книги / Статистический анализ временных рядов
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703 |
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Таблица А.2.1 (продолжение) |
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в . |
Pt |
•sxs |
-0.7, p z — 0.49. ( Выборка № Z Вольда) |
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— |
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Корреляции |
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А |
ChiС0 |
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h |
СнЮо |
h |
ChIC0 |
А |
C J C 0 |
1 |
0.5113 |
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26 |
-0 .0 1 1 0 |
51 |
-0 .0 3 7 6 |
76 |
0.1672 |
2 |
—0.0473 |
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27 |
-0 .0 8 7 7 |
52 |
0.1676 |
77 |
0.0497 |
3 |
-0 .3001 |
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28 |
0.0399 |
53 |
0.1763 |
78 |
-0 .0 9 2 0 |
4 |
-0 .2 5 4 9 |
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29 |
0.1242 |
54 |
0.0466 |
79 |
-0 .2 3 6 6 |
5 |
-0 .0 1 8 7 |
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30 |
-0 .0 0 0 5 |
55 |
-0 .1 0 6 4 |
80 |
-0 .1 1 0 8 |
6 |
0.1613 |
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31 |
-0 .1 5 8 3 |
56 |
-0 .2 4 1 9 |
81 |
0.1287 |
7 |
0.0997 |
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32 |
-0 .2 0 7 5 |
57 |
-0 .1 2 9 2 |
82 |
0.1821 |
8 |
-0 .0 1 7 4 |
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33 |
-0 .0 8 2 6 |
58 |
0.0752 |
83 |
0.0397 |
9 |
-0 .1 0 2 6 |
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34 |
0.1879 |
59 |
0.1397 |
84 |
-0 .1851 |
10 |
-0 .0 5 6 2 |
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35 |
0.2784 |
60 |
0.1258 |
85 |
-0 .2 5 3 3 |
И |
0.0579 |
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36 |
0.1175 |
61 |
0.0377 |
86 |
-0 .1 0 0 9 |
12 |
0.1689 |
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37 |
-0 .0 8 6 4 |
62 |
0.0106 |
87 |
0.1201 |
13 |
0.1357 |
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38 |
-0 .1 6 4 6 |
63 |
-0 .0 2 4 3 |
88 |
0.2470 |
14 |
-0 .0 4 3 5 |
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39 |
-0 .1 0 7 8 |
64 |
-0 .0 4 5 4 |
89 |
0.1869 |
15 |
-0 .1 5 5 7 |
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40 |
0.0305 |
65 |
0.0227 |
90 |
-0 .0 2 8 6 |
16 |
' -0 .1 3 2 9 |
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41 |
0.1551 |
66 |
-0 .0 3 6 9 |
91 |
-0 .1 0 8 8 |
17 |
-0 .0 1 0 3 |
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42 |
0.1619 |
67 |
-0 .1 3 2 6 |
92 |
-0 .0 5 5 2 |
18 |
0.0901 |
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43 |
0.0052 |
68 |
-0 .1 0 8 9 |
93 |
0.0818 |
19 |
0.0174 |
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44 |
-0 .1 3 5 9 |
69 |
0.0122 |
94 |
0.1601 |
20 |
-0 .1 1 0 8 |
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45 |
-0 .1 1 1 4 |
70 |
0.0313 |
95 |
0.0282 |
21 |
-0 .2 3 2 9 |
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46 |
0.0724 |
71 |
-0 .0 1 6 0 |
96 |
-0 .1 7 6 6 |
22 |
-0 .1 4 4 9 |
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47 |
0.2417 |
72 |
-0 .0 4 7 6 |
97 |
-0 .2 5 6 3 |
23 |
0.0673 |
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48 |
0.1541 |
73 |
-0 .0523 |
98 |
-0 .1 8 6 0 |
24 |
0.1277 |
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49 |
0.0337 |
74 |
-0 .0 2 3 4 |
99 |
0.0093 |
25 |
0.0629 |
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50 |
-0 .1 0 0 0 |
75 |
0.1654 |
100 |
0.1701 |
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С0 = |
