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

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：

# @author: "Thomas.Shih"
# @date: 2018/3/5 0005
# !/usr/bin/python3
# -*- coding:utf-8 -*-
TimeSeries = [11.67602657, 5.637492979, 1.375516942, 0.618705492, -0.152047234, -0.508555434, -6.065288121, -9.417602801, 
              -10.47205437, -8.018063902, 0.523277554, 4.86893283, 4.23977562, -10.2344375, -3.463362573, 36.51326577, 
              -8.518370963, -15.37474905, -7.687911176, 4.818978874, 7.876681639, 1.763788865]
Zt = []
LZt = []
AutoCovariance = []
# 自协方差存为列表形式，显示格式如下：
# [γ0,γ1,γ2,γ3,....]
# [γk,....]  k = 0,1,2,3....
total = 0
i = 1
while i < len(TimeSeries):
    L = TimeSeries[i::]
    LL = TimeSeries[:-i:]
    total = total + TimeSeries[i - 1]
    Zt.append(L)
    LZt.append(LL)
    i += 1
total = total + TimeSeries[-1]
avg = total / len(TimeSeries)

k = 0
result_temp0 = 0
# 首先求γ0的值
while k < len(TimeSeries):
    result_temp0 = result_temp0 + pow((TimeSeries[k] - avg), 2)
    k += 1
AutoCovariance.append(result_temp0/len(TimeSeries))
# print(AutoCovariance)
# 显示结果：
#[2418.4380925669107]

# 然后计算分子
p = 0
q = 0
length = 0
while p < len(Zt):
    q = 0
    result_temp1 = 0
    while q < len(Zt[p]):
        result_temp1 = result_temp1 + (Zt[p][q] - avg) * (LZt[p][q] - avg)
        q += 1
    # print(result_temp1)
    # print(len(Zt)-p)
    AutoCovariance.append(result_temp1/len(TimeSeries))
    p += 1
print(AutoCovariance)
# print(len(AutoCovariance))
# print(len(Zt))

# 显示结果：
# [109.92900420758684, 7.033249208759847, -41.331023616868386, -9.818640497993421, 17.321104958520728, 11.540453909308482,
# -20.71675731505552, -23.35193308926872, -10.671711257152637, 2.3511837591142006, 12.09337228027552, 5.284907080510467,
# -3.4833058404578527, -9.53177380894126, 3.568570997073478, 15.31665885468035, -8.901077316598432, -9.619216801963882,
# -2.303250941136475, 4.686244739096256, 4.632349610445184, 0.9360929838586473]