test_arima.py

from statsmodels.compat.platform import (PLATFORM_OSX, PLATFORM_WIN,
                                         PLATFORM_WIN32)
from statsmodels.compat.python import lrange

import os
import pickle
import warnings
from io import BytesIO

import numpy as np
import pandas as pd
import pytest
from numpy.testing import assert_almost_equal, assert_allclose, assert_raises
from pandas import DatetimeIndex, date_range, period_range

import statsmodels.sandbox.tsa.fftarma as fa
from statsmodels.datasets.macrodata import load_pandas as load_macrodata_pandas
from statsmodels.regression.linear_model import OLS
from statsmodels.tools.sm_exceptions import (
    ValueWarning, HessianInversionWarning, SpecificationWarning,
    MissingDataError)
from statsmodels.tools.testing import assert_equal
from statsmodels.tsa.ar_model import AutoReg
from statsmodels.tsa.arima_model import ARMA, ARIMA
from statsmodels.tsa.arima_process import arma_generate_sample
from statsmodels.tsa.arma_mle import Arma
from statsmodels.tsa.tests.results import results_arma, results_arima

DECIMAL_4 = 4
DECIMAL_3 = 3
DECIMAL_2 = 2
DECIMAL_1 = 1

current_path = os.path.dirname(os.path.abspath(__file__))
ydata_path = os.path.join(current_path, 'results', 'y_arma_data.csv')
with open(ydata_path, "rb") as fd:
    y_arma = np.genfromtxt(fd, delimiter=",", skip_header=1, dtype=float)

cpi_dates = period_range(start='1959q1', end='2009q3', freq='Q')
sun_dates = period_range(start='1700', end='2008', freq='A')
cpi_predict_dates = period_range(start='2009q3', end='2015q4', freq='Q')
sun_predict_dates = period_range(start='2008', end='2033', freq='A')


def test_compare_arma():
    # this is a preliminary test to compare arma_kf, arma_cond_ls
    # and arma_cond_mle
    # the results returned by the fit methods are incomplete
    # for now without random.seed

    np.random.seed(9876565)
    x = fa.ArmaFft([1, -0.5], [1., 0.4], 40).generate_sample(nsample=200,
                                                             burnin=1000)

    modkf = ARMA(x, (1, 1))
    reskf = modkf.fit(trend='nc', disp=-1)
    dres = reskf

    modc = Arma(x)
    resls = modc.fit(order=(1, 1))
    rescm = modc.fit_mle(order=(1, 1), start_params=[0.4, 0.4, 1.], disp=0)

    # decimal 1 corresponds to threshold of 5% difference
    # still different sign  corrcted
    assert_almost_equal(resls[0] / dres.params, np.ones(dres.params.shape),
                        decimal=1)

    # rescm also contains variance estimate as last element of params
    assert_almost_equal(rescm.params[:-1] / dres.params,
                        np.ones(dres.params.shape), decimal=1)


class CheckArmaResultsMixin(object):
    """
    res2 are the results from gretl.  They are in results/results_arma.
    res1 are from statsmodels
    """
    decimal_params = DECIMAL_4

    def test_params(self):
        assert_almost_equal(self.res1.params, self.res2.params,
                            self.decimal_params)

    decimal_aic = DECIMAL_4

    def test_aic(self):
        assert_almost_equal(self.res1.aic, self.res2.aic, self.decimal_aic)

    decimal_bic = DECIMAL_4

    def test_bic(self):
        assert_almost_equal(self.res1.bic, self.res2.bic, self.decimal_bic)

    decimal_arroots = DECIMAL_4

    def test_arroots(self):
        assert_almost_equal(self.res1.arroots, self.res2.arroots,
                            self.decimal_arroots)

    decimal_maroots = DECIMAL_4

    def test_maroots(self):
        assert_almost_equal(self.res1.maroots, self.res2.maroots,
                            self.decimal_maroots)

    decimal_bse = DECIMAL_2

    def test_bse(self):
        assert_almost_equal(self.res1.bse, self.res2.bse, self.decimal_bse)

    decimal_cov_params = DECIMAL_4

    def test_covparams(self):
        assert_almost_equal(self.res1.cov_params(), self.res2.cov_params,
                            self.decimal_cov_params)

    decimal_hqic = DECIMAL_4

    def test_hqic(self):
        assert_almost_equal(self.res1.hqic, self.res2.hqic, self.decimal_hqic)

    decimal_llf = DECIMAL_4

    def test_llf(self):
        assert_almost_equal(self.res1.llf, self.res2.llf, self.decimal_llf)

    decimal_resid = DECIMAL_4

    def test_resid(self):
        assert_almost_equal(self.res1.resid, self.res2.resid,
                            self.decimal_resid)

    decimal_fittedvalues = DECIMAL_4

    def test_fittedvalues(self):
        assert_almost_equal(self.res1.fittedvalues, self.res2.fittedvalues,
                            self.decimal_fittedvalues)

    decimal_pvalues = DECIMAL_2

    def test_pvalues(self):
        assert_almost_equal(self.res1.pvalues, self.res2.pvalues,
                            self.decimal_pvalues)

    decimal_t = DECIMAL_2  # only 2 decimal places in gretl output

    def test_tvalues(self):
        assert_almost_equal(self.res1.tvalues, self.res2.tvalues,
                            self.decimal_t)

    decimal_sigma2 = DECIMAL_4

    def test_sigma2(self):
        assert_almost_equal(self.res1.sigma2, self.res2.sigma2,
                            self.decimal_sigma2)

    @pytest.mark.smoke
    def test_summary(self):
        self.res1.summary()