1.0837 |
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704
Таблица А.2.2 (продолжение)
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\с. pt |
т - 0 . 9 , Рг = 0.81. (Вы борка № 1 Вольда) |
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Корреляции |
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h |
С л/Со |
h |
C J C 0 |
h |
c hic 0 |
h |
e y e * |
1 |
0.5011 |
26 |
-0.1094 |
51 |
-0.1857 |
76 |
-0.0906 |
2 |
—0.3858 |
27 |
-0.4210 |
52 |
-0.2829 |
77 |
-0.1983 |
3 |
-0.7726 |
28 |
-0.3308 |
53 |
-0.1160 |
78 |
-0.0742 |
4 |
-0.3711 |
29 |
0.0565 |
54 |
0.1330 |
79 |
0.1669 |
5 |
0.3371 |
30 |
0.3689 |
55 |
0.2395 |
80 |
0.2586 |
6 |
0.6311 |
31 |
0.3321 |
56 |
0.1117 |
81 |
0.0823 |
7 |
0.2843 |
32 |
-0.0101 |
Si |
-0.0918 |
82 |
-0.2097 |
8 |
-0.2853 |
33 |
-0.3317 |
58 |
-0.1697 |
83 |
-0.3125 |
9 |
-0.5178 |
34 |
-0.3582 |
59 |
-0.0819 |
84 |
-0.1023 |
10 |
-0.2291 |
35 |
-0.0762 |
60 |
0.0897 |
85 |
0.2119 |
11 |
0.2813 |
36 |
0.2481 |
61 |
0.1699 |
86 |
0.3365 |
12 |
0.5056 |
37 |
0.3487 |
62 |
0.1023 |
87 |
0.1426 |
13 |
0.2361 |
38 |
0.1280 |
65 |
-0.0524 |
88 |
-0.2054 |
14 |
-0.2348 |
39 |
-0.2110 |
64 |
-0.1794 |
89 |
-0.3622 |
15 |
-0.4581 |
40 |
-0.3080 |
65 |
-0.1506 |
90 |
-0.1475 |
16 |
-0.2402 |
41 |
-0.0980 |
66 |
-0.0135 |
91 |
0.1975 |
17 |
0.1880 |
42 |
0.1736 |
67 |
0.1098 |
92 |
0.2815 |
18 |
0.4203 |
43 |
0.2451 |
68 |
0.1333 |
93 |
0.0362 |
19 |
0.2518 |
44 |
0.0404 |
69 |
0.0326 |
94 |
-0.2656 |
20 |
-0.1416 |
45 |
-0.2251 |
70 |
-0.1287 |
95 |
-0.2595 . |
21 |
-0.3953 |
46 |
-0.2614 |
71 |
-0.2059 |
96 |
0.0260 |
22 |
-0.2578 |
47 |
-0.0504 |
72 |
-0.1163 |
97 |
0.2556 |
23 |
0.1495 |
48 |
0.2085 |
73 |
0.0803 |
98 |
0.2187 |
24 |
0.4303 |
49 |
0.2903 |
74 |
0.1935 |
99 |
-0.0230 |
25 |
0.3123 |
50 |
0.0979 |
75 |
0.1078 |
100 |
-0.2242 |
Со = 1.2224
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705 |
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Т абли ц а А . 2 .3 |
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НОРМИРОВАННАЯ ВЫБОРОЧНАЯ СПЕКТРАЛЬНАЯ ПЛОТНОСТЬ |
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A . |
рх в -0.25, Рг ш 0.0625. (Вы борка № 1 Вольда) |
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2ir |
(2irk\ |
2тг |
(2irk\ |
2п |
/2ггк\ |
2ir /2чгк\ |
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к |
\200/ |
Q |
к |
С0 |
к |
С о \2 0 0 |
/ |
Q |
\200/ |
\200/ |
О1.5087
1 |
1.5029 |
26 |
0.5243 |
51 |
0.1236 |
76 |
0.2538 |
2 |
0.5606 |
27 |
0.9970 |
52 |
1.7227 |
77 |
3.8915 |
3 |
1.0695 |
28 |
0.4683 |
53 |
0.1063 |
78 |
0.2601 |
4 |
3.8996 |
29 |
2.2405 |
54 |
0.4195 |
79- |
0.4844 |
5 |
3.3980 |
30 |
1.5876 |
55 |
0.5291 |
80 |
1.9956 |
6 |
0.6895 |
31 |
0.7753 |
56 |
0.3043 |
81 |
0.0868 |
7 |
0.8402 |
32 |
1.1055 |
57 |
0.1007 |
82 |
0.3921 |
8 |
1.7680 |
33 |
1.0494 |
58 |
1.5100 |
83 |
0.1838 |
9 |
1.9260 |
34 |
6.0570 |
59 |
0.3572 |
84 |
0.0284 |
10 |
0.1815 |
35 |
0.5693 |
60 |
0.0249 |
85 |
0.7412 |
11 |
0.7431 |
36 |
0.4151 |
61 |
2.2647 |
86 |
0.1808 |
12 |
0.6993 |
37 |
0.0128 |
62 |
1.2785 |
87 |
0.3800 |
13 |
3.0737 |
38 |
0.1682 |
63 |
0.8900 |
88 |
0.1344 |
14 |
0.9221 |
39 |
0.2226 |
64 |
1.0273 |
89 |
0.0748 |
15 |
0.6206 |
40 |
0.3264 |
65 |
0.5327 |
90 |
1.6157 |
16 |
5.8050 |
41 |
1.6880 |
66 |
0.3617 |
91 |
0.2269 |
17 |
1.2231 |
42 |
1.0313 |
67 |
0.0274 |
92 |
0.3397 |
18 |
1.4275 |
43 |
0.3604 |
68 |
0.8100 |
93 |
1.2194 |
19 |
1.0515 |
44 |
0.3232 |
69 |
3.5494 |
94 |
0.7040 |
20 |
1.2780 |
45 |
0.3270 |
70 |
1.1472 |
95 |
0.5200 |
21 |
1.1196 |
46 |
0.9212 |
71 |
0.3027 |
96 |
0.0886 |
22 |
