Myujth

The equation for AR(1) is :

Cases:

This is what it looks like:

So I came up with this code:

from random import gauss
from random import seed
from matplotlib import pyplot
seed(1)
N = 100
b1 = [1, 0.8]
b2 = [1, -0.8]
b3 = [0.1, 1]
b4 = [0, 1.1]
sigma1to2 = 0.1
sigma3to4 = 0.5
e1to2 = [gauss(0, sigma1to2) for i in range(N)]
e3to4 = [gauss(0, sigma3to4) for i in range(N)]

x1 = np.zeros(N)
x2 = np.zeros(N)
x3 = np.zeros(N)
x4 = np.zeros(N)
for i in range(1,N):
 x1[i] = b1[0] + (b1[1]* x1[i-1]) + e1to2[i]
 x2[i] = b2[0] + (b2[1]* x2[i-1]) + e1to2[i]
 x3[i] = b3[0] + (b3[1]* x3[i-1]) + e3to4[i]
 x4[i] = b4[0] + (b4[1]* x4[i-1]) + e3to4[i]
fig = plt.figure(figsize=(15,5))
plt.subplot(221)
plt.plot(x1,label='series1')
plt.title('series1')
plt.subplot(222)
plt.plot(x2,label='series2')
plt.title('series2')
plt.subplot(223)
plt.plot(x3,label='series3')
plt.title('series3')
plt.subplot(224)
plt.plot(x4,label='series4')
plt.title('series4')
plt.show()

This is what I get:

What I am doing wrong? The 1st and last graph is not matching with that one. Actually, I am finding out the ACF after plotting the graph and there are cases where ACF will be different depending upon those three parameters value. ACF for those 1st and last case will be different in my case. Hence I ain't able to generalize the cases properly.