相关性不在 -1 到 1 之间的 Hayashi yoshida 估计器

Question

我采集了两个带有时间戳的时间序列数据，总共 141 个数据点。我发现它们之间的实际相关性约为 0.97。现在我找到了相关性的 Hayashi Yoshida 估计器。它大于 3。Hy 相关性估计器应该给出的相关性接近于实际相关性。

虽然这个 HY 相关性估计器不像实际相关性那样从-1 到 1 有界，但仍然不应该给它一个更好的估计吗？我的数据集是不是太小了？

Hayashi yohida 相关估计器在http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2225753 中给出 作为

数据是： 1,100,62
2,100.5,62
3,100.6,62
4,100.6,62.05
5,100.6,62.1
6,100.6,62.15
7,100.6,62.2
8,100.6,62.25
9,100.6,62.3
10,100.6,62.35
11,100.6,62.4
12,100.6,62.45
13,100.6,62.5
14,100.6,62.55
15,100.6,62.6
16,101.1,62.6
17,101.2,62.6
18,101.2,62.65
19,101.2,62.7
20,101.2,62.75
21,101.2,62.8
22,101.2,62.85
23,101.2,62.9
24,101.2,62.95
25,101.2,63
26,101.2,63.05
27,101.2,63.1
28,101.2,63.15
29,101.2,63.2
30,101.7,63.2
31,101.8,63.2
32,101.8,63.25
33,101.8,63.3
34,101.8,63.35
35,101.8,63.4
36,101.8,63.45
37,101.8,63.5
38,101.8,63.55
39,101.8,63.6
40,101.8,63.65
41,101.8,63.7
42,101.8,63.75
43,101.8,63.8
44,102.3,63.8
45,102.4,63.8
46,102.4,63.85
47,102.4,63.9
48,102.4,63.95
49,102.4,64
50,102.4,64.05
51,102.4,64.1
52,102.4,64.15
53,102.4,64.2
54,102.4,64.25
55,102.4,64.3
56,102.4,64.35
57,102.4,64.4
58,102.9,64.4
59,103,64.4
60,103,64.45
61,103,64.5
62,103,64.55
63,103,64.6
64,103,64.65
65,103,64.7
66,103,64.75
67,103,64.8
68,103,64.85
69,103,64.9
70,103,64.95
71,103,65
72,103.5,65
73,103.6,65
74,103.6,65.05
75,103.6,65.1
76,103.6,65.15
77,103.6,65.2
78,103.6,65.25
79,103.6,65.3
80,103.6,65.35
81,103.6,65.4
82,103.6,65.45
83,103.6,65.5
84,103.6,65.55
85,103.6,65.6
86,104.1,65.6
87,104.2,65.6
88,104.2,65.65
89,104.2,65.7
90,104.2,65.75
91,104.2,65.8
92,104.2,65.85
93,104.2,65.9
94,104.2,65.95
95,104.2,66
96,104.2,66.05
97,104.2,66.1
98,104.2,66.15
99,104.2,66.2
100,104.7,66.2
101,104.8,66.2
102,104.8,66.25
103,104.8,66.3
104,104.8,66.35
105,104.8,66.4
106,104.8,66.45
107,104.8,66.5
108,104.8,66.55
109,104.8,66.6
110,104.8,66.65
111,104.8,66.7
112,104.8,66.75
113,104.8,66.8
114,105.3,66.8
115,105.4,66.8
116,105.4,66.85
117,105.4,66.9
118,105.4,66.95
119,105.4,67
120,105.4,67.05
121,105.4,67.1
122,105.4,67.15
123,105.4,67.2
124,105.4,67.25
125,105.4,67.3
126,105.4,67.35
127,105.4,67.4
128,105.9,67.4
129,106,67.4
130,106,67.45
131,106,67.5
132,106,67.55
133,106,67.6
134,106,67.65
135,106,67.7
136,106,67.75
137,106,67.8
138,106,67.85
139,106,67.9
140,106,67.95
141,106,68

Answer 1

那些重复的值看起来像是用于填充“缺失”数据的事后常量插值。第二个系列也是一样，看起来没有太多真实数据，只是线性插值（虽然我不太了解三元组）。如果确实如此，则可能是问题所在，您应该（至少）计算实际数据的回报的实现方差（而不是每日方差），而不是人工插值。就像现在一样，它会人为地给出一个低方差来解释过度相关。

要测试 H-Y，您最好生成两个具有正常增量的相关布朗路径，然后为每个系列随机选择一些值。首先是更长的时间间隔。