1.1128 |
47 |
0.9579 |
72 |
0.7541 |
97 |
0.7174 |
23 |
1.7322 |
48 |
0.7229 |
73 |
0.2701 |
98 |
0.5979 |
24 |
3.0603 |
49 |
0.2063 |
74 |
0.2194 |
99 |
1.6979 |
25 |
0.4891 |
50 |
0.1732 |
75 |
0.1076 |
100 |
0.4220 |
706
Таблица А.2.3 (продолжение)
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В. |
« -0.7, |
h = 0.49. (Выборка N 4 Вольда) |
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2п |
/2тг*\ |
2п |
(гпк\ |
2п |
/2пк\ |
к |
\200/ |
к |
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к |
к |
Со |
’с01\ ш ) |
Q |
\200/ |
О1.1189
1 |
0.9664 |
26 |
1.0541 |
51 |
0.0877 |
76 |
2 |
0.4030 |
27 |
1.8778 |
52 |
1.1702 |
77 |
3 |
0.7823 |
28 |
1.0098 |
53 |
0.0617 |
78 |
4 |
2.6466 |
29 |
5.0956 |
54 |
0.2595 |
79 |
5 |
2.3570 |
30 |
3.5765 |
55 |
0.3281 |
80 |
б |
0.5149 |
31 |
1.7633 |
56 |
0.1525 |
81 |
7 |
0.5969 |
32 |
2.4765 |
57 |
0.0426 |
82 |
8 |
1.4281 |
33 |
2.4593 |
58 |
0.7922 |
83 |
9 |
1.5064 |
34 |
15.0876 |
59 |
0.1625 |
84 |
10 |
0.1523 |
35 |
1.2011 |
60 |
0.0080 |
85 |
11 |
0.6217 |
36 |
0.8276 |
61 |
1.0016 |
86 |
12 |
0.6459 |
37 |
0.0150 |
62 |
0.5806 |
87 |
13 |
2.8789 |
38 |
0.3897 |
63 |
0.3768 |
88 |
14 |
0.8066 |
39 |
0.4910 |
64 |
0.3807 |
89 |
15 |
0.5380 |
40 |
0.5550 |
65 |
0.2053 |
90 |
16 |
6.0875 |
41 |
2.7688 |
66 |
0.1410 |
91 |
17 |
1.4132 |
42 |
1.4481 |
67 |
0.0067 |
92 |
18 |
1.5177 |
43 |
0.5413 |
68 |
0.2936 |
93 |
19 |
1.2673 |
44 |
0.4815 |
69 |
1.2444 |
94 |
20 |
1.6300 |
45 |
0.3843 |
70 |
0.3671 |
95 |
21 |
1.5202 |
46 |
1.0904 |
71 |
0.0891 |
96 |
22 |
1.7333 |
47 |
0.9157 |
72 |
0.2535 |
97 |
23 |
2.5668 |
48 |
0.7222 |
73 |
0.0851 |
98 |
24 |
4.8883 |
49 |
0.2032 |
74 |
0.0706 |
99 |
25 |
0.7624 |
50 |
0.1366 |
75 |
0.0374 |
100 |
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Т а б ли ц а |
А .2 .3 |
(продолж ение) |
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С, |
рх 9 |
-0 .9 , Рц« 0.81. (Выборка №1 бомба) |
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к |
2тг |
(Ътк\ |
к |
2я |
/2тгк\ |
к |
2тг !2vk\ |
к |
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CV |
\200/ |
Q |
\200/ |
Q A M O / |
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О |
0.1835 |
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1 |
0.5806 |
26 |
3.6521 |
51 |
0.0902 |
76 |
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2 |
0.5042 |
27 |
2.6660 |
52 |
0.4664 |
77 |
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3 |
0.5937 |
28 |
0.9321 |
53 |
0.0246 |
78 |
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4 |
0.2787 |
29 |
0.6410 |
54 |
0.2046 |
79 |
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5 |
0.0850 |
30 |
0.1841 |
55 |
0.0311 |
80 |
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6 |
0.0430 |
31 |
4.7018 |
56 |
0.0621 |
81 |
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7 |
0.4200 |
32 |
15.7755 |
57 |
0.1469 |
82 |
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8 |
0.2520 |
33 |
24.4907 |
58 |
0.1169 |
83 |
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9 |
0.0175 |
34 |
6.2684 |
59 |
0.0315 |
84 |
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10 |
0.7423 |
35 |
8.8254 |
60 |
0.1073 |
85 |
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11 |
0.1452 |
36 |
0.1490 |
61 |
0.0048 |
86 |
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12 |
0.1305 |
37 |
7.4089 |
62 |
0.0045 |
87 |
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13 |
0.2365 |
38 |
0.0970 |
63 |
0.0708 |
88 |
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14 |
0.0259 |
39 |
2.6194 |
64 |
0.2145 |
