"""
Tests for python wrapper of state space representation and filtering

Author: Chad Fulton
License: Simplified-BSD

References
----------

Kim, Chang-Jin, and Charles R. Nelson. 1999.
"State-Space Models with Regime Switching:
Classical and Gibbs-Sampling Approaches with Applications".
MIT Press Books. The MIT Press.
"""
from __future__ import division, absolute_import, print_function

import os
import warnings

import numpy as np
import pandas as pd
import pytest

from statsmodels.tsa.statespace.representation import Representation
from statsmodels.tsa.statespace.kalman_filter import (
    KalmanFilter, FilterResults, PredictionResults)
from statsmodels.tsa.statespace import tools, sarimax
from .results import results_kalman_filter
from numpy.testing import (
    assert_equal, assert_almost_equal, assert_raises, assert_allclose)

current_path = os.path.dirname(os.path.abspath(__file__))

clark1989_path = os.path.join('results', 'results_clark1989_R.csv')
clark1989_results = pd.read_csv(os.path.join(current_path, clark1989_path))


class Clark1987(object):
    """
    Clark's (1987) univariate unobserved components model of real GDP (as
    presented in Kim and Nelson, 1999)

    Test data produced using GAUSS code described in Kim and Nelson (1999) and
    found at http://econ.korea.ac.kr/~cjkim/SSMARKOV.htm

    See `results.results_kalman_filter` for more information.
    """
    @classmethod
    def setup_class(cls, dtype=float, **kwargs):
        cls.true = results_kalman_filter.uc_uni
        cls.true_states = pd.DataFrame(cls.true['states'])

        # GDP, Quarterly, 1947.1 - 1995.3
        data = pd.DataFrame(
            cls.true['data'],
            index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'),
            columns=['GDP']
        )
        data['lgdp'] = np.log(data['GDP'])

        # Construct the statespace representation
        k_states = 4
        cls.model = KalmanFilter(k_endog=1, k_states=k_states, **kwargs)
        cls.model.bind(data['lgdp'].values)

        cls.model.design[:, :, 0] = [1, 1, 0, 0]
        cls.model.transition[([0, 0, 1, 1, 2, 3],
                              [0, 3, 1, 2, 1, 3],
                              [0, 0, 0, 0, 0, 0])] = [1, 1, 0, 0, 1, 1]
        cls.model.selection = np.eye(cls.model.k_states)

        # Update matrices with given parameters
        (sigma_v, sigma_e, sigma_w, phi_1, phi_2) = np.array(
            cls.true['parameters']
        )
        cls.model.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2]
        cls.model.state_cov[
            np.diag_indices(k_states)+(np.zeros(k_states, dtype=int),)] = [
            sigma_v**2, sigma_e**2, 0, sigma_w**2
        ]

        # Initialization
        initial_state = np.zeros((k_states,))
        initial_state_cov = np.eye(k_states)*100

        # Initialization: modification
        initial_state_cov = np.dot(
            np.dot(cls.model.transition[:, :, 0], initial_state_cov),
            cls.model.transition[:, :, 0].T
        )
        cls.model.initialize_known(initial_state, initial_state_cov)

    @classmethod
    def run_filter(cls):
        # Filter the data
        return cls.model.filter()

    def test_loglike(self):
        assert_almost_equal(
            self.results.llf_obs[self.true['start']:].sum(),
            self.true['loglike'], 5
        )

    def test_filtered_state(self):
        assert_almost_equal(
            self.results.filtered_state[0][self.true['start']:],
            self.true_states.iloc[:, 0], 4
        )
        assert_almost_equal(
            self.results.filtered_state[1][self.true['start']:],
            self.true_states.iloc[:, 1], 4
        )
        assert_almost_equal(
            self.results.filtered_state[3][self.true['start']:],
            self.true_states.iloc[:, 2], 4
        )


class TestClark1987Single(Clark1987):
    """
    Basic single precision test for the loglikelihood and filtered states.
    """
    @classmethod
    def setup_class(cls):
        pytest.skip('Not implemented')
        super(TestClark1987Single, cls).setup_class(
            dtype=np.float32, conserve_memory=0
        )
        cls.results = cls.run_filter()


class TestClark1987Double(Clark1987):
    """
    Basic double precision test for the loglikelihood and filtered states.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1987Double, cls).setup_class(
            dtype=float, conserve_memory=0
        )
        cls.results = cls.run_filter()


@pytest.mark.skip('Not implemented')
class TestClark1987SingleComplex(Clark1987):
    """
    Basic single precision complex test for the loglikelihood and filtered
    states.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1987SingleComplex, cls).setup_class(
            dtype=np.complex64, conserve_memory=0
        )
        cls.results = cls.run_filter()


class TestClark1987DoubleComplex(Clark1987):
    """
    Basic double precision complex test for the loglikelihood and filtered
    states.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1987DoubleComplex, cls).setup_class(
            dtype=complex, conserve_memory=0
        )
        cls.results = cls.run_filter()


class TestClark1987Conserve(Clark1987):
    """
    Memory conservation test for the loglikelihood and filtered states.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1987Conserve, cls).setup_class(
            dtype=float, conserve_memory=0x01 | 0x02
        )
        cls.results = cls.run_filter()


class Clark1987Forecast(Clark1987):
    """
    Forecasting test for the loglikelihood and filtered states.
    """
    @classmethod
    def setup_class(cls, dtype=float, nforecast=100, conserve_memory=0):
        super(Clark1987Forecast, cls).setup_class(
            dtype=dtype, conserve_memory=conserve_memory
        )
        cls.nforecast = nforecast