    @pytest.mark.smoke
    def test_summary2(self):
        self.res1.summary2()


class CheckForecastMixin(object):
    decimal_forecast = DECIMAL_4

    def test_forecast(self):
        assert_almost_equal(self.res1.forecast_res, self.res2.forecast,
                            self.decimal_forecast)

    decimal_forecasterr = DECIMAL_4

    def test_forecasterr(self):
        assert_almost_equal(self.res1.forecast_err, self.res2.forecasterr,
                            self.decimal_forecasterr)


class CheckDynamicForecastMixin(object):
    decimal_forecast_dyn = 4

    def test_dynamic_forecast(self):
        assert_almost_equal(self.res1.forecast_res_dyn, self.res2.forecast_dyn,
                            self.decimal_forecast_dyn)

    def test_forecasterr(self):
        assert_almost_equal(self.res1.forecast_err_dyn,
                            self.res2.forecasterr_dyn,
                            DECIMAL_4)


class CheckArimaResultsMixin(CheckArmaResultsMixin):
    def test_order(self):
        assert self.res1.k_diff == self.res2.k_diff
        assert self.res1.k_ar == self.res2.k_ar
        assert self.res1.k_ma == self.res2.k_ma

    decimal_predict_levels = DECIMAL_4

    def test_predict_levels(self):
        assert_almost_equal(self.res1.predict(typ='levels'), self.res2.linear,
                            self.decimal_predict_levels)


class Test_Y_ARMA11_NoConst(CheckArmaResultsMixin, CheckForecastMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 0]
        cls.res1 = ARMA(endog, order=(1, 1)).fit(trend='nc', disp=-1)
        (cls.res1.forecast_res, cls.res1.forecast_err,
         confint) = cls.res1.forecast(10)
        cls.res2 = results_arma.Y_arma11()

    def test_pickle(self):
        fh = BytesIO()
        # test wrapped results load save pickle
        self.res1.save(fh)
        fh.seek(0, 0)
        res_unpickled = self.res1.__class__.load(fh)
        assert type(res_unpickled) is type(self.res1)  # noqa: E721


class Test_Y_ARMA14_NoConst(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 1]
        cls.res1 = ARMA(endog, order=(1, 4)).fit(trend='nc', disp=-1)
        cls.res2 = results_arma.Y_arma14()


@pytest.mark.slow
class Test_Y_ARMA41_NoConst(CheckArmaResultsMixin, CheckForecastMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 2]
        cls.res1 = ARMA(endog, order=(4, 1)).fit(trend='nc', disp=-1)
        (cls.res1.forecast_res, cls.res1.forecast_err,
         confint) = cls.res1.forecast(10)
        cls.res2 = results_arma.Y_arma41()
        cls.decimal_maroots = DECIMAL_3


class Test_Y_ARMA22_NoConst(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 3]
        cls.res1 = ARMA(endog, order=(2, 2)).fit(trend='nc', disp=-1)
        cls.res2 = results_arma.Y_arma22()


class Test_Y_ARMA50_NoConst(CheckArmaResultsMixin, CheckForecastMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 4]
        cls.res1 = ARMA(endog, order=(5, 0)).fit(trend='nc', disp=-1)
        (cls.res1.forecast_res, cls.res1.forecast_err,
         confint) = cls.res1.forecast(10)
        cls.res2 = results_arma.Y_arma50()


class Test_Y_ARMA02_NoConst(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 5]
        cls.res1 = ARMA(endog, order=(0, 2)).fit(trend='nc', disp=-1)
        cls.res2 = results_arma.Y_arma02()


class Test_Y_ARMA11_Const(CheckArmaResultsMixin, CheckForecastMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 6]
        cls.res1 = ARMA(endog, order=(1, 1)).fit(trend="c", disp=-1)
        (cls.res1.forecast_res, cls.res1.forecast_err,
         confint) = cls.res1.forecast(10)
        cls.res2 = results_arma.Y_arma11c()


class Test_Y_ARMA14_Const(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 7]
        cls.res1 = ARMA(endog, order=(1, 4)).fit(trend="c", disp=-1)
        cls.res2 = results_arma.Y_arma14c()


class Test_Y_ARMA41_Const(CheckArmaResultsMixin, CheckForecastMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 8]
        cls.res2 = results_arma.Y_arma41c()
        cls.res1 = ARMA(endog, order=(4, 1)).fit(trend="c", disp=-1,
                                                 start_params=cls.res2.params)
        (cls.res1.forecast_res, cls.res1.forecast_err,
         confint) = cls.res1.forecast(10)
        cls.decimal_cov_params = DECIMAL_3
        cls.decimal_fittedvalues = DECIMAL_3
        cls.decimal_resid = DECIMAL_3
        cls.decimal_params = DECIMAL_3


class Test_Y_ARMA22_Const(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 9]
        cls.res1 = ARMA(endog, order=(2, 2)).fit(trend="c", disp=-1)
        cls.res2 = results_arma.Y_arma22c()

    def test_summary(self):
        # regression test for html of roots table #4434
        # we ignore whitespace in the assert
        summ = self.res1.summary()
        summ_roots = """\
        <tableclass="simpletable">
        <caption>Roots</caption>
        <tr>
        <td></td><th>Real</th><th>Imaginary</th><th>Modulus</th><th>Frequency</th>
        </tr>
        <tr>
        <th>AR.1</th><td>1.0991</td><td>-1.2571j</td><td>1.6698</td><td>-0.1357</td>
        </tr>
        <tr>
        <th>AR.2</th><td>1.0991</td><td>+1.2571j</td><td>1.6698</td><td>0.1357</td>
        </tr>
        <tr>
        <th>MA.1</th><td>-1.1702</td><td>+0.0000j</td><td>1.1702</td><td>0.5000</td>
        </tr>
        <tr>
        <th>MA.2</th><td>1.2215</td><td>+0.0000j</td><td>1.2215</td><td>0.0000</td>
        </tr>
        </table>"""
        assert_equal(summ.tables[2]._repr_html_().replace(' ', ''),
                     summ_roots.replace(' ', ''))


class Test_Y_ARMA50_Const(CheckArmaResultsMixin, CheckForecastMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 10]
        cls.res1 = ARMA(endog, order=(5, 0)).fit(trend="c", disp=-1)
        (cls.res1.forecast_res, cls.res1.forecast_err,
         confint) = cls.res1.forecast(10)
        cls.res2 = results_arma.Y_arma50c()


class Test_Y_ARMA02_Const(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 11]
        cls.res1 = ARMA(endog, order=(0, 2)).fit(trend="c", disp=-1)
        cls.res2 = results_arma.Y_arma02c()


