计量经济与时间序列_自协方差(AutoCovariance)算法解析(Python)

Posted 2020-10-26 时海涛 | Thomas.Shih

1　　样本的自协方差函数的通式如下：

2　　其实，后面要计算的自相关函数也可以用自协方差来表示：

 1 # @author: "Thomas.Shih"
 2 # @date: 2018/3/5 0005
 3 # !/usr/bin/python3
 4 # -*- coding:utf-8 -*-
 5 TimeSeries = [11.67602657, 5.637492979, 1.375516942, 0.618705492, -0.152047234, -0.508555434, -6.065288121, -9.417602801, \\
 6               -10.47205437, -8.018063902, 0.523277554, 4.86893283, 4.23977562, -10.2344375, -3.463362573, 36.51326577, \\
 7               -8.518370963, -15.37474905, -7.687911176, 4.818978874, 7.876681639, 1.763788865]
 8 Zt = []
 9 LZt = []
10 AutoCovariance = []
11 # 自协方差存为列表形式，显示格式如下：
12 # [γ0,γ1,γ2,γ3,....]
13 # [γk,....]  k = 0,1,2,3....
14 total = 0
15 i = 1
16 while i < len(TimeSeries):
17     L = TimeSeries[i::]
18     LL = TimeSeries[:-i:]
19     total = total + TimeSeries[i - 1]
20     Zt.append(L)
21     LZt.append(LL)
22     i += 1
23 total = total + TimeSeries[-1]
24 avg = total / len(TimeSeries)
25 
26 k = 0
27 result_temp0 = 0
28 # 首先求γ0的值
29 while k < len(TimeSeries):
30     result_temp0 = result_temp0 + pow((TimeSeries[k] - avg), 2)
31     k += 1
32 AutoCovariance.append(result_temp0/len(TimeSeries))
33 # print(AutoCovariance)
34 # 显示结果：
35 #[2418.4380925669107]
36 
37 # 然后计算分子
38 p = 0
39 q = 0
40 length = 0
41 while p < len(Zt):
42     q = 0
43     result_temp1 = 0
44     while q < len(Zt[p]):
45         result_temp1 = result_temp1 + (Zt[p][q] - avg) * (LZt[p][q] - avg)
46         q += 1
47     # print(result_temp1)
48     # print(len(Zt)-p)
49     AutoCovariance.append(result_temp1/len(TimeSeries))
50     p += 1
51 print(AutoCovariance)
52 # print(len(AutoCovariance))
53 # print(len(Zt))
54 
55 # 显示结果：
56 # [109.92900420758684, 7.033249208759847, -41.331023616868386, -9.818640497993421, 17.321104958520728, 11.540453909308482,
57 # -20.71675731505552, -23.35193308926872, -10.671711257152637, 2.3511837591142006, 12.09337228027552, 5.284907080510467,
58 # -3.4833058404578527, -9.53177380894126, 3.568570997073478, 15.31665885468035, -8.901077316598432, -9.619216801963882,
59 # -2.303250941136475, 4.686244739096256, 4.632349610445184, 0.9360929838586473]