def __init__(self, y_0=100, y_1=100, α=0.8, β=0.9, γ=10, σ=1, g=10):
self.α, self.β = α, β
self.y_0, self.y_1, self.g = y_0, y_1, g
self.γ, self.σ = γ, σ
# Define intial conditions
self.μ_0 = [1, y_0, y_1]
self.ρ1 = α + β
self.ρ2 = -β
# Define transition matrix
self.A = [[1, 0, 0], [γ + g, self.ρ1, self.ρ2], [0, 1, 0]]
# Define output matrix
self.G = [
[γ + g, self.ρ1, self.ρ2], # this is Y_{t+1}
[γ, α, 0], # this is C_{t+1}
[0, β, -β]
] # this is I_{t+1}
self.C = np.zeros((3, 1))
self.C[1] = σ # stochastic
# Initialize LSS with parameters from Samuleson model
LinearStateSpace.__init__(self, self.A, self.C, self.G, mu_0=self.μ_0)
def load_matrices(self, A, C, G):
self.A = A
self.C = C
self.G = G
self.ar = LinearStateSpace(A, C, G, mu_0=np.ones(4))
x, y = self.ar.simulate(ts_length=2000)
y = y.flatten()
self.__y_max = 1.3 * np.max(y)
self.__y_min = 1.3 * np.min(y)
class Ensemble_plot:
def __init__(self):
print("nyan")
def load_matrices(self, A, C, G):
self.A = A
self.C = C
self.G = G
self.ar = LinearStateSpace(A, C, G, mu_0=np.ones(4))
x, y = self.ar.simulate(ts_length=2000)
y = y.flatten()
self.__y_max = 1.3 * np.max(y)
self.__y_min = 1.3 * np.min(y)
def set_plot(self):
self.fig, self.ax = plt.subplots(figsize=(8, 5))
self.ax.set_ylim(self.__y_min, self.__y_max)
self.ax.set_xlabel("time", fontsize=16)
self.ax.set_ylabel("y_t", fontsize=16)
def calc_ensemble_mean(self):
self.ensemble_mean = np.zeros(T)
for i in range(I):
x, y = self.ar.simulate(ts_length=T)
y = y.flatten()
self.ax.plot(y, "c~", lw=0.8, alpha=0.5)
self.ensemble_mean = self.ensemble_mean + y
self.ensemble_mean = self.ensemble_mean / I
self.ax.plot(self.ensemble_mean,
color="b",
lw=2,
alpha=0.8,
label=r'$\bar y_t$')
def calc_moment(self):
print()
def likelihood_params(phi1, phi2, psi, data, sigma_v):
# For the given matrices the moments for the likelihood function are obtained using a Kalman filter
ss = LinearStateSpace(phi1, phi2, psi, np.ones((1, 1)) * np.sqrt(sigma_v))
kalman = Kalman(
ss, [0, 0, 1],
[[1000, 1000, 1000], [1000, 1000, 1000], [1000, 1000, 1000]])
mu = []
sigma = []
for i in range(len(data)):
kalman.update(data[i])
mu.append(psi.dot(kalman.x_hat))
sigma.append(psi.dot(kalman.Sigma).dot(np.transpose(psi)) + sigma_v**2)
return mu[-1], sigma[-1]
import numpy as np
import matplotlib.pyplot as plt
from quantecon import LinearStateSpace
from scipy.stats import norm
import random
phi_0, phi_1, phi_2 = 1.1, 0.8, -0.8
A = [[1, 0, 0], [phi_0, phi_1, phi_2], [0, 1, 0]]
C = np.ones((3, 1))
G = [0, 1, 0]
ar = LinearStateSpace(A, C, G, mu_0=np.ones(3))
x, y = ar.simulate(ts_length=50)
fig, ax = plt.subplots(figsize=(8, 4.6))
y = y.flatten()
print(y)
ax.plot(y, "-b", lw=2, alpha=0.7)
ax.grid()
ax.set_xlabel("time")
ax.set_ylabel("y")
plt.show()
##calc esemble_mean
esemble_mean = np.zeros(T)
I = 20
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 = LinearStateSpace(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 LinearStateSpace
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 = LinearStateSpace(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 LinearStateSpace 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 = LinearStateSpace(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) ax.plot(ygrid, f_y.pdf(ygrid), 'k-', lw=2, alpha=0.8, label='true density')
g = 10
n = 100
A = [[1, 0, 0],
[γ + g, ρ1, ρ2],
[0, 1, 0]]
G = [[γ + g, ρ1, ρ2], # this is Y_{t+1}
[γ, α, 0], # this is C_{t+1}
[0, β, -β]] # this is I_{t+1}
μ_0 = [1, 100, 100]
C = np.zeros((3,1))
C[1] = σ # stochastic
sam_t = LinearStateSpace(A, C, G, mu_0=μ_0)
x, y = sam_t.simulate(ts_length=n)
fig, axes = plt.subplots(3, 1, sharex=True, figsize=(12, 8))
titles = ['Output ($Y_t$)', 'Consumption ($C_t$)', 'Investment ($I_t$)']
colors = ['darkblue', 'red', 'purple']
for ax, series, title, color in zip(axes, y, titles, colors):
ax.plot(series, color=color)
ax.set(title=title, xlim=(0, n))
ax.grid()
axes[-1].set_xlabel('Iteration')
plt.show()
n = 100
A = [[1, 0, 0], [γ + g, ρ1, ρ2], [0, 1, 0]]
G = [
[γ + g, ρ1, ρ2], # this is Y_{t+1}
[γ, α, 0], # this is C_{t+1}
[0, β, -β]
] # this is I_{t+1}
μ_0 = [1, 100, 100]
C = np.zeros((3, 1))
# stochastic
C[1] = σ
sam_t = LinearStateSpace(A, C, G, mu_0=μ_0)
x, y = sam_t.simulate(ts_length=n)
fig, axes = plt.subplots(3, 1, sharex=True, figsize=(12, 8))
titles = ['Output ($Y_t$)', 'Consumption ($C_t$)', 'Investment ($I_t$)']
colors = ['darkblue', 'red', 'purple']
for ax, series, title, color in zip(axes, y, titles, colors):
ax.plot(series, color=color)
ax.set(title=title, xlim=(0, n))
ax.grid()
axes[-1].set_xlabel('Iteration')
plt.show()
import numpy as np
import matplotlib.pyplot as plt
from quantecon import Kalman
from quantecon import LinearStateSpace
from scipy.stats import norm
theta = 10
A, C, G, H = 1, 0, 1, 1
#mu_0は x0 の初期分布の平均パラメータ
ss = LinearStateSpace(A, C, G, H, mu_0=theta)
x_hat_0, Sigma_0 = 8, 1
kalman = Kalman(ss, x_hat_0, Sigma_0)
N = 5
x, y = ss.simulate(N)
y = y.flatten()
print(y)
#
fig, ax = plt.subplots(figsize=(10, 8))
xgrid = np.linspace(theta - 5, theta + 2, 200)
for i in range(N):
m, v = [float(z) for z in (kalman.x_hat, kalman.Sigma)]
print(m)
ax.plot(xgrid,
norm.pdf(xgrid, loc=m, scale=np.sqrt(v)),
label=r't={}'.format(i))
kalman.update(y[i])