# cov_params and tvalues are off still but not as much vs. R
class Test_Y_ARMA11_NoConst_CSS(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 0]
        cls.res1 = ARMA(endog, order=(1, 1)).fit(method="css", trend='nc',
                                                 disp=-1)
        cls.res2 = results_arma.Y_arma11("css")
        cls.decimal_t = DECIMAL_1


# better vs. R
class Test_Y_ARMA14_NoConst_CSS(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 1]
        cls.res1 = ARMA(endog, order=(1, 4)).fit(method="css", trend='nc',
                                                 disp=-1)
        cls.res2 = results_arma.Y_arma14("css")
        cls.decimal_fittedvalues = DECIMAL_3
        cls.decimal_resid = DECIMAL_3
        cls.decimal_t = DECIMAL_1


# bse, etc. better vs. R
# maroot is off because maparams is off a bit (adjust tolerance?)
class Test_Y_ARMA41_NoConst_CSS(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 2]
        cls.res1 = ARMA(endog, order=(4, 1)).fit(method="css", trend='nc',
                                                 disp=-1)
        cls.res2 = results_arma.Y_arma41("css")
        cls.decimal_t = DECIMAL_1
        cls.decimal_pvalues = 0
        cls.decimal_cov_params = DECIMAL_3
        cls.decimal_maroots = DECIMAL_1


# same notes as above
class Test_Y_ARMA22_NoConst_CSS(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 3]
        cls.res1 = ARMA(endog, order=(2, 2)).fit(method="css", trend='nc',
                                                 disp=-1)
        cls.res2 = results_arma.Y_arma22("css")
        cls.decimal_t = DECIMAL_1
        cls.decimal_resid = DECIMAL_3
        cls.decimal_pvalues = DECIMAL_1
        cls.decimal_fittedvalues = DECIMAL_3


# NOTE: gretl just uses least squares for AR CSS
# so BIC, etc. is
# -2*res1.llf + np.log(nobs)*(res1.q+res1.p+res1.k)
# with no adjustment for p and no extra sigma estimate
# NOTE: so our tests use x-12 arima results which agree with us and are
# consistent with the rest of the models
class Test_Y_ARMA50_NoConst_CSS(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 4]
        cls.res1 = ARMA(endog, order=(5, 0)).fit(method="css", trend='nc',
                                                 disp=-1)
        cls.res2 = results_arma.Y_arma50("css")
        cls.decimal_t = 0
        cls.decimal_llf = DECIMAL_1  # looks like rounding error?


class Test_Y_ARMA02_NoConst_CSS(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 5]
        cls.res1 = ARMA(endog, order=(0, 2)).fit(method="css", trend='nc',
                                                 disp=-1)
        cls.res2 = results_arma.Y_arma02("css")


# NOTE: our results are close to --x-12-arima option and R
class Test_Y_ARMA11_Const_CSS(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 6]
        cls.res1 = ARMA(endog, order=(1, 1)).fit(trend="c", method="css",
                                                 disp=-1)
        cls.res2 = results_arma.Y_arma11c("css")
        cls.decimal_params = DECIMAL_3
        cls.decimal_cov_params = DECIMAL_3
        cls.decimal_t = DECIMAL_1


class Test_Y_ARMA14_Const_CSS(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 7]
        cls.res1 = ARMA(endog, order=(1, 4)).fit(trend="c", method="css",
                                                 disp=-1)
        cls.res2 = results_arma.Y_arma14c("css")
        cls.decimal_t = DECIMAL_1
        cls.decimal_pvalues = DECIMAL_1


class Test_Y_ARMA41_Const_CSS(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 8]
        cls.res1 = ARMA(endog, order=(4, 1)).fit(trend="c", method="css",
                                                 disp=-1)
        cls.res2 = results_arma.Y_arma41c("css")
        cls.decimal_t = DECIMAL_1
        cls.decimal_cov_params = DECIMAL_1
        cls.decimal_maroots = DECIMAL_3
        cls.decimal_bse = DECIMAL_1


class Test_Y_ARMA22_Const_CSS(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 9]
        cls.res1 = ARMA(endog, order=(2, 2)).fit(trend="c", method="css",
                                                 disp=-1)
        cls.res2 = results_arma.Y_arma22c("css")
        cls.decimal_t = 0
        cls.decimal_pvalues = DECIMAL_1


class Test_Y_ARMA50_Const_CSS(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 10]
        cls.res1 = ARMA(endog, order=(5, 0)).fit(trend="c", method="css",
                                                 disp=-1)
        cls.res2 = results_arma.Y_arma50c("css")
        cls.decimal_t = DECIMAL_1
        cls.decimal_params = DECIMAL_3
        cls.decimal_cov_params = DECIMAL_2


class Test_Y_ARMA02_Const_CSS(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 11]
        cls.res1 = ARMA(endog, order=(0, 2)).fit(trend="c", method="css",
                                                 disp=-1)
        cls.res2 = results_arma.Y_arma02c("css")


def test_reset_trend_error():
    endog = y_arma[:, 0]
    mod = ARMA(endog, order=(1, 1))
    mod.fit(trend="c", disp=-1)
    with pytest.raises(RuntimeError):
        mod.fit(trend="nc", disp=-1)