        # Add missing observations to the end (to forecast)
        cls.model.endog = np.array(
            np.r_[cls.model.endog[0, :], [np.nan]*nforecast],
            ndmin=2, dtype=dtype, order="F"
        )
        cls.model.nobs = cls.model.endog.shape[1]

    def test_filtered_state(self):
        assert_almost_equal(
            self.results.filtered_state[0][self.true['start']:-self.nforecast],
            self.true_states.iloc[:, 0], 4
        )
        assert_almost_equal(
            self.results.filtered_state[1][self.true['start']:-self.nforecast],
            self.true_states.iloc[:, 1], 4
        )
        assert_almost_equal(
            self.results.filtered_state[3][self.true['start']:-self.nforecast],
            self.true_states.iloc[:, 2], 4
        )


class TestClark1987ForecastDouble(Clark1987Forecast):
    """
    Basic double forecasting test for the loglikelihood and filtered states.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1987ForecastDouble, cls).setup_class()
        cls.results = cls.run_filter()


class TestClark1987ForecastDoubleComplex(Clark1987Forecast):
    """
    Basic double complex forecasting test for the loglikelihood and filtered
    states.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1987ForecastDoubleComplex, cls).setup_class(
            dtype=complex
        )
        cls.results = cls.run_filter()


class TestClark1987ForecastConserve(Clark1987Forecast):
    """
    Memory conservation forecasting test for the loglikelihood and filtered
    states.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1987ForecastConserve, cls).setup_class(
            dtype=float, conserve_memory=0x01 | 0x02
        )
        cls.results = cls.run_filter()


class TestClark1987ConserveAll(Clark1987):
    """
    Memory conservation forecasting test for the loglikelihood and filtered
    states.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1987ConserveAll, cls).setup_class(
            dtype=float, conserve_memory=0x01 | 0x02 | 0x04 | 0x08
        )
        cls.model.loglikelihood_burn = cls.true['start']
        cls.results = cls.run_filter()

    def test_loglike(self):
        assert_almost_equal(
            self.results.llf_obs[0], self.true['loglike'], 5
        )

    def test_filtered_state(self):
        end = self.true_states.shape[0]
        assert_almost_equal(
            self.results.filtered_state[0][-1],
            self.true_states.iloc[end-1, 0], 4
        )
        assert_almost_equal(
            self.results.filtered_state[1][-1],
            self.true_states.iloc[end-1, 1], 4
        )


class Clark1989(object):
    """
    Clark's (1989) bivariate unobserved components model of real GDP (as
    presented in Kim and Nelson, 1999)

    Tests two-dimensional observation data.

    Test data produced using GAUSS code described in Kim and Nelson (1999) and
    found at http://econ.korea.ac.kr/~cjkim/SSMARKOV.htm

    See `results.results_kalman_filter` for more information.
    """
    @classmethod
    def setup_class(cls, dtype=float, **kwargs):
        cls.true = results_kalman_filter.uc_bi
        cls.true_states = pd.DataFrame(cls.true['states'])

        # GDP and Unemployment, Quarterly, 1948.1 - 1995.3
        data = pd.DataFrame(
            cls.true['data'],
            index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'),
            columns=['GDP', 'UNEMP']
        )[4:]
        data['GDP'] = np.log(data['GDP'])
        data['UNEMP'] = (data['UNEMP']/100)

        k_states = 6
        cls.model = KalmanFilter(k_endog=2, k_states=k_states, **kwargs)
        cls.model.bind(np.ascontiguousarray(data.values))

        # Statespace representation
        cls.model.design[:, :, 0] = [[1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1]]
        cls.model.transition[
            ([0, 0, 1, 1, 2, 3, 4, 5],
             [0, 4, 1, 2, 1, 2, 4, 5],
             [0, 0, 0, 0, 0, 0, 0, 0])
        ] = [1, 1, 0, 0, 1, 1, 1, 1]
        cls.model.selection = np.eye(cls.model.k_states)

        # Update matrices with given parameters
        (sigma_v, sigma_e, sigma_w, sigma_vl, sigma_ec,
         phi_1, phi_2, alpha_1, alpha_2, alpha_3) = np.array(
            cls.true['parameters'],
        )
        cls.model.design[([1, 1, 1], [1, 2, 3], [0, 0, 0])] = [
            alpha_1, alpha_2, alpha_3
        ]
        cls.model.transition[([1, 1], [1, 2], [0, 0])] = [phi_1, phi_2]
        cls.model.obs_cov[1, 1, 0] = sigma_ec**2
        cls.model.state_cov[
            np.diag_indices(k_states)+(np.zeros(k_states, dtype=int),)] = [
            sigma_v**2, sigma_e**2, 0, 0, sigma_w**2, sigma_vl**2
        ]

        # Initialization
        initial_state = np.zeros((k_states,))
        initial_state_cov = np.eye(k_states)*100

        # Initialization: cls.modelification
        initial_state_cov = np.dot(
            np.dot(cls.model.transition[:, :, 0], initial_state_cov),
            cls.model.transition[:, :, 0].T
        )
        cls.model.initialize_known(initial_state, initial_state_cov)

