Research Article
The Structure of Autocovariance Matrix of Discrete Time Subfractional Brownian Motion
Table 3
The eigenvalues for
and
.
| Eigenvalues | | | | | | | | |
| | 1.7622 | 0.9587 | 0.6917 | 0.5645 | 0.4767 | 0.4949 | 0.5758 | 0.7896 | 44.2 | 106.5 | 328.0 | 1114.9 | 14864.7 | 56663.7 | | |
| | 1.6747 | 0.8565 | 0.5727 | 0.4250 | 0.2708 | 0.2257 | 0.1921 | 0.1675 | 2.0243 | 1.2651 | 1.0483 | 0.9828 | 1.0946 | 1.3023 | 1.7272 | 2.6539 | 65.2 | 159.1 | 491.5 | 1672.2 | 22303.1 | 85024.5 | | |
| | 1.6388 | 0.8185 | 0.5334 | 0.3849 | 0.2303 | 0.1854 | 0.1519 | 0.1269 | 1.8072 | 1.0002 | 0.7255 | 0.5853 | 0.4432 | 0.4036 | 0.3759 | 0.3579 | 2.3187 | 1.6280 | 1.4955 | 1.5388 | 2.0259 | 2.6015 | 3.7024 | 6.0461 | 86.2 | 211.6 | 654.9 | 2229.4 | 29745.5 | | | |
| | 1.6253 | 0.8040 | 0.5181 | 0.3689 | 0.2134 | 0.1680 | 0.1341 | 0.1086 | 1.7163 | 0.9008 | 0.6189 | 0.4726 | 0.3202 | 0.2756 | 0.2428 | 0.2170 | 1.9592 | 1.1711 | 0.9143 | 0.7914 | 0.6848 | 0.6647 | 0.6586 | 0.6634 | 2.6332 | 2.0335 | 2.0185 | 2.2211 | 3.2863 | 4.4486 | 6.6462 | 11.3163 | 107.0 | 263.9 | 818.1 | 2786.6 | 37191.8 | | | |
| | 1.6169 | 0.7953 | 0.5093 | 0.3602 | 0.2052 | 0.1602 | 0.1267 | 0.1008 | 1.6795 | 0.8604 | 0.5756 | 0.4265 | 0.2691 | 0.2221 | 0.1864 | 0.1580 | 1.8090 | 1.0015 | 0.7263 | 0.5856 | 0.4428 | 0.4028 | 0.3740 | 0.3538 | 2.1224 | 1.3607 | 1.1312 | 1.0370 | 0.9950 | 1.0131 | 1.0512 | 1.1094 | 2.9630 | 2.4748 | 2.6099 | 3.0231 | 4.8897 | 6.8923 | 10.6886 | 18.7933 | 127.7 | 316.1 | 981.2 | 3343.8 | 44642.2 | | | |
| | 1.6124 | 0.7906 | 0.5044 | 0.3553 | 0.2004 | 0.1554 | 0.1221 | 0.0956 | 1.6559 | 0.8357 | 0.5502 | 0.4010 | 0.2442 | 0.1978 | 0.1626 | 0.1366 | 1.7459 | 0.9310 | 0.6488 | 0.5014 | 0.3448 | 0.2974 | 0.2609 | 0.2329 | 1.9101 | 1.1141 | 0.8495 | 0.7189 | 0.5959 | 0.5664 | 0.5490 | 0.5396 | 2.2934 | 1.5654 | 1.3727 | 1.3191 | 1.3754 | 1.4548 | 1.5658 | 1.7135 | 3.3053 | 2.9477 | 3.2645 | 3.9403 | 6.8485 | 9.9760 | 15.9484 | 28.7840 | 148.4 | 368.2 | 1144.2 | 3900.9 | 52096.5 | | | |
| | 1.6092 | 0.7873 | 0.5011 | 0.3521 | 0.1974 | 0.1526 | 0.1194 | 0.0931 | 1.6426 | 0.8216 | 0.5356 | 0.3861 | 0.2290 | 0.1828 | 0.1477 | 0.1240 | 1.7051 | 0.8874 | 0.6034 | 0.4547 | 0.2972 | 0.2497 | 0.2135 | 0.1825 | 1.8193 | 1.0105 | 0.7332 | 0.5895 | 0.4381 | 0.3924 | 0.3574 | 0.3303 | 2.0169 | 1.2358 | 0.9860 | 0.8703 | 0.7792 | 0.7677 | 0.7703 | 0.7820 | 2.4707 | 1.7834 | 1.6368 | 1.6363 | 1.8276 | 1.9952 | 2.2138 | 2.4955 | 3.6584 | 3.4491 | 3.9781 | 4.9689 | 9.1732 | 13.7385 | 22.5349 | 41.5840 | 169.0 | 420.3 | 1307.1 | 4458.1 | 59554.7 | | | |
| | 1.6328 | 0.7852 | 0.4990 | 0.3499 | 0.1953 | 0.1506 | 0.1174 | 0.0919 | 1.6071 | 0.8116 | 0.5255 | 0.3760 | 0.2196 | 0.1737 | 0.1392 | 0.1151 | 1.6815 | 0.8621 | 0.5768 | 0.4271 | 0.2684 | 0.2208 | 0.1845 | 0.1531 | 1.7604 | 0.9465 | 0.6650 | 0.5181 | 0.3620 | 0.3147 | 0.2779 | 0.2508 | 1.8974 | 1.0967 | 0.8265 | 0.6890 | 0.5482 | 0.5072 | 0.4767 | 0.4532 | 2.1281 | 1.3653 | 1.1344 | 1.0387 | 0.9931 | 1.0083 | 1.0414 | 1.0888 | 2.6532 | 2.0132 | 1.9220 | 1.9873 | 2.3536 | 2.6395 | 3.0064 | 3.4756 | 4.0210 | 3.9767 | 4.7478 | 6.1060 | 11.8735 | 18.2155 | 30.5512 | 57.4685 | 189.5 | 472.2 | 1469.9 | 5015.3 | 67016.9 | | | |
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