@pytest.mark.slow
def test_start_params_bug():
    data = np.array([1368., 1187, 1090, 1439, 2362, 2783, 2869, 2512, 1804,
                     1544, 1028, 869, 1737, 2055, 1947, 1618, 1196, 867, 997,
                     1862, 2525,
                     3250, 4023, 4018, 3585, 3004, 2500, 2441, 2749, 2466,
                     2157, 1847, 1463,
                     1146, 851, 993, 1448, 1719, 1709, 1455, 1950, 1763, 2075,
                     2343, 3570,
                     4690, 3700, 2339, 1679, 1466, 998, 853, 835, 922, 851,
                     1125, 1299, 1105,
                     860, 701, 689, 774, 582, 419, 846, 1132, 902, 1058, 1341,
                     1551, 1167,
                     975, 786, 759, 751, 649, 876, 720, 498, 553, 459, 543,
                     447, 415, 377,
                     373, 324, 320, 306, 259, 220, 342, 558, 825, 994, 1267,
                     1473, 1601,
                     1896, 1890, 2012, 2198, 2393, 2825, 3411, 3406, 2464,
                     2891, 3685, 3638,
                     3746, 3373, 3190, 2681, 2846, 4129, 5054, 5002, 4801,
                     4934, 4903, 4713,
                     4745, 4736, 4622, 4642, 4478, 4510, 4758, 4457, 4356,
                     4170, 4658, 4546,
                     4402, 4183, 3574, 2586, 3326, 3948, 3983, 3997, 4422,
                     4496, 4276, 3467,
                     2753, 2582, 2921, 2768, 2789, 2824, 2482, 2773, 3005,
                     3641, 3699, 3774,
                     3698, 3628, 3180, 3306, 2841, 2014, 1910, 2560, 2980,
                     3012, 3210, 3457,
                     3158, 3344, 3609, 3327, 2913, 2264, 2326, 2596, 2225,
                     1767, 1190, 792,
                     669, 589, 496, 354, 246, 250, 323, 495, 924, 1536, 2081,
                     2660, 2814, 2992,
                     3115, 2962, 2272, 2151, 1889, 1481, 955, 631, 288, 103,
                     60, 82, 107, 185,
                     618, 1526, 2046, 2348, 2584, 2600, 2515, 2345, 2351, 2355,
                     2409, 2449,
                     2645, 2918, 3187, 2888, 2610, 2740, 2526, 2383, 2936,
                     2968, 2635, 2617,
                     2790, 3906, 4018, 4797, 4919, 4942, 4656, 4444, 3898,
                     3908, 3678, 3605,
                     3186, 2139, 2002, 1559, 1235, 1183, 1096, 673, 389, 223,
                     352, 308, 365,
                     525, 779, 894, 901, 1025, 1047, 981, 902, 759, 569, 519,
                     408, 263, 156,
                     72, 49, 31, 41, 192, 423, 492, 552, 564, 723, 921, 1525,
                     2768, 3531, 3824,
                     3835, 4294, 4533, 4173, 4221, 4064, 4641, 4685, 4026,
                     4323, 4585, 4836,
                     4822, 4631, 4614, 4326, 4790, 4736, 4104, 5099, 5154,
                     5121, 5384, 5274,
                     5225, 4899, 5382, 5295, 5349, 4977, 4597, 4069, 3733,
                     3439, 3052, 2626,
                     1939, 1064, 713, 916, 832, 658, 817, 921, 772, 764, 824,
                     967, 1127, 1153,
                     824, 912, 957, 990, 1218, 1684, 2030, 2119, 2233, 2657,
                     2652, 2682, 2498,
                     2429, 2346, 2298, 2129, 1829, 1816, 1225, 1010, 748, 627,
                     469, 576, 532,
                     475, 582, 641, 605, 699, 680, 714, 670, 666, 636, 672,
                     679, 446, 248, 134,
                     160, 178, 286, 413, 676, 1025, 1159, 952, 1398, 1833,
                     2045, 2072, 1798,
                     1799, 1358, 727, 353, 347, 844, 1377, 1829, 2118, 2272,
                     2745, 4263, 4314,
                     4530, 4354, 4645, 4547, 5391, 4855, 4739, 4520, 4573,
                     4305, 4196, 3773,
                     3368, 2596, 2596, 2305, 2756, 3747, 4078, 3415, 2369,
                     2210, 2316, 2263,
                     2672, 3571, 4131, 4167, 4077, 3924, 3738, 3712, 3510,
                     3182, 3179, 2951,
                     2453, 2078, 1999, 2486, 2581, 1891, 1997, 1366, 1294,
                     1536, 2794, 3211,
                     3242, 3406, 3121, 2425, 2016, 1787, 1508, 1304, 1060,
                     1342, 1589, 2361,
                     3452, 2659, 2857, 3255, 3322, 2852, 2964, 3132, 3033,
                     2931, 2636, 2818,
                     3310, 3396, 3179, 3232, 3543, 3759, 3503, 3758, 3658,
                     3425, 3053, 2620,
                     1837, 923, 712, 1054, 1376, 1556, 1498, 1523, 1088, 728,
                     890, 1413, 2524,
                     3295, 4097, 3993, 4116, 3874, 4074, 4142, 3975, 3908,
                     3907, 3918, 3755,
                     3648, 3778, 4293, 4385, 4360, 4352, 4528, 4365, 3846,
                     4098, 3860, 3230,
                     2820, 2916, 3201, 3721, 3397, 3055, 2141, 1623, 1825,
                     1716, 2232, 2939,
                     3735, 4838, 4560, 4307, 4975, 5173, 4859, 5268, 4992,
                     5100, 5070, 5270,
                     4760, 5135, 5059, 4682, 4492, 4933, 4737, 4611, 4634,
                     4789, 4811, 4379,
                     4689, 4284, 4191, 3313, 2770, 2543, 3105, 2967, 2420,
                     1996, 2247, 2564,
                     2726, 3021, 3427, 3509, 3759, 3324, 2988, 2849, 2340,
                     2443, 2364, 1252,
                     623, 742, 867, 684, 488, 348, 241, 187, 279, 355, 423,
                     678, 1375, 1497,
                     1434, 2116, 2411, 1929, 1628, 1635, 1609, 1757, 2090,
                     2085, 1790, 1846,
                     2038, 2360, 2342, 2401, 2920, 3030, 3132, 4385, 5483,
                     5865, 5595, 5485,
                     5727, 5553, 5560, 5233, 5478, 5159, 5155, 5312, 5079,
                     4510, 4628, 4535,
                     3656, 3698, 3443, 3146, 2562, 2304, 2181, 2293, 1950,
                     1930, 2197, 2796,
                     3441, 3649, 3815, 2850, 4005, 5305, 5550, 5641, 4717,
                     5131, 2831, 3518,
                     3354, 3115, 3515, 3552, 3244, 3658, 4407, 4935, 4299,
                     3166, 3335, 2728,
                     2488, 2573, 2002, 1717, 1645, 1977, 2049, 2125, 2376,
                     2551, 2578, 2629,
                     2750, 3150, 3699, 4062, 3959, 3264, 2671, 2205, 2128,
                     2133, 2095, 1964,
                     2006, 2074, 2201, 2506, 2449, 2465, 2064, 1446, 1382, 983,
                     898, 489, 319,
                     383, 332, 276, 224, 144, 101, 232, 429, 597, 750, 908,
                     960, 1076, 951,
                     1062, 1183, 1404, 1391, 1419, 1497, 1267, 963, 682, 777,
                     906, 1149, 1439,
                     1600, 1876, 1885, 1962, 2280, 2711, 2591, 2411])
    with warnings.catch_warnings():
        warnings.simplefilter("ignore")
        ARMA(data, order=(4, 1)).fit(start_ar_lags=5, disp=-1)