    @classmethod
    def run_filter(cls):
        # Filter the data
        return cls.model.filter()

    def test_loglike(self):
        assert_almost_equal(
            # self.results.llf_obs[self.true['start']:].sum(),
            self.results.llf_obs[0:].sum(),
            self.true['loglike'], 2
        )

    def test_filtered_state(self):
        assert_almost_equal(
            self.results.filtered_state[0][self.true['start']:],
            self.true_states.iloc[:, 0], 4
        )
        assert_almost_equal(
            self.results.filtered_state[1][self.true['start']:],
            self.true_states.iloc[:, 1], 4
        )
        assert_almost_equal(
            self.results.filtered_state[4][self.true['start']:],
            self.true_states.iloc[:, 2], 4
        )
        assert_almost_equal(
            self.results.filtered_state[5][self.true['start']:],
            self.true_states.iloc[:, 3], 4
        )


class TestClark1989(Clark1989):
    """
    Basic double precision test for the loglikelihood and filtered
    states with two-dimensional observation vector.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1989, cls).setup_class(dtype=float, conserve_memory=0)
        cls.results = cls.run_filter()

    def test_kalman_gain(self):
        assert_allclose(self.results.kalman_gain.sum(axis=1).sum(axis=0),
                        clark1989_results['V1'], atol=1e-4)


class TestClark1989Conserve(Clark1989):
    """
    Memory conservation test for the loglikelihood and filtered states with
    two-dimensional observation vector.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1989Conserve, cls).setup_class(
            dtype=float, conserve_memory=0x01 | 0x02
        )
        cls.results = cls.run_filter()


class Clark1989Forecast(Clark1989):
    """
    Memory conservation test for the loglikelihood and filtered states with
    two-dimensional observation vector.
    """
    @classmethod
    def setup_class(cls, dtype=float, nforecast=100, conserve_memory=0):
        super(Clark1989Forecast, cls).setup_class(
            dtype=dtype, conserve_memory=conserve_memory
        )
        cls.nforecast = nforecast

        # Add missing observations to the end (to forecast)
        cls.model.endog = np.array(
            np.c_[
                cls.model.endog,
                np.r_[[np.nan, np.nan]*nforecast].reshape(2, nforecast)
            ],
            ndmin=2, dtype=dtype, order="F"
        )
        cls.model.nobs = cls.model.endog.shape[1]

        cls.results = cls.run_filter()

    def test_filtered_state(self):
        assert_almost_equal(
            self.results.filtered_state[0][self.true['start']:-self.nforecast],
            self.true_states.iloc[:, 0], 4
        )
        assert_almost_equal(
            self.results.filtered_state[1][self.true['start']:-self.nforecast],
            self.true_states.iloc[:, 1], 4
        )
        assert_almost_equal(
            self.results.filtered_state[4][self.true['start']:-self.nforecast],
            self.true_states.iloc[:, 2], 4
        )
        assert_almost_equal(
            self.results.filtered_state[5][self.true['start']:-self.nforecast],
            self.true_states.iloc[:, 3], 4
        )


class TestClark1989ForecastDouble(Clark1989Forecast):
    """
    Basic double forecasting test for the loglikelihood and filtered states.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1989ForecastDouble, cls).setup_class()
        cls.results = cls.run_filter()


class TestClark1989ForecastDoubleComplex(Clark1989Forecast):
    """
    Basic double complex forecasting test for the loglikelihood and filtered
    states.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1989ForecastDoubleComplex, cls).setup_class(
            dtype=complex
        )
        cls.results = cls.run_filter()


class TestClark1989ForecastConserve(Clark1989Forecast):
    """
    Memory conservation forecasting test for the loglikelihood and filtered
    states.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1989ForecastConserve, cls).setup_class(
            dtype=float, conserve_memory=0x01 | 0x02
        )
        cls.results = cls.run_filter()


class TestClark1989ConserveAll(Clark1989):
    """
    Memory conservation forecasting test for the loglikelihood and filtered
    states.
    """
    @classmethod
    def setup_class(cls):
        super(TestClark1989ConserveAll, cls).setup_class(
            dtype=float, conserve_memory=0x01 | 0x02 | 0x04 | 0x08
        )
        # cls.model.loglikelihood_burn = cls.true['start']
        cls.model.loglikelihood_burn = 0
        cls.results = cls.run_filter()

    def test_loglike(self):
        assert_almost_equal(
            self.results.llf_obs[0], self.true['loglike'], 2
        )

    def test_filtered_state(self):
        end = self.true_states.shape[0]
        assert_almost_equal(
            self.results.filtered_state[0][-1],
            self.true_states.iloc[end-1, 0], 4
        )
        assert_almost_equal(
            self.results.filtered_state[1][-1],
            self.true_states.iloc[end-1, 1], 4
        )
        assert_almost_equal(
            self.results.filtered_state[4][-1],
            self.true_states.iloc[end-1, 2], 4
        )
        assert_almost_equal(
            self.results.filtered_state[5][-1],
            self.true_states.iloc[end-1, 3], 4
        )


class TestClark1989PartialMissing(Clark1989):
    @classmethod
    def setup_class(cls):
        super(TestClark1989PartialMissing, cls).setup_class()
        endog = cls.model.endog
        endog[1, -51:] = np.NaN
        cls.model.bind(endog)

        cls.results = cls.run_filter()

    def test_loglike(self):
        assert_allclose(self.results.llf_obs[0:].sum(), 1232.113456)

    def test_filtered_state(self):
        # Could do this, but no need really.
        pass

    def test_predicted_state(self):
        assert_allclose(
            self.results.predicted_state.T[1:], clark1989_results.iloc[:, 1:],
            atol=1e-8
        )


# Miscellaneous coverage-related tests
def test_slice_notation():
    # Test setting and getting state space representation matrices using the
    # slice notation.

    endog = np.arange(10)*1.0
    mod = KalmanFilter(k_endog=1, k_states=2)
    mod.bind(endog)

    # Test invalid __setitem__
    def set_designs():
        mod['designs'] = 1

    def set_designs2():
        mod['designs', 0, 0] = 1

    def set_designs3():
        mod[0] = 1

    assert_raises(IndexError, set_designs)
    assert_raises(IndexError, set_designs2)
    assert_raises(IndexError, set_designs3)

