Agfdhyk

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.

I just had to change the xlimit and the starting function value to be other than zero.