class Test_ARIMA101(CheckArmaResultsMixin):
    @classmethod
    def setup_class(cls):
        endog = y_arma[:, 6]
        cls.res1 = ARIMA(endog, (1, 0, 1)).fit(trend="c", disp=-1)
        (cls.res1.forecast_res, cls.res1.forecast_err,
         confint) = cls.res1.forecast(10)
        cls.res2 = results_arma.Y_arma11c()
        cls.res2.k_diff = 0
        cls.res2.k_ar = 1
        cls.res2.k_ma = 1


class Test_ARIMA111(CheckArimaResultsMixin, CheckForecastMixin,
                    CheckDynamicForecastMixin):
    @classmethod
    def setup_class(cls):
        cpi = load_macrodata_pandas().data['cpi'].values
        cls.res1 = ARIMA(cpi, (1, 1, 1)).fit(disp=-1)
        cls.res2 = results_arima.ARIMA111()
        # make sure endog names changes to D.cpi
        cls.decimal_llf = 3
        cls.decimal_aic = 3
        cls.decimal_bic = 3
        # TODO: why has dec_cov_params changed, used to be better
        cls.decimal_cov_params = 2
        cls.decimal_t = 0
        (cls.res1.forecast_res,
         cls.res1.forecast_err,
         conf_int) = cls.res1.forecast(25)
        # TODO: fix the indexing for the end here, I do not think this is right
        # if we're going to treat it like indexing
        # the forecast from 2005Q1 through 2009Q4 is indices
        # 184 through 227 not 226
        # note that the first one counts in the count so 164 + 64 is 65
        # predictions
        cls.res1.forecast_res_dyn = cls.res1.predict(start=164, end=164 + 63,
                                                     typ='levels',
                                                     dynamic=True)

    def test_freq(self):
        assert_almost_equal(self.res1.arfreq, [0.0000], 4)
        assert_almost_equal(self.res1.mafreq, [0.0000], 4)


class Test_ARIMA111CSS(CheckArimaResultsMixin, CheckForecastMixin,
                       CheckDynamicForecastMixin):
    @classmethod
    def setup_class(cls):
        cpi = load_macrodata_pandas().data['cpi'].values
        cls.res1 = ARIMA(cpi, (1, 1, 1)).fit(disp=-1, method='css')
        cls.res2 = results_arima.ARIMA111(method='css')
        cls.res2.fittedvalues = - cpi[1:-1] + cls.res2.linear
        # make sure endog names changes to D.cpi
        (cls.res1.forecast_res,
         cls.res1.forecast_err,
         conf_int) = cls.res1.forecast(25)
        cls.decimal_forecast = 2
        cls.decimal_forecast_dyn = 2
        cls.decimal_forecasterr = 3
        cls.res1.forecast_res_dyn = cls.res1.predict(start=164, end=164 + 63,
                                                     typ='levels',
                                                     dynamic=True)

