (0.0000) |
4.5440 (0.0000) |
5.0854 (0.0000) |
| 3 | 5.8883 (0.0000) |
5.5943 (0.0000) |
5.3281 (0.0000) |
5.7661 (0.0000) |
|
| THETA | 2 | 3.9868 (0.0000) |
4.2423 (0.0000) |
3.7313 (0.0000) |
3.3431 (0.0000) |
| 3 | 4.5573 (0.0000) |
3.4912 (0.0000) |
4.4230 (0.0000) |
3.7923 (0.0000) |
|
| TRX | 2 | 6.1200 (0.0000) |
5.3054 (0.0000) |
4.2226 (0.0000) |
3.4537 (0.0000) |
| 3 | 7.9228 (0.0000) |
6.3764 (0.0000) |
5.0925 (0.0000) |
3.9047 (0.0000) |
|
| XMR | 2 | 4.5862 (0.0000) |
3.8254 (0.0001) |
3.1035 (0.0019) |
2.7417 (0.0006) |
| 3 | 4.1952 (0.0000) |
3.6294 (0.0002) |
2.6828 (0.0073) |
2.4519 (0.0011) |
|
| LUNA | 2 | 4.5730 (0.0000) |
4.2742 (0.0000) |
4.3347 (0.0000) |
3.9288 (0.0000) |
| 3 | 7.8450 (0.0000) |
5.7269 (0.0000) |
4.8076 (0.0000) |
4.2964 (0.0000) |
|
| EOS | 2 | 4.2419 (0.0000) |
4.5851 (0.0000) |
5.0691 (0.0000) |
4.8544 (0.0000) |
| 3 | 5.4566 (0.0000) |
5.1855 (0.0000) |
5.2238 (0.0000) |
4.6803 (0.0000) |
|
| MIOTA | 2 | 2.2292 (0.0002) |
3.3372 (0.0000) |
4.2766 (0.0000) |
4.0858 (0.0000) |
| 3 | 3.0465 (0.0002) |
4.5497 (0.0000) |
5.7261 (0.0000) |
5.5685 (0.0000) |
|
| CRO | 2 | 3.0030 (0.0020) |
3.5625 (0.0003) |
3.5455 (0.0000) |
4.2989 (0.0000) |
| 3 | 3.8226 (0.0001) |
4.5618 (0.0000) |
4.1952 (0.0003) |
4.3306 (0.0000) |
|
| BTT | 2 | 5.7594 (0.0000) |
4.2001 (0.0000) |
3.5203 (0.0000) |
3.1646 (0.0000) |
| 3 | 7.0120 (0.0000) |
5.1449 (0.0000) |
4.4588 (0.0000) |
4.2519 (0.0000) |
|
| HT | 2 | 8.8155 (0.0000) |
7.7846 (0.0000) |
8.4584 (0.0000) |
8.4622 (0.0000) |
| 3 | 9.7909 (0.0000) |
8.1637 (0.0000) |
8.4173 (0.0000) |
8.7302 (0.0000) |
|
| XTZ | 2 | 3.6261 (0.0000) |
3.7040 (0.0000) |
3.5781 (0.0000) |
3.4627 (0.0000) |
| 3 | 4.5142 (0.0000) |
4.5377 (0.0000) |
4.5720 (0.0000) |
3.9142 (0.0000) |
|
| ETC | 2 | 5.8804 (0.0000) |
4.9576 (0.0000) |
4.4929 (0.0000) |
4.3038 (0.0000) |
| 3 | 7.2440 (0.0000) |
5.7141 (0.0000) |
4.8466 (0.0000) |
3.9393 (0.0000) |
|
| ALGO | 2 | 2.2928 (0.0002) |
2.4566 (0.0000) |
2.0716 (0.0020) |
2.4315 (0.0004) |
| 3 | 2.7630 (0.0001) |
2.4352 (0.0000) |
2.4203 (0.0012) |
2.4306 (0.0005) |
|
| DAI | 2 | 8.7258 (0.0000) |
8.3196 (0.0000) |
9.7448 (0.0000) |
10.1192 (0.0000) |
| 3 | 15.1222 (0.0000) |
11.3237 (0.0000) |
11.5154 (0.0000) |
11.4856 (0.0000) |
|
| RUNE | 2 | 3.2956 (0.0009) |
2.8392 (0.0040) |
2.5374 (0.0011) |
1.9622 (0.0049) |
| 3 | 3.3511 (0.0008) |
3.3151 (0.0009) |
3.2717 (0.0001) |
2.7881 (0.0053) |
|
| DASH | 2 | 5.3407 (0.0000) |
5.4767 (0.0000) |
5.8032 (0.0000) |
4.7984 (0.0000) |
| 3 | 5.8277 (0.0000) |
6.1344 (0.0000) |
6.3439 (0.0000) |
5.1384 (0.0000) |
|
| CHZ | 2 | 7.7515 (0.0000) |
7.9099 (0.0000) |
7.0493 (0.0000) |
6.8442 (0.0000) |
| 3 | 9.4837 (0.0000) |
8.7427 (0.0000) |
7.7078 (0.0000) |
7.0862 (0.0000) |
|
| XEM | 2 | 6.6542 (0.0000) |
5.7325 (0.0000) |
4.2819 (0.0000) |
3.0915 (0.0000) |
| 3 | 8.2862 (0.0000) |
6.7722 (0.0000) |
5.1389 (0.0000) |
3.2580 (0.0000) |
|
| STX | 2 | 2.2920 (0.0021) |
2.1225 (0.0033) |
2.2529 (0.0024) |
2.2573 (0.0000) |
| 3 | 3.9890 (0.0000) |
4.3345 (0.0000) |
4.2216 (0.0000) |
3.5092 (0.0000) |
Note: The entries are the BDS test (Broock et al., 1996) statistics, and p-values are within brackets. The parameter m is the embedding dimension, and is the epsilon values for close points.