import numpy as np import matplotlib.pyplot as plt from lss import LSS phi_1, phi_2, phi_3, phi_4 = 0.5, -0.2, 0, 0.5 sigma = 0.2 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] ar = LSS(A, C, G, mu_0=np.ones(4)) x, y = ar.simulate(ts_length=200) fig, ax = plt.subplots(figsize=(8, 4.6)) y = y.flatten() ax.plot(y, 'b-', lw=2, alpha=0.7) ax.grid() ax.set_xlabel('time') ax.set_ylabel(r'$y_t$', fontsize=16) plt.show()
from scipy.stats import norm from lss 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=500000, mu_0=np.ones(4)) mu_x, mu_y, Sigma_x, Sigma_y = ar.moments(T=T, mu_0=np.ones(4)) 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)