        # precisions
        cls.decimal_arroots = 3
        cls.decimal_cov_params = 3
        cls.decimal_hqic = 3
        cls.decimal_maroots = 3
        cls.decimal_t = 1
        cls.decimal_fittedvalues = 2  # because of rounding when copying
        cls.decimal_resid = 2
        cls.decimal_predict_levels = DECIMAL_2


class Test_ARIMA112CSS(CheckArimaResultsMixin):
    @classmethod
    def setup_class(cls):
        cpi = load_macrodata_pandas().data['cpi'].values
        cls.res1 = ARIMA(cpi, (1, 1, 2)).fit(disp=-1, method='css',
                                             start_params=[.905322, -.692425,
                                                           1.07366,
                                                           0.172024])
        cls.res2 = results_arima.ARIMA112(method='css')
        cls.res2.fittedvalues = - cpi[1:-1] + cls.res2.linear
        # make sure endog names changes to D.cpi
        cls.decimal_llf = 3
        cls.decimal_aic = 3
        cls.decimal_bic = 3
        # TODO: fix the indexing for the end here, I do not think this is right
        # if we're going to treat it like indexing
        # the forecast from 2005Q1 through 2009Q4 is indices
        # 184 through 227 not 226
        # note that the first one counts in the count so 164 + 64 is 65
        # predictions
        # cls.res1.forecast_res_dyn = self.predict(start=164, end=164+63,
        #                                         typ='levels', dynamic=True)
        # since we got from gretl do not have linear prediction in differences
        cls.decimal_arroots = 3
        cls.decimal_maroots = 2
        cls.decimal_t = 1
        cls.decimal_resid = 2
        cls.decimal_fittedvalues = 3
        cls.decimal_predict_levels = DECIMAL_3

    def test_freq(self):
        assert_almost_equal(self.res1.arfreq, [0.5000], 4)
        assert_almost_equal(self.res1.mafreq, [0.5000, 0.5000], 4)


def test_arima_predict_mle_dates():
    cpi = load_macrodata_pandas().data['cpi'].values
    res1 = ARIMA(cpi, (4, 1, 1), dates=cpi_dates, freq='Q').fit(disp=-1)
    file_path = os.path.join(current_path, 'results',
                             'results_arima_forecasts_all_mle.csv')
    with open(file_path, "rb") as test_data:
        arima_forecasts = np.genfromtxt(test_data, delimiter=",",
                                        skip_header=1, dtype=float)

    fc = arima_forecasts[:, 0]
    fcdyn = arima_forecasts[:, 1]
    fcdyn2 = arima_forecasts[:, 2]

    start, end = 2, 51
    fv = res1.predict('1959Q3', '1971Q4', typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    assert_equal(res1.data.predict_dates, cpi_dates[start:end + 1])

    start, end = 202, 227
    fv = res1.predict('2009Q3', '2015Q4', typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    assert_equal(res1.data.predict_dates, cpi_predict_dates)

    # make sure dynamic works

    start, end = '1960q2', '1971q4'
    fv = res1.predict(start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn[5:51 + 1], DECIMAL_4)

    start, end = '1965q1', '2015q4'
    fv = res1.predict(start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn2[24:227 + 1], DECIMAL_4)


def test_arma_predict_mle_dates():
    from statsmodels.datasets.sunspots import load_pandas
    sunspots = load_pandas().data['SUNACTIVITY'].values
    mod = ARMA(sunspots, (9, 0), dates=sun_dates, freq='A')
    mod.method = 'mle'

    assert_raises(ValueError, mod._get_prediction_index, '1701', '1751', True)

    start, end = 2, 51
    mod._get_prediction_index('1702', '1751', False)
    assert_equal(mod.data.predict_dates, sun_dates[start:end + 1])

    start, end = 308, 333
    mod._get_prediction_index('2008', '2033', False)
    assert_equal(mod.data.predict_dates, sun_predict_dates)


def test_arima_predict_css_dates():
    cpi = load_macrodata_pandas().data['cpi'].values
    res1 = ARIMA(cpi, (4, 1, 1), dates=cpi_dates, freq='Q').fit(disp=-1,
                                                                method='css',
                                                                trend='nc')

    params = np.array([1.231272508473910,
                       -0.282516097759915,
                       0.170052755782440,
                       -0.118203728504945,
                       -0.938783134717947])
    file_path = os.path.join(current_path, 'results',
                             'results_arima_forecasts_all_css.csv')
    with open(file_path, "rb") as test_data:
        arima_forecasts = np.genfromtxt(test_data, delimiter=",",
                                        skip_header=1, dtype=float)

    fc = arima_forecasts[:, 0]
    fcdyn = arima_forecasts[:, 1]
    fcdyn2 = arima_forecasts[:, 2]

    start, end = 5, 51
    fv = res1.model.predict(params, '1960Q2', '1971Q4', typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    assert_equal(res1.data.predict_dates, cpi_dates[start:end + 1])

    start, end = 202, 227
    fv = res1.model.predict(params, '2009Q3', '2015Q4', typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    assert_equal(res1.data.predict_dates, cpi_predict_dates)

    # make sure dynamic works
    start, end = 5, 51
    fv = res1.model.predict(params, '1960Q2', '1971Q4', typ='levels',
                            dynamic=True)
    assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4)

    start, end = '1965q1', '2015q4'
    fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn2[24:227 + 1], DECIMAL_4)


def test_arma_predict_css_dates():
    from statsmodels.datasets.sunspots import load_pandas
    sunspots = load_pandas().data['SUNACTIVITY'].values
    mod = ARMA(sunspots, (9, 0), dates=sun_dates, freq='A')
    mod.method = 'css'
    assert_raises(ValueError, mod._get_prediction_index, '1701', '1751', False)


def test_arima_predict_mle():
    cpi = load_macrodata_pandas().data['cpi'].values
    res1 = ARIMA(cpi, (4, 1, 1)).fit(disp=-1)
    # fit the model so that we get correct endog length but use
    file_path = os.path.join(current_path, 'results',
                             'results_arima_forecasts_all_mle.csv')
    with open(file_path, "rb") as test_data:
        arima_forecasts = np.genfromtxt(test_data, delimiter=",",
                                        skip_header=1, dtype=float)
    fc = arima_forecasts[:, 0]
    fcdyn = arima_forecasts[:, 1]
    fcdyn2 = arima_forecasts[:, 2]
    fcdyn3 = arima_forecasts[:, 3]
    fcdyn4 = arima_forecasts[:, 4]

