# Importing various packages
from math import exp, sqrt
from random import random, seed
import numpy as np
import matplotlib.pyplot as plt

def autocovariance(x, n, k, mean_x):
    sum = 0.0
    for i in range(0, n-k):
        sum += (x[(i+k)]-mean_x)*(x[i]-mean_x)
    return  sum/n

n = 1000
x=np.random.normal(size=n)
autocor = np.zeros(n)
figaxis = np.zeros(n)
mean_x=np.mean(x)
var_x = np.var(x)
print(mean_x, var_x)
for i in range (0, n):
    figaxis[i] = i
    autocor[i]=(autocovariance(x, n, i, mean_x))/var_x    

plt.plot(figaxis, autocor, "r-")
plt.axis([0,n,-0.1, 1.0])
plt.xlabel(r'$i$')
plt.ylabel(r'$\gamma_i$')
plt.title(r'Autocorrelation function')
plt.show()