import numpy as np
import matplotlib.pyplot as plt
"""
AR(1)的时序图：x[t]=a*x[t-1]+e
"""
num = 2000
e = np.random.rand(num)
x = np.empty(num)
 
"""
平稳AR(1)
"""
a = -0.5
x[0] = 2
for i in range(1,num):
 x[i] = a*x[i-1]+e[i]
plt.subplot(321,title = "AR({0}):x[t]={1}*x[t-1]+e".format(1,a))
plt.plot(x,"or")
 
"""
非平稳AR(1)
"""
a = -1.01
x[0] = 2
for i in range(1,num):
 x[i] = a*x[i-1]+e[i]
plt.subplot(322,title = "AR({0}):x[t]={1}*x[t-1]+e".format(1,a))
plt.plot(x,".b")
 
"""
平稳AR(2)
"""
a = -0.2
b = 0.7
x[0] = 2
for i in range(2,num):
 x[i] = a*x[i-1]+b*x[i-2]+e[i]
plt.subplot(323,title = "AR({0}):x[t]={1}*x[t-1]+{2}*x[t-2]+e".format(2,a,b))
plt.plot(x,"og")
 
"""
非平稳AR(2)
"""
a = -0.3
b = 0.8
x[0] = 2
for i in range(2,num):
 x[i] = a*x[i-1]+b*x[i-2]+e[i]
plt.subplot(324,title = "AR({0}):x[t]={1}*x[t-1]+{2}*x[t-2]+e".format(2,a,b))
plt.plot(x,".y")
 
"""
非平稳AR(2)
"""
a = -0.2
b = 0.8
x[0] = 2
for i in range(2,num):
 x[i] = a*x[i-1]+b*x[i-2]+e[i]
plt.subplot(313,title = "AR({0}):x[t]={1}*x[t-1]+{2}*x[t-2]+e".format(2,a,b))
plt.plot(x,"+",color="purple")
 
plt.show()