    # 0 indicates the first sample-observation below
    # ie., the index after the pre-sample, these are also differenced once
    # so the indices are moved back once from the cpi in levels
    # start < p, end <p 1959q2 - 1959q4
    start, end = 1, 3
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start < p, end 0 1959q3 - 1960q1
    start, end = 2, 4
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start < p, end >0 1959q3 - 1971q4
    start, end = 2, 51
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start < p, end nobs 1959q3 - 2009q3
    start, end = 2, 202
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start < p, end >nobs 1959q3 - 2015q4
    start, end = 2, 227
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start 0, end >0 1960q1 - 1971q4
    start, end = 4, 51
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start 0, end nobs 1960q1 - 2009q3
    start, end = 4, 202
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start 0, end >nobs 1960q1 - 2015q4
    start, end = 4, 227
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >p, end >0 1965q1 - 1971q4
    start, end = 24, 51
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >p, end nobs 1965q1 - 2009q3
    start, end = 24, 202
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >p, end >nobs 1965q1 - 2015q4
    start, end = 24, 227
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start nobs, end nobs 2009q3 - 2009q3
    start, end = 202, 202
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_3)
    # start nobs, end >nobs 2009q3 - 2015q4
    start, end = 202, 227
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_3)
    # start >nobs, end >nobs 2009q4 - 2015q4
    start, end = 203, 227
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # defaults
    start, end = None, None
    fv = res1.predict(start, end, typ='levels')
    assert_almost_equal(fv, fc[1:203], DECIMAL_4)

    # Dynamic

    # start < p, end <p 1959q2 - 1959q4
    start, end = 1, 3
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        fv = res1.predict(start, end, dynamic=True, typ='levels')

    # start < p, end 0 1959q3 - 1960q1
    start, end = 2, 4
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True, typ='levels')

    # start < p, end >0 1959q3 - 1971q4
    start, end = 2, 51
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True, typ='levels')

    # start < p, end nobs 1959q3 - 2009q3
    start, end = 2, 202
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True, typ='levels')

    # start < p, end >nobs 1959q3 - 2015q4
    start, end = 2, 227
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True, typ='levels')

    # start 0, end >0 1960q1 - 1971q4
    start, end = 5, 51
    fv = res1.predict(start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4)
    # start 0, end nobs 1960q1 - 2009q3
    start, end = 5, 202
    fv = res1.predict(start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4)
    # start 0, end >nobs 1960q1 - 2015q4
    start, end = 5, 227
    fv = res1.predict(start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4)
    # start >p, end >0 1965q1 - 1971q4
    start, end = 24, 51
    fv = res1.predict(start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4)
    # start >p, end nobs 1965q1 - 2009q3
    start, end = 24, 202
    fv = res1.predict(start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4)
    # start >p, end >nobs 1965q1 - 2015q4
    start, end = 24, 227
    fv = res1.predict(start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4)
    # start nobs, end nobs 2009q3 - 2009q3
    start, end = 202, 202
    fv = res1.predict(start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn3[start:end + 1], DECIMAL_4)
    # start nobs, end >nobs 2009q3 - 2015q4
    start, end = 202, 227
    fv = res1.predict(start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn3[start:end + 1], DECIMAL_4)
    # start >nobs, end >nobs 2009q4 - 2015q4
    start, end = 203, 227
    fv = res1.predict(start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn4[start:end + 1], DECIMAL_4)
    # defaults
    start, end = None, None
    fv = res1.predict(start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn[5:203], DECIMAL_4)


def _check_start(model, given, expected, dynamic):
    start, _, _, _ = model._get_prediction_index(given, None, dynamic)
    assert_equal(start, expected)


def _check_end(model, given, end_expect, out_of_sample_expect):
    _, end, out_of_sample, _ = model._get_prediction_index(None, given, False)
    assert_equal((end, out_of_sample), (end_expect, out_of_sample_expect))


def test_arma_predict_indices():
    from statsmodels.datasets.sunspots import load_pandas
    sunspots = load_pandas().data['SUNACTIVITY'].values
    model = ARMA(sunspots, (9, 0), dates=sun_dates, freq='A')
    model.method = 'mle'

    # raises - pre-sample + dynamic
    with pytest.raises(ValueError):
        model._get_prediction_index(0, None, True)
    with pytest.raises(ValueError):
        model._get_prediction_index(8, None, True)
    with pytest.raises(ValueError):
        model._get_prediction_index('1700', None, True)
    with pytest.raises(ValueError):
        model._get_prediction_index('1708', None, True)

    # raises - start out of sample

    # works - in-sample
    # None
    start_test_cases = [
        # given, expected, dynamic
        (None, 9, True),
        # all start get moved back by k_diff
        (9, 9, True),
        (10, 10, True),
        # what about end of sample start - last value is first
        # forecast
        (309, 309, True),
        (308, 308, True),
        (0, 0, False),
        (1, 1, False),
        (4, 4, False),

        # all start get moved back by k_diff
        ('1709', 9, True),
        ('1710', 10, True),
        # what about end of sample start - last value is first
        # forecast
        ('2008', 308, True),
        ('2009', 309, True),
        ('1700', 0, False),
        ('1708', 8, False),
        ('1709', 9, False),
    ]

    for case in start_test_cases:
        _check_start(*((model,) + case))

    # the length of sunspot is 309, so last index is 208
    end_test_cases = [(None, 308, 0),
                      (307, 307, 0),
                      (308, 308, 0),
                      (309, 308, 1),
                      (312, 308, 4),
                      (51, 51, 0),
                      (333, 308, 25),