# 89 |
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15 |
0.0354 |
40 |
1.3477 |
65 |
0.0586 |
90 |
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16 |
1.2747 |
41 |
0.2229 |
66 |
0.0730 |
91 |
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17 |
1.0938 |
42 |
1.8378 |
67 |
0.0349 |
92 |
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18 |
0.1598 |
43 |
0.9971 |
68 |
0.1006 |
93 |
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19 |
0.0107 |
44 |
0.2457 |
69 |
0.1786 |
94 |
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20 |
0.0607 |
45 |
0.1095 |
70 |
0.1164 |
95 |
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21 |
2.6171 |
46 |
0.5497 |
71 |
0.0238 |
96 |
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22 |
0.3760 |
47 |
0.5808 |
72 |
0.0073 |
97 |
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23 |
0.2992 |
48 |
1.0833 |
73 |
0.2072 |
98 |
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24 |
0 7754 |
49 |
0.1481 |
74 |
0.0119 |
99 |
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25 |
0.0146 |
50 |
0.3898 |
75 |
0.0025 |
100 |
708
Таблица А.2.4
НОРМИРОВАННЫЕ ОЦЕНКИ БАРТЛЕТТА ДЛЯ СПЕКТРАЛЬНОЙ ПЛОТНОСТИ
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А . к |
« -0.25, /32 = 0.0625. |
(Выборка№2 Вольда) |
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к - / т |
( — ) |
к |
Г \200/ |
к ^ f J — ) |
к - / г ( — ) |
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С0 |
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т \200/ |
С0 |
С0 |
Т\ 200/ |
Со |
\200/ |
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0 |
1.5349 |
26 |
1.2662 |
51 |
0.8224 |
76 |
0.7793 |
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1 |
1.5345 |
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2 |
1.5334 |
27 |
1.2455 |
52 |
0.8153 |
77 |
0.7755 |
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, |
3 |
1.5316 |
28 |
1.2244 |
53 |
0.8092 |
78 |
0.7713 |
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4 |
1.5291 |
29 |
1.2030 |
54 |
0.8041 |
79 |
0.7665 |
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5 |
1.5258 |
30 |
1.1813 |
55 |
0.7999 |
80 |
0.7613 |
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6 |
1.5217 |
31 |
1.1594 |
56 |
0.7965 |
81 |
0.7558 |
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7 |
1.5169 |
32 |
1.1374 |
57 |
0.7940 |
82 |
0.7498 |
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8 |
1.5112 |
33 |
1.1155 |
58 |
0.7921 |
83 |
0.7436 |
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9 |
1.5048 |
34 |
1.0936 |
59 |
0.7908 |
84 |
0.7372 |
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10 |
1.4975 |
35 |
1.0720 |
60 |
0.7900 |
85 |
0.7306 |
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11 |
1.4894 |
36 |
1.0507 |
61 |
0.7897 |
86 |
0.7240 |
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12 |
1.4805 |
37 |
1.0298 |
62 |
0.7898 |
87 |
0.7173 |
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13 |
1.4707 |
38 |
1.0094 |
63 |
0.7900 |
88 |
0.7107 |
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14 |
1.4600 |
39 |
0.9896 |
64 |
0.7905 |
89 |
0.7043 |
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15 |
1.4484 |
40 |
0.9705 |
65 |
0.7909 |
90 |
0.6982 |
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16 |
1.4360 |
41 |
0.9521 |
66 |
0.7914 |
91 |
0.6923 |
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17 |
1.4226 |
42 |
0.9346 |
67 |
0.7917 |
92 |
0.6869 |
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18 |
1,4084 |
43 |
0.9180 |
68 |
0.7919 |
93 |
0.6819 |
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19 |