    # Test invalid __getitem__
    assert_raises(IndexError, lambda: mod['designs'])
    assert_raises(IndexError, lambda: mod['designs', 0, 0, 0])
    assert_raises(IndexError, lambda: mod[0])

    # Test valid __setitem__, __getitem__
    assert_equal(mod.design[0, 0, 0], 0)
    mod['design', 0, 0, 0] = 1
    assert_equal(mod['design'].sum(), 1)
    assert_equal(mod.design[0, 0, 0], 1)
    assert_equal(mod['design', 0, 0, 0], 1)

    # Test valid __setitem__, __getitem__ with unspecified time index
    mod['design'] = np.zeros(mod['design'].shape)
    assert_equal(mod.design[0, 0], 0)
    mod['design', 0, 0] = 1
    assert_equal(mod.design[0, 0], 1)
    assert_equal(mod['design', 0, 0], 1)


def test_representation():
    # Test Representation construction

    # Test an invalid number of states
    def zero_kstates():
        Representation(1, 0)
    assert_raises(ValueError, zero_kstates)

    # Test an invalid endogenous array
    def empty_endog():
        endog = np.zeros((0, 0))
        Representation(endog, k_states=2)
    assert_raises(ValueError, empty_endog)

    # Test a Fortran-ordered endogenous array (which will be assumed to be in
    # wide format: k_endog x nobs)
    nobs = 10
    k_endog = 2
    arr = np.arange(nobs*k_endog).reshape(k_endog, nobs)*1.
    endog = np.asfortranarray(arr)
    mod = Representation(endog, k_states=2)
    assert_equal(mod.nobs, nobs)
    assert_equal(mod.k_endog, k_endog)

    # Test a C-ordered endogenous array (which will be assumed to be in
    # tall format: nobs x k_endog)
    nobs = 10
    k_endog = 2
    endog = np.arange(nobs*k_endog).reshape(nobs, k_endog)*1.
    mod = Representation(endog, k_states=2)
    assert_equal(mod.nobs, nobs)
    assert_equal(mod.k_endog, k_endog)

    # Test getting the statespace representation
    assert_equal(mod._statespace, None)
    mod._initialize_representation()
    assert_equal(mod._statespace is not None, True)


def test_bind():
    # Test binding endogenous data to Kalman filter

    mod = Representation(2, k_states=2)

    # Test invalid endogenous array (it must be ndarray)
    assert_raises(ValueError, lambda: mod.bind([1, 2, 3, 4]))

    # Test valid (nobs x 1) endogenous array
    mod.bind(np.arange(10).reshape((5, 2))*1.)
    assert_equal(mod.nobs, 5)

    # Test valid (k_endog x 0) endogenous array
    mod.bind(np.zeros((0, 2), dtype=np.float64))

    # Test invalid (3-dim) endogenous array
    with pytest.raises(ValueError):
        mod.bind(np.arange(12).reshape(2, 2, 3)*1.)

    # Test valid F-contiguous
    mod.bind(np.asfortranarray(np.arange(10).reshape(2, 5)))
    assert_equal(mod.nobs, 5)

    # Test valid C-contiguous
    mod.bind(np.arange(10).reshape(5, 2))
    assert_equal(mod.nobs, 5)

    # Test invalid F-contiguous
    with pytest.raises(ValueError):
        mod.bind(np.asfortranarray(np.arange(10).reshape(5, 2)))

    # Test invalid C-contiguous
    assert_raises(ValueError, lambda: mod.bind(np.arange(10).reshape(2, 5)))


def test_initialization():
    # Test Kalman filter initialization

    mod = Representation(1, k_states=2)

    # Test invalid state initialization
    assert_raises(RuntimeError, lambda: mod._initialize_state())

    # Test valid initialization
    initial_state = np.zeros(2,) + 1.5
    initial_state_cov = np.eye(2) * 3.
    mod.initialize_known(initial_state, initial_state_cov)
    assert_equal(mod.initialization.constant.sum(), 3)
    assert_equal(mod.initialization.stationary_cov.diagonal().sum(), 6)

    # Test invalid initial_state
    initial_state = np.zeros(10,)
    with pytest.raises(ValueError):
        mod.initialize_known(initial_state, initial_state_cov)
    initial_state = np.zeros((10, 10))
    with pytest.raises(ValueError):
        mod.initialize_known(initial_state, initial_state_cov)

    # Test invalid initial_state_cov
    initial_state = np.zeros(2,) + 1.5
    initial_state_cov = np.eye(3)
    with pytest.raises(ValueError):
        mod.initialize_known(initial_state, initial_state_cov)


def test_init_matrices_time_invariant():
    # Test setting state space system matrices in __init__, with time-invariant
    # matrices
    k_endog = 2
    k_states = 3
    k_posdef = 1

    endog = np.zeros((10, 2))
    obs_intercept = np.arange(k_endog) * 1.0
    design = np.reshape(
        np.arange(k_endog * k_states) * 1.0, (k_endog, k_states))
    obs_cov = np.reshape(np.arange(k_endog**2) * 1.0, (k_endog, k_endog))
    state_intercept = np.arange(k_states) * 1.0
    transition = np.reshape(np.arange(k_states**2) * 1.0, (k_states, k_states))
    selection = np.reshape(
        np.arange(k_states * k_posdef) * 1.0, (k_states, k_posdef))
    state_cov = np.reshape(np.arange(k_posdef**2) * 1.0, (k_posdef, k_posdef))

