def test_simulate():
# Test for simulation of new time-series
from scipy.signal import lfilter
# Common parameters
nsimulations = 10
sigma2 = 2
measurement_shocks = np.zeros(nsimulations)
state_shocks = np.random.normal(scale=sigma2**0.5, size=nsimulations)
# Random walk model, so simulated series is just the cumulative sum of
# the shocks
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(nsimulations,
measurement_shocks=measurement_shocks,
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[0, np.cumsum(state_shocks)[:-1]]
assert_allclose(actual, desired)
# Local level model, so simulated series is just the cumulative sum of
# the shocks plus the measurement shock
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(nsimulations,
measurement_shocks=np.ones(nsimulations),
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[1, np.cumsum(state_shocks)[:-1] + 1]
assert_allclose(actual, desired)
# Local level-like model with observation and state intercepts, so
# simulated series is just the cumulative sum of the shocks minus the state
# intercept, plus the observation intercept and the measurement shock
mod = KalmanFilter(k_endog=1, k_states=1)
mod['obs_intercept', 0, 0] = 5.
mod['design', 0, 0] = 1.
mod['state_intercept', 0, 0] = -2.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(nsimulations,
measurement_shocks=np.ones(nsimulations),
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[1 + 5, np.cumsum(state_shocks - 2)[:-1] + 1 + 5]
assert_allclose(actual, desired)
# Model with time-varying observation intercept
mod = KalmanFilter(k_endog=1, k_states=1, nobs=10)
mod['obs_intercept'] = (np.arange(10) * 1.).reshape(1, 10)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(nsimulations,
measurement_shocks=measurement_shocks,
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[0, np.cumsum(state_shocks)[:-1] + np.arange(1, 10)]
assert_allclose(actual, desired)
# Model with time-varying observation intercept, check that error is raised
# if more simulations are requested than are nobs.
mod = KalmanFilter(k_endog=1, k_states=1, nobs=10)
mod['obs_intercept'] = (np.arange(10) * 1.).reshape(1, 10)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
assert_raises(ValueError, mod.simulate, nsimulations + 1,
measurement_shocks, state_shocks)
# ARMA(1,1): phi = [0.1], theta = [0.5], sigma^2 = 2
phi = 0.1
theta = 0.5
mod = sarimax.SARIMAX([0], order=(1, 0, 1))
mod.update(np.r_[phi, theta, sigma2])
actual = mod.ssm.simulate(nsimulations,
measurement_shocks=measurement_shocks,
state_shocks=state_shocks,
initial_state=np.zeros(
mod.k_states))[0].squeeze()
desired = lfilter([1, theta], [1, -phi], np.r_[0, state_shocks[:-1]])
assert_allclose(actual, desired)
# SARIMAX(1,0,1)x(1,0,1,4), this time using the results object call
mod = sarimax.SARIMAX([0.1, 0.5, -0.2],
order=(1, 0, 1),
seasonal_order=(1, 0, 1, 4))
res = mod.filter([0.1, 0.5, 0.2, -0.3, 1])
actual = res.simulate(nsimulations,
measurement_shocks=measurement_shocks,
state_shocks=state_shocks,
initial_state=np.zeros(mod.k_states))
desired = lfilter(res.polynomial_reduced_ma, res.polynomial_reduced_ar,
np.r_[0, state_shocks[:-1]])
assert_allclose(actual, desired)
#If we can only observe y, what can we say about α? #This acts like a filter trying to recover a signal by filtering out noise. #A linear filter. # a is the state and y is the observation (equations) import statsmodels.tsa.statespace.kalman_filter from statsmodels.tsa.statespace.kalman_filter import KalmanFilter kf = KalmanFilter(1,1) kf.obs_cov = np.array([sigma_e]) # H kf.state_cov = np.array([sigma_h]) # Q kf.design = np.array([1.0]) # Z kf.transition = np.array([1.0]) # T kf.selection = np.array([1.0]) # R ys, ah = kf.simulate(100)
def test_simulate():
# Test for simulation of new time-series
from scipy.signal import lfilter
# Common parameters
nsimulations = 10
sigma2 = 2
measurement_shocks = np.zeros(nsimulations)
state_shocks = np.random.normal(scale=sigma2**0.5, size=nsimulations)
# Random walk model, so simulated series is just the cumulative sum of
# the shocks
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(
nsimulations, measurement_shocks=measurement_shocks,
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[0, np.cumsum(state_shocks)[:-1]]
assert_allclose(actual, desired)
# Local level model, so simulated series is just the cumulative sum of
# the shocks plus the measurement shock
mod = KalmanFilter(k_endog=1, k_states=1)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(
nsimulations, measurement_shocks=np.ones(nsimulations),
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[1, np.cumsum(state_shocks)[:-1] + 1]
assert_allclose(actual, desired)
# Local level-like model with observation and state intercepts, so
# simulated series is just the cumulative sum of the shocks minus the state
# intercept, plus the observation intercept and the measurement shock
mod = KalmanFilter(k_endog=1, k_states=1)
mod['obs_intercept', 0, 0] = 5.
