1　　樣本的自協方差函數的通式如下：

2　　其實，後面要計算的自相關函數也可以用自協方差來表示：

 1 TimeSeries = [11.67602657, 5.637492979, 1.375516942, 0.618705492, -0.152047234, -0.508555434, -6.065288121, -9.417602801,  2               -10.47205437, -8.018063902, 0.523277554, 4.86893283, 4.23977562, -10.2344375, -3.463362573, 36.51326577,  3               -8.518370963, -15.37474905, -7.687911176, 4.818978874, 7.876681639, 1.763788865]
 
 4 Zt = []
 5 LZt = []
 6 AutoCovariance = []
 7 # 自協方差存為列表形式，顯示格式如下：
 8 # [γ0,γ1,γ2,γ3,....]
 9 # [γk,....]  k = 0,1,2,3....
10 total = 0
11 i = 1
12 while i < len(TimeSeries):
13     L = TimeSeries[i::]
14     LL = TimeSeries[:-i:]
15     total = total + TimeSeries[i - 1]
16     Zt.append(L)
17     LZt.append(LL)
 
18     i += 1
19 total = total + TimeSeries[-1]
20 avg = total / len(TimeSeries)
21 
22 k = 0
23 result_temp0 = 0
24 # 首先求γ0的值
25 while k < len(TimeSeries):
26     result_temp0 = result_temp0 + pow((TimeSeries[k] - avg), 2)
27     k += 1
28 AutoCovariance.append(result_temp0)
29 print(AutoCovariance)
30 # 顯示結果：
 

31 #[2418.4380925669107]
32 
33 # 然後計算分子
34 p = 0
35 q = 0
36 while p < len(Zt):
37     q = 0
38     result_temp1 = 0
39     while q < len(Zt[p]):
40         result_temp1 = result_temp1 + (Zt[p][q] - avg) * (LZt[p][q] - avg)
41         q += 1
42     AutoCovariance.append(result_temp1)  # 保留小數點後三位
43     p += 1
44 print(AutoCovariance)
45 print(len(AutoCovariance))
46 # 顯示結果：
47 # [2418.4380925669107, 154.73148259271665, -909.2825195711046, -216.01009095585525, 381.064309087456, 253.8899860047866,
48 #  -455.76866093122146, -513.7425279639118, -234.77764765735802, 51.726042700512416, 266.05419016606146, 116.26795577123028,
49 #  -76.63272849007276, -209.6990237967077, 78.50856193561651, 336.9664948029677, -195.8237009651655, -211.6227696432054, -50.67152070500246,
50 #  103.09738426011762, 101.91169142979405, 20.59404564489024]

計量經濟與時間序列_自協方差(AutoCovariance)算法解析(Python)