    mod = Representation(endog, k_states=k_states, k_posdef=k_posdef,
                         obs_intercept=obs_intercept, design=design,
                         obs_cov=obs_cov, state_intercept=state_intercept,
                         transition=transition, selection=selection,
                         state_cov=state_cov)

    assert_allclose(mod['obs_intercept'], obs_intercept)
    assert_allclose(mod['design'], design)
    assert_allclose(mod['obs_cov'], obs_cov)
    assert_allclose(mod['state_intercept'], state_intercept)
    assert_allclose(mod['transition'], transition)
    assert_allclose(mod['selection'], selection)
    assert_allclose(mod['state_cov'], state_cov)


def test_init_matrices_time_varying():
    # Test setting state space system matrices in __init__, with time-varying
    # matrices
    nobs = 10
    k_endog = 2
    k_states = 3
    k_posdef = 1

    endog = np.zeros((10, 2))
    obs_intercept = np.reshape(np.arange(k_endog * nobs) * 1.0,
                               (k_endog, nobs))
    design = np.reshape(
        np.arange(k_endog * k_states * nobs) * 1.0, (k_endog, k_states, nobs))
    obs_cov = np.reshape(
        np.arange(k_endog**2 * nobs) * 1.0, (k_endog, k_endog, nobs))
    state_intercept = np.reshape(
        np.arange(k_states * nobs) * 1.0, (k_states, nobs))
    transition = np.reshape(
        np.arange(k_states**2 * nobs) * 1.0, (k_states, k_states, nobs))
    selection = np.reshape(
        np.arange(k_states * k_posdef * nobs) * 1.0,
        (k_states, k_posdef, nobs))
    state_cov = np.reshape(
        np.arange(k_posdef**2 * nobs) * 1.0, (k_posdef, k_posdef, nobs))

    mod = Representation(endog, k_states=k_states, k_posdef=k_posdef,
                         obs_intercept=obs_intercept, design=design,
                         obs_cov=obs_cov, state_intercept=state_intercept,
                         transition=transition, selection=selection,
                         state_cov=state_cov)

    assert_allclose(mod['obs_intercept'], obs_intercept)
    assert_allclose(mod['design'], design)
    assert_allclose(mod['obs_cov'], obs_cov)
    assert_allclose(mod['state_intercept'], state_intercept)
    assert_allclose(mod['transition'], transition)
    assert_allclose(mod['selection'], selection)
    assert_allclose(mod['state_cov'], state_cov)


def test_no_endog():
    # Test for RuntimeError when no endog is provided by the time filtering
    # is initialized.

    mod = KalmanFilter(k_endog=1, k_states=1)

    # directly call the _initialize_filter function
    assert_raises(RuntimeError, mod._initialize_filter)
    # indirectly call it through filtering
    mod.initialize_approximate_diffuse()
    assert_raises(RuntimeError, mod.filter)


def test_cython():
    # Test the cython _kalman_filter creation, re-creation, calling, etc.

    # Check that datatypes are correct:
    for prefix, dtype in tools.prefix_dtype_map.items():
        endog = np.array(1., ndmin=2, dtype=dtype)
        mod = KalmanFilter(k_endog=1, k_states=1, dtype=dtype)

        # Bind data and initialize the ?KalmanFilter object
        mod.bind(endog)
        mod._initialize_filter()

        # Check that the dtype and prefix are correct
        assert_equal(mod.prefix, prefix)
        assert_equal(mod.dtype, dtype)

        # Test that a dKalmanFilter instance was created
        assert_equal(prefix in mod._kalman_filters, True)
        kf = mod._kalman_filters[prefix]
        assert isinstance(kf, tools.prefix_kalman_filter_map[prefix])

        # Test that the default returned _kalman_filter is the above instance
        assert_equal(mod._kalman_filter, kf)

    # Check that upcasting datatypes / ?KalmanFilter works (e.g. d -> z)
    mod = KalmanFilter(k_endog=1, k_states=1)

    # Default dtype is float
    assert_equal(mod.prefix, 'd')
    assert_equal(mod.dtype, np.float64)

    # Prior to initialization, no ?KalmanFilter exists
    assert_equal(mod._kalman_filter, None)

    # Bind data and initialize the ?KalmanFilter object
    endog = np.ascontiguousarray(np.array([1., 2.], dtype=np.float64))
    mod.bind(endog)
    mod._initialize_filter()
    kf = mod._kalman_filters['d']

    # Rebind data, still float, check that we haven't changed
    mod.bind(endog)
    mod._initialize_filter()
    assert_equal(mod._kalman_filter, kf)

    # Force creating new ?Statespace and ?KalmanFilter, by changing the
    # time-varying character of an array
    mod.design = np.zeros((1, 1, 2))
    mod._initialize_filter()
    assert_equal(mod._kalman_filter == kf, False)
    kf = mod._kalman_filters['d']

    # Rebind data, now complex, check that the ?KalmanFilter instance has
    # changed
    endog = np.ascontiguousarray(np.array([1., 2.], dtype=np.complex128))
    mod.bind(endog)
    assert_equal(mod._kalman_filter == kf, False)


def test_filter():
    # Tests of invalid calls to the filter function

    endog = np.ones((10, 1))
    mod = KalmanFilter(endog, k_states=1, initialization='approximate_diffuse')
    mod['design', :] = 1
    mod['selection', :] = 1
    mod['state_cov', :] = 1

    # Test default filter results
    res = mod.filter()
    assert_equal(isinstance(res, FilterResults), True)


def test_loglike():
    # Tests of invalid calls to the loglike function

    endog = np.ones((10, 1))
    mod = KalmanFilter(endog, k_states=1, initialization='approximate_diffuse')
    mod['design', :] = 1
    mod['selection', :] = 1
    mod['state_cov', :] = 1