1.3933 |
44 |
0.9023 |
69 |
0.7918 |
94 |
0.6775 |
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20 |
1.3774 |
45 |
0.8877 |
70 |
0.7913 |
95 |
0.6736 |
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21 |
1.3607 |
46 |
0.8741 |
71 |
0.7905 |
96 |
0.6704 |
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22 |
1,3432 |
47 |
0.8616 |
72 |
0.7892 |
97 |
0.6679 |
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23 |
1.3249 |
48 |
0.8501 |
73 |
0.7875 |
98 |
0.6660 |
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24 |
1.3060 |
49 |
0.8398 |
74 |
0.7853 |
99 |
0.6649 |
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25 |
1.2864 |
50 |
0.8306 |
75 |
0.7826 |
100 |
0.6646 |
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709 |
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Таблица А .2А |
(продолжение) |
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в. рх = -0 .7, |
р2 « 0.49 |
(Выборка №2 Вольда) |
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к |
\200/ |
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С0 |
J \200/ |
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С0 |
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О |
1.2499 |
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1 |
1.2506 |
26 |
|
2.2623 |
51 |
0.5270 |
76 |
0.2781 |
2 |
1.2522 |
27 |
|
2.4148 |
52 |
0.4735 |
77 |
0.2712 |
3 |
1.2530 |
28 |
|
2.5912 |
53 |
0.4326 |
78 |
0.2621 |
4 |
1.2515 |
29 |
|
2.7682 |
54 |
0.4062 |
79 |
0.2497 |
5 |
1.2466 |
30 |
|
2.9190 |
55 |
0.3936 |
80 |
0.2341 |
6 |
1.2389 |
31 |
|
3.0173 |
56 |
0.3920 |
81 |
0.2160 |
7 |
1.2314 |
32 |
|
3.0422 |
57 |
0.3974 |
82 |
0.1969 |
8 |
1.2289 |
33 |
|
2.9823 |
58 |
0.4058 |
83 |
0.1788 |
9 |
1.2378 |
34 |
|
2.8375 |
59 |
0.4139 |
84 |
0.1633 |
10 |
1.2648 |
35 |
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2.6194 |
60 |
0.4197 |
85 |
0.1519 |
11 |
1.3152 |
36 |
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2.3489 |
61 |
0.4223 |
86 |
0.1452 |
12 |
1.3912 |
37 |
• 2.0529 |
62 |
0.4218 |
87 |
0.1430 |
|
13 |
1.4909 |
38 |
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1.7591 |
63 |
0.4184 |
88 |
0.1447 |
14 |
1.6077 |
39 |
|
1.4920 |
64 |
0.4128 |
89 |
0.1491 |
15 |
1.7315 |
40 |
|
1.2691 |
65 |
0.4052 |
90 |
0.1551 |
16 |
1.8497 |
41 |
|
1.0987 |
66 |
0.3956 |
91 |
0.1618 |
17 |
1.9500 |
42 |
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0.9798 |
67 |
0.3839 |
92 |
0.1687 |
18 |
2.0228 |
43 |
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0.9037 |
68 |
0.3702 |
93 |
0.1755 |
19 |
2.0639 |
44 |
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0.8572 |
69 |
0.3551 |
94 |
0.1821 |
20 |
2.0756 |
45 |
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0.8254 |
70 |
0.3393 |
95 |
0.1886 |
21 |
2.0673 |
46 |
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0.7952 |
71 |
0.3241 |
96 |
0.1949 |
22 |
2.0538 |
47 |
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0.7579 |
72 |
0.3105 |
97 |
0.2004 |
23 |
2.0526 |
48 |
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0.7096 |
73 |
0.2994 |
98 |
0.2049 |
24 |
2.0803 |
49 |
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0.6515 |
74 |
0.2908 |
99 |
0.2078 |
25 |
2.1489 |
50 |
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0.5885 |
75 |
0.2841 |
100 |
0.2087 |
712
Рис. А .2 .6 .
Нормированная выборочная спектральная плотность и нормированная оценка Бартлетта для ряда с у — 0.9.
Рис. А .2 .7 .
Нормированные спектральные плотности исходного процесса (сплошная линия) и двух подобранных процессов для у = 0.25.