Exemplo n.º 1
0
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 = np.r_[0.1]
    theta = np.r_[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)[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).squeeze()
    desired = lfilter(res.polynomial_reduced_ma, res.polynomial_reduced_ar,
                      np.r_[0, state_shocks[:-1]])

    assert_allclose(actual, desired)
Exemplo n.º 2
0
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 = np.r_[0.1]
    theta = np.r_[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)[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).squeeze()
    desired = lfilter(
        res.polynomial_reduced_ma, res.polynomial_reduced_ar,
        np.r_[0, state_shocks[:-1]])

    assert_allclose(actual, desired)