    # Test that self.memory_no_likelihood = True raises an error
    mod.memory_no_likelihood = True
    assert_raises(RuntimeError, mod.loglike)
    assert_raises(RuntimeError, mod.loglikeobs)


def test_predict():
    # Tests of invalid calls to the predict function

    warnings.simplefilter("always")

    endog = np.ones((10, 1))
    mod = KalmanFilter(endog, k_states=1, initialization='approximate_diffuse')
    mod['design', :] = 1
    mod['obs_intercept'] = np.zeros((1, 10))
    mod['selection', :] = 1
    mod['state_cov', :] = 1

    # Check that we need both forecasts and predicted output for prediction
    mod.memory_no_forecast = True
    res = mod.filter()
    assert_raises(ValueError, res.predict)
    mod.memory_no_forecast = False

    mod.memory_no_predicted = True
    res = mod.filter()
    assert_raises(ValueError, res.predict)
    mod.memory_no_predicted = False

    # Now get a clean filter object
    res = mod.filter()

    # Check that start < 0 is an error
    assert_raises(ValueError, res.predict, start=-1)

    # Check that end < start is an error
    assert_raises(ValueError, res.predict, start=2, end=1)

    # Check that dynamic < 0 is an error
    assert_raises(ValueError, res.predict, dynamic=-1)

    # Check that dynamic > end is an warning
    with warnings.catch_warnings(record=True) as w:
        res.predict(end=1, dynamic=2)
        message = ('Dynamic prediction specified to begin after the end of'
                   ' prediction, and so has no effect.')
        assert_equal(str(w[0].message), message)

    # Check that dynamic > nobs is an warning
    with warnings.catch_warnings(record=True) as w:
        res.predict(end=11, dynamic=11, obs_intercept=np.zeros((1, 1)))
        message = ('Dynamic prediction specified to begin during'
                   ' out-of-sample forecasting period, and so has no'
                   ' effect.')
        assert_equal(str(w[0].message), message)

    # Check for a warning when providing a non-used statespace matrix
    with warnings.catch_warnings(record=True) as w:
        res.predict(end=res.nobs+1, design=True,
                    obs_intercept=np.zeros((1, 1)))
        message = ('Model has time-invariant design matrix, so the design'
                   ' argument to `predict` has been ignored.')
        assert_equal(str(w[0].message), message)

    # Check that an error is raised when a new time-varying matrix is not
    # provided
    assert_raises(ValueError, res.predict, end=res.nobs+1)

    # Check that an error is raised when a non-two-dimensional obs_intercept
    # is given
    assert_raises(ValueError, res.predict, end=res.nobs+1,
                  obs_intercept=np.zeros(1))

    # Check that an error is raised when an obs_intercept with incorrect length
    # is given
    assert_raises(ValueError, res.predict, end=res.nobs+1,
                  obs_intercept=np.zeros(2))

    # Check that start=None gives start=0 and end=None gives end=nobs
    assert_equal(res.predict().forecasts.shape, (1, res.nobs))

    # Check that dynamic=True begins dynamic prediction immediately
    # TODO just a smoke test
    res.predict(dynamic=True)

    # Check that on success, PredictionResults object is returned
    prediction_results = res.predict(start=3, end=5)
    assert_equal(isinstance(prediction_results, PredictionResults), True)

    # Check for correctly subset representation arrays
    # (k_endog, npredictions) = (1, 2)
    assert_equal(prediction_results.endog.shape, (1, 2))
    # (k_endog, npredictions) = (1, 2)
    assert_equal(prediction_results.obs_intercept.shape, (1, 2))
    # (k_endog, k_states) = (1, 1)
    assert_equal(prediction_results.design.shape, (1, 1))
    # (k_endog, k_endog) = (1, 1)
    assert_equal(prediction_results.obs_cov.shape, (1, 1))
    # (k_state,) = (1,)
    assert_equal(prediction_results.state_intercept.shape, (1,))
    # (k_state, npredictions) = (1, 2)
    assert_equal(prediction_results.obs_intercept.shape, (1, 2))
    # (k_state, k_state) = (1, 1)
    assert_equal(prediction_results.transition.shape, (1, 1))
    # (k_state, k_posdef) = (1, 1)
    assert_equal(prediction_results.selection.shape, (1, 1))
    # (k_posdef, k_posdef) = (1, 1)
    assert_equal(prediction_results.state_cov.shape, (1, 1))

    # Check for correctly subset filter output arrays
    # (k_endog, npredictions) = (1, 2)
    assert_equal(prediction_results.forecasts.shape, (1, 2))
    assert_equal(prediction_results.forecasts_error.shape, (1, 2))
    # (k_states, npredictions) = (1, 2)
    assert_equal(prediction_results.filtered_state.shape, (1, 2))
    assert_equal(prediction_results.predicted_state.shape, (1, 2))
    # (k_endog, k_endog, npredictions) = (1, 1, 2)
    assert_equal(prediction_results.forecasts_error_cov.shape, (1, 1, 2))
    # (k_states, k_states, npredictions) = (1, 1, 2)
    assert_equal(prediction_results.filtered_state_cov.shape, (1, 1, 2))
    assert_equal(prediction_results.predicted_state_cov.shape, (1, 1, 2))

    # Check for invalid attribute
    assert_raises(AttributeError, getattr, prediction_results, 'test')

    # Check that an error is raised when a non-two-dimensional obs_cov
    # is given
    # ...and...
    # Check that an error is raised when an obs_cov with incorrect length
    # is given
    mod = KalmanFilter(endog, k_states=1, initialization='approximate_diffuse')
    mod['design', :] = 1
    mod['obs_cov'] = np.zeros((1, 1, 10))
    mod['selection', :] = 1
    mod['state_cov', :] = 1
    res = mod.filter()

    assert_raises(ValueError, res.predict, end=res.nobs+1,
                  obs_cov=np.zeros((1, 1)))
    assert_raises(ValueError, res.predict, end=res.nobs+1,
                  obs_cov=np.zeros((1, 1, 2)))


def test_standardized_forecasts_error():
    # Simple test that standardized forecasts errors are calculated correctly.