mod['design', 0, 0] = 1.
mod['state_intercept', 0, 0] = -2.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(
nsimulations, measurement_shocks=np.ones(nsimulations),
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[1 + 5, np.cumsum(state_shocks - 2)[:-1] + 1 + 5]
assert_allclose(actual, desired)
# Model with time-varying observation intercept
mod = KalmanFilter(k_endog=1, k_states=1, nobs=10)
mod['obs_intercept'] = (np.arange(10)*1.).reshape(1, 10)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
actual = mod.simulate(
nsimulations, measurement_shocks=measurement_shocks,
state_shocks=state_shocks)[0].squeeze()
desired = np.r_[0, np.cumsum(state_shocks)[:-1] + np.arange(1, 10)]
assert_allclose(actual, desired)
# Model with time-varying observation intercept, check that error is raised
# if more simulations are requested than are nobs.
mod = KalmanFilter(k_endog=1, k_states=1, nobs=10)
mod['obs_intercept'] = (np.arange(10)*1.).reshape(1, 10)
mod['design', 0, 0] = 1.
mod['transition', 0, 0] = 1.
mod['selection', 0, 0] = 1.
assert_raises(ValueError, mod.simulate, nsimulations+1, measurement_shocks,
state_shocks)
# ARMA(1,1): phi = [0.1], theta = [0.5], sigma^2 = 2
phi = 0.1
theta = 0.5
mod = sarimax.SARIMAX([0], order=(1, 0, 1))
mod.update(np.r_[phi, theta, sigma2])
actual = mod.ssm.simulate(
nsimulations, measurement_shocks=measurement_shocks,
state_shocks=state_shocks,
initial_state=np.zeros(mod.k_states))[0].squeeze()
desired = lfilter([1, theta], [1, -phi], np.r_[0, state_shocks[:-1]])
assert_allclose(actual, desired)
# SARIMAX(1,0,1)x(1,0,1,4), this time using the results object call
mod = sarimax.SARIMAX([0.1, 0.5, -0.2], order=(1, 0, 1),
seasonal_order=(1, 0, 1, 4))
res = mod.filter([0.1, 0.5, 0.2, -0.3, 1])
actual = res.simulate(
nsimulations, measurement_shocks=measurement_shocks,
state_shocks=state_shocks, initial_state=np.zeros(mod.k_states))
desired = lfilter(
res.polynomial_reduced_ma, res.polynomial_reduced_ar,
np.r_[0, state_shocks[:-1]])
assert_allclose(actual, desired)
'''
https://datascienceschool.net/view-notebook/c645d51f308b4047aa78e8b343a2e181/
'''
from statsmodels.tsa.statespace.kalman_filter import KalmanFilter
import numpy as np
import matplotlib.pyplot as plt
model1 = KalmanFilter(k_endog=1,
k_states=1,
transition=[[1]],
selection=[[1]],
state_cov=[[10]],
design=[[1]],
obs_cov=[[100]])
np.random.seed(0)
y1, x1 = model1.simulate(100)
print(x1)
print(y1)
plt.plot(y1, 'r:', label="관측값")
plt.plot(x1, 'g-', label="상태값")
plt.legend()
plt.title("로컬레벨 모형의 시뮬레이션 ($\sigma_w^2 = 10$, $\sigma_v^2 = 100$)")
plt.show()
