phi_1, phi_2, phi_3, phi_4 = 0.5, -0.2, 0, 0.5
sigma = 0.1
A = [[phi_1, phi_2, phi_3, phi_4],
[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0]]
C = [sigma, 0, 0, 0]
G = [1, 0, 0, 0]
T0 = 10
T1 = 50
T2 = 75
T4 = 100
ar = LSS(A, C, G, mu_0=np.ones(4))
ymin, ymax = -0.8, 1.25
fig, ax = plt.subplots(figsize=(8, 5))
ax.grid(alpha=0.4)
ax.set_ylim(ymin, ymax)
ax.set_ylabel(r'$y_t$', fontsize=16)
ax.vlines((T0, T1, T2), -1.5, 1.5)
ax.set_xticks((T0, T1, T2))
ax.set_xticklabels((r"$T$", r"$T'$", r"$T''$"), fontsize=14)
sample = []
for i in range(80):
rcolor = random.choice(('c', 'g', 'b'))
import matplotlib.pyplot as plt
from scipy.stats import norm
from quantecon import LSS
phi_1, phi_2, phi_3, phi_4 = 0.5, -0.2, 0, 0.5
sigma = 0.1
A = [[phi_1, phi_2, phi_3, phi_4],
[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0]]
C = [sigma, 0, 0, 0]
G = [1, 0, 0, 0]
T = 30
ar = LSS(A, C, G)
ymin, ymax = -0.8, 1.25
fig, ax = plt.subplots(figsize=(8, 4))
ax.set_xlim(ymin, ymax)
ax.set_xlabel(r'$y_t$', fontsize=16)
x, y = ar.replicate(T=T, num_reps=100000)
mu_x, mu_y, Sigma_x, Sigma_y = ar.stationary_distributions()
f_y = norm(loc=float(mu_y), scale=float(np.sqrt(Sigma_y)))
y = y.flatten()
ax.hist(y, bins=50, normed=True, alpha=0.4)
import numpy as np import matplotlib.pyplot as plt from scipy.stats import norm from quantecon import LSS import random phi_1, phi_2, phi_3, phi_4 = 0.5, -0.2, 0, 0.5 sigma = 0.1 A = [[phi_1, phi_2, phi_3, phi_4], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0]] C = [sigma, 0, 0, 0] G = [1, 0, 0, 0] T = 30 ar = LSS(A, C, G) ymin, ymax = -0.8, 1.25 fig, ax = plt.subplots(figsize=(8, 4)) ax.set_xlim(ymin, ymax) ax.set_xlabel(r'$y_t$', fontsize=16) x, y = ar.replicate(T=T, num_reps=100000) mu_x, mu_y, Sigma_x, Sigma_y = ar.stationary_distributions() f_y = norm(loc=float(mu_y), scale=float(np.sqrt(Sigma_y))) y = y.flatten() ax.hist(y, bins=50, normed=True, alpha=0.4) ygrid = np.linspace(ymin, ymax, 150)
from quantecon import LSS
import random
phi_1, phi_2, phi_3, phi_4 = 0.5, -0.2, 0, 0.5
sigma = 0.1
A = [[phi_1, phi_2, phi_3, phi_4], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0]]
C = [sigma, 0, 0, 0]
G = [1, 0, 0, 0]
T0 = 10
T1 = 50
T2 = 75
T4 = 100
ar = LSS(A, C, G, mu_0=np.ones(4))
ymin, ymax = -0.8, 1.25
fig, ax = plt.subplots(figsize=(8, 5))
ax.grid(alpha=0.4)
ax.set_ylim(ymin, ymax)
ax.set_ylabel(r'$y_t$', fontsize=16)
ax.vlines((T0, T1, T2), -1.5, 1.5)
ax.set_xticks((T0, T1, T2))
ax.set_xticklabels((r"$T$", r"$T'$", r"$T''$"), fontsize=14)
sample = []
for i in range(80):
rcolor = random.choice(('c', 'g', 'b'))