    # Just uses a different calculation method on a univariate series.

    # Get the dataset
    true = results_kalman_filter.uc_uni
    data = pd.DataFrame(
        true['data'],
        index=pd.date_range('1947-01-01', '1995-07-01', freq='QS'),
        columns=['GDP']
    )
    data['lgdp'] = np.log(data['GDP'])

    # Fit an ARIMA(1, 1, 0) to log GDP
    mod = sarimax.SARIMAX(data['lgdp'], order=(1, 1, 0))
    res = mod.fit(disp=-1)

    standardized_forecasts_error = (
        res.filter_results.forecasts_error[0] /
        np.sqrt(res.filter_results.forecasts_error_cov[0, 0])
    )

    assert_allclose(
        res.filter_results.standardized_forecasts_error[0],
        standardized_forecasts_error,
    )


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)


def test_impulse_responses():
    # Test for impulse response functions

    # Random walk: 1-unit impulse response (i.e. non-orthogonalized irf) is 1
    # for all periods
    mod = KalmanFilter(k_endog=1, k_states=1)
    mod['design', 0, 0] = 1.
    mod['transition', 0, 0] = 1.
    mod['selection', 0, 0] = 1.
    mod['state_cov', 0, 0] = 2.

    actual = mod.impulse_responses(steps=10)
    desired = np.ones((11, 1))

    assert_allclose(actual, desired)

    # Random walk: 2-unit impulse response (i.e. non-orthogonalized irf) is 2
    # for all periods
    mod = KalmanFilter(k_endog=1, k_states=1)
    mod['design', 0, 0] = 1.
    mod['transition', 0, 0] = 1.
    mod['selection', 0, 0] = 1.
    mod['state_cov', 0, 0] = 2.

    actual = mod.impulse_responses(steps=10, impulse=[2])
    desired = np.ones((11, 1)) * 2

    assert_allclose(actual, desired)

    # Random walk: 1-standard-deviation response (i.e. orthogonalized irf) is
    # sigma for all periods (here sigma^2 = 2)
    mod = KalmanFilter(k_endog=1, k_states=1)
    mod['design', 0, 0] = 1.
    mod['transition', 0, 0] = 1.
    mod['selection', 0, 0] = 1.
    mod['state_cov', 0, 0] = 2.

    actual = mod.impulse_responses(steps=10, orthogonalized=True)
    desired = np.ones((11, 1)) * 2**0.5

    assert_allclose(actual, desired)

    # Random walk: 1-standard-deviation cumulative response (i.e. cumulative
    # orthogonalized irf)
    mod = KalmanFilter(k_endog=1, k_states=1)
    mod['design', 0, 0] = 1.
    mod['transition', 0, 0] = 1.
    mod['selection', 0, 0] = 1.
    mod['state_cov', 0, 0] = 2.

    actual = mod.impulse_responses(steps=10, orthogonalized=True,
                                   cumulative=True)
    desired = np.cumsum(np.ones((11, 1)) * 2**0.5)[:, np.newaxis]

    actual = mod.impulse_responses(steps=10, impulse=[1], orthogonalized=True,
                                   cumulative=True)
    desired = np.cumsum(np.ones((11, 1)) * 2**0.5)[:, np.newaxis]

    assert_allclose(actual, desired)

    # Random walk: 1-unit impulse response (i.e. non-orthogonalized irf) is 1
    # for all periods, even when intercepts are present
    mod = KalmanFilter(k_endog=1, k_states=1)
    mod['state_intercept', 0] = 100.
    mod['design', 0, 0] = 1.
    mod['obs_intercept', 0] = -1000.
    mod['transition', 0, 0] = 1.
    mod['selection', 0, 0] = 1.
    mod['state_cov', 0, 0] = 2.

    actual = mod.impulse_responses(steps=10)
    desired = np.ones((11, 1))

    assert_allclose(actual, desired)

    # Univariate model (random walk): test that an error is thrown when
    # a multivariate or empty "impulse" is sent
    mod = KalmanFilter(k_endog=1, k_states=1)
    assert_raises(ValueError, mod.impulse_responses, impulse=1)
    assert_raises(ValueError, mod.impulse_responses, impulse=[1, 1])
    assert_raises(ValueError, mod.impulse_responses, impulse=[])

    # Univariate model with two uncorrelated shocks
    mod = KalmanFilter(k_endog=1, k_states=2)
    mod['design', 0, 0:2] = 1.
    mod['transition', :, :] = np.eye(2)
    mod['selection', :, :] = np.eye(2)
    mod['state_cov', :, :] = np.eye(2)

    desired = np.ones((11, 1))

    actual = mod.impulse_responses(steps=10, impulse=0)
    assert_allclose(actual, desired)

    actual = mod.impulse_responses(steps=10, impulse=[1, 0])
    assert_allclose(actual, desired)

    actual = mod.impulse_responses(steps=10, impulse=1)
    assert_allclose(actual, desired)

    actual = mod.impulse_responses(steps=10, impulse=[0, 1])
    assert_allclose(actual, desired)

    # In this case (with sigma=sigma^2=1), orthogonalized is the same as not
    actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True)
    assert_allclose(actual, desired)

    actual = mod.impulse_responses(
        steps=10, impulse=[1, 0], orthogonalized=True)
    assert_allclose(actual, desired)

    actual = mod.impulse_responses(
        steps=10, impulse=[0, 1], orthogonalized=True)
    assert_allclose(actual, desired)

    # Univariate model with two correlated shocks
    mod = KalmanFilter(k_endog=1, k_states=2)
    mod['design', 0, 0:2] = 1.
    mod['transition', :, :] = np.eye(2)
    mod['selection', :, :] = np.eye(2)
    mod['state_cov', :, :] = np.array([[1, 0.5], [0.5, 1.25]])

    desired = np.ones((11, 1))

    # Non-orthogonalized (i.e. 1-unit) impulses still just generate 1's
    actual = mod.impulse_responses(steps=10, impulse=0)
    assert_allclose(actual, desired)

    actual = mod.impulse_responses(steps=10, impulse=1)
    assert_allclose(actual, desired)

    # Orthogonalized (i.e. 1-std-dev) impulses now generate different responses
    actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True)
    assert_allclose(actual, desired + desired * 0.5)

    actual = mod.impulse_responses(steps=10, impulse=1, orthogonalized=True)
    assert_allclose(actual, desired)

    # Multivariate model with two correlated shocks
    mod = KalmanFilter(k_endog=2, k_states=2)
    mod['design', :, :] = np.eye(2)
    mod['transition', :, :] = np.eye(2)
    mod['selection', :, :] = np.eye(2)
    mod['state_cov', :, :] = np.array([[1, 0.5], [0.5, 1.25]])

    ones = np.ones((11, 1))
    zeros = np.zeros((11, 1))

    # Non-orthogonalized (i.e. 1-unit) impulses still just generate 1's, but
    # only for the appropriate series
    actual = mod.impulse_responses(steps=10, impulse=0)
    assert_allclose(actual, np.c_[ones, zeros])

    actual = mod.impulse_responses(steps=10, impulse=1)
    assert_allclose(actual, np.c_[zeros, ones])

    # Orthogonalized (i.e. 1-std-dev) impulses now generate different
    # responses, and only for the appropriate series
    actual = mod.impulse_responses(steps=10, impulse=0, orthogonalized=True)
    assert_allclose(actual, np.c_[ones, ones * 0.5])

    actual = mod.impulse_responses(steps=10, impulse=1, orthogonalized=True)
    assert_allclose(actual, np.c_[zeros, ones])

    # AR(1) model generates a geometrically declining series
    mod = sarimax.SARIMAX([0.1, 0.5, -0.2], order=(1, 0, 0))
    phi = 0.5
    mod.update([phi, 1])

    desired = np.cumprod(np.r_[1, [phi]*10])

    # Test going through the model directly
    actual = mod.ssm.impulse_responses(steps=10)
    assert_allclose(actual[:, 0], desired)

    # Test going through the results object
    res = mod.filter([phi, 1.])
    actual = res.impulse_responses(steps=10)
    assert_allclose(actual, desired)


def test_missing():
    # Datasets
    endog = np.arange(10).reshape(10, 1)
    endog_pre_na = np.ascontiguousarray(np.c_[
        endog.copy() * np.nan, endog.copy() * np.nan, endog, endog])
    endog_post_na = np.ascontiguousarray(np.c_[
        endog, endog, endog.copy() * np.nan, endog.copy() * np.nan])
    endog_inject_na = np.ascontiguousarray(np.c_[
        endog, endog.copy() * np.nan, endog, endog.copy() * np.nan])

    # Base model
    mod = KalmanFilter(np.ascontiguousarray(np.c_[endog, endog]), k_states=1,
                       initialization='approximate_diffuse')
    mod['design', :, :] = 1
    mod['obs_cov', :, :] = np.eye(mod.k_endog)*0.5
    mod['transition', :, :] = 0.5
    mod['selection', :, :] = 1
    mod['state_cov', :, :] = 0.5
    llf = mod.loglikeobs()

    # Model with prepended nans
    mod = KalmanFilter(endog_pre_na, k_states=1,
                       initialization='approximate_diffuse')
    mod['design', :, :] = 1
    mod['obs_cov', :, :] = np.eye(mod.k_endog)*0.5
    mod['transition', :, :] = 0.5
    mod['selection', :, :] = 1
    mod['state_cov', :, :] = 0.5
    llf_pre_na = mod.loglikeobs()

    assert_allclose(llf_pre_na, llf)

    # Model with appended nans
    mod = KalmanFilter(endog_post_na, k_states=1,
                       initialization='approximate_diffuse')
    mod['design', :, :] = 1
    mod['obs_cov', :, :] = np.eye(mod.k_endog)*0.5
    mod['transition', :, :] = 0.5
    mod['selection', :, :] = 1
    mod['state_cov', :, :] = 0.5
    llf_post_na = mod.loglikeobs()

    assert_allclose(llf_post_na, llf)

    # Model with injected nans
    mod = KalmanFilter(endog_inject_na, k_states=1,
                       initialization='approximate_diffuse')
    mod['design', :, :] = 1
    mod['obs_cov', :, :] = np.eye(mod.k_endog)*0.5
    mod['transition', :, :] = 0.5
    mod['selection', :, :] = 1
    mod['state_cov', :, :] = 0.5
    llf_inject_na = mod.loglikeobs()

    assert_allclose(llf_inject_na, llf)