                      ('2007', 307, 0),
                      ('2008', 308, 0),
                      ('2009', 308, 1),
                      ('2012', 308, 4),
                      ('1815', 115, 0),
                      ('2033', 308, 25),
                      ]

    for case in end_test_cases:
        _check_end(*((model,) + case))


def test_arima_predict_indices():
    cpi = load_macrodata_pandas().data['cpi'].values
    model = ARIMA(cpi, (4, 1, 1), dates=cpi_dates, freq='Q')
    model.method = 'mle'

    # starting indices

    # raises - pre-sample + dynamic
    with pytest.raises(ValueError):
        model._get_prediction_index(0, None, True)
    with pytest.raises(ValueError):
        model._get_prediction_index(4, None, True)
    with pytest.raises(KeyError):
        model._get_prediction_index('1959Q1', None, True)
    with pytest.raises(ValueError):
        model._get_prediction_index('1960Q1', None, True)

    # raises - index differenced away
    with pytest.raises(ValueError):
        model._get_prediction_index(0, None, False)
    with pytest.raises(KeyError):
        model._get_prediction_index('1959Q1', None, False)

    # raises - start out of sample

    # works - in-sample
    # None
    start_test_cases = [
        # given, expected, dynamic
        (None, 4, True),
        # all start get moved back by k_diff
        (5, 4, True),
        (6, 5, True),
        # what about end of sample start - last value is first
        # forecast
        (203, 202, True),
        (1, 0, False),
        (4, 3, False),
        (5, 4, False),
        # all start get moved back by k_diff
        ('1960Q2', 4, True),
        ('1960Q3', 5, True),
        # what about end of sample start - last value is first
        # forecast
        ('2009Q4', 202, True),
        ('1959Q2', 0, False),
        ('1960Q1', 3, False),
        ('1960Q2', 4, False),
    ]

    for case in start_test_cases:
        _check_start(*((model,) + case))

    # TODO: make sure dates are passing through unmolested

    # the length of diff(cpi) is 202, so last index is 201
    end_test_cases = [(None, 201, 0),
                      (201, 200, 0),
                      (202, 201, 0),
                      (203, 201, 1),
                      (204, 201, 2),
                      (51, 50, 0),
                      (164 + 63, 201, 25),

                      ('2009Q2', 200, 0),
                      ('2009Q3', 201, 0),
                      ('2009Q4', 201, 1),
                      ('2010Q1', 201, 2),
                      ('1971Q4', 50, 0),
                      ('2015Q4', 201, 25),
                      ]

    for case in end_test_cases:
        _check_end(*((model,) + case))

    # check higher k_diff
    # model.k_diff = 2
    model = ARIMA(cpi, (4, 2, 1), dates=cpi_dates, freq='Q')
    model.method = 'mle'

    # raises - pre-sample + dynamic
    assert_raises(ValueError, model._get_prediction_index, 0, None, True)
    assert_raises(ValueError, model._get_prediction_index, 5, None, True)
    assert_raises(KeyError, model._get_prediction_index,
                  '1959Q1', None, True)
    assert_raises(ValueError, model._get_prediction_index,
                  '1960Q1', None, True)

    # raises - index differenced away
    assert_raises(ValueError, model._get_prediction_index, 1, None, False)
    assert_raises(KeyError, model._get_prediction_index,
                  '1959Q2', None, False)

    start_test_cases = [(None, 4, True),
                        # all start get moved back by k_diff
                        (6, 4, True),
                        # what about end of sample start - last value is first
                        # forecast
                        (203, 201, True),
                        (2, 0, False),
                        (4, 2, False),
                        (5, 3, False),
                        ('1960Q3', 4, True),
                        # what about end of sample start - last value is first
                        # forecast
                        ('2009Q4', 201, True),
                        ('2009Q4', 201, True),
                        ('1959Q3', 0, False),
                        ('1960Q1', 2, False),
                        ('1960Q2', 3, False),
                        ]

    for case in start_test_cases:
        _check_start(*((model,) + case))

    end_test_cases = [(None, 200, 0),
                      (201, 199, 0),
                      (202, 200, 0),
                      (203, 200, 1),
                      (204, 200, 2),
                      (51, 49, 0),
                      (164 + 63, 200, 25),

                      ('2009Q2', 199, 0),
                      ('2009Q3', 200, 0),
                      ('2009Q4', 200, 1),
                      ('2010Q1', 200, 2),
                      ('1971Q4', 49, 0),
                      ('2015Q4', 200, 25),
                      ]

    for case in end_test_cases:
        _check_end(*((model,) + case))


def test_arima_predict_indices_css():
    cpi = load_macrodata_pandas().data['cpi'].values
    # NOTE: Doing no-constant for now to kick the conditional exogenous
    # issue 274 down the road
    # go ahead and git the model to set up necessary variables
    model = ARIMA(cpi, (4, 1, 1))
    model.method = 'css'

    assert_raises(ValueError, model._get_prediction_index, 0, None, False)
    assert_raises(ValueError, model._get_prediction_index, 0, None, True)
    assert_raises(ValueError, model._get_prediction_index, 2, None, False)
    assert_raises(ValueError, model._get_prediction_index, 2, None, True)


def test_arima_predict_css():
    cpi = load_macrodata_pandas().data['cpi'].values
    # NOTE: Doing no-constant for now to kick the conditional exogenous
    # issue 274 down the road
    # go ahead and git the model to set up necessary variables
    res1 = ARIMA(cpi, (4, 1, 1)).fit(disp=-1, method="css",
                                     trend="nc")
    # but use gretl parameters to predict to avoid precision problems
    params = np.array([1.231272508473910,
                       -0.282516097759915,
                       0.170052755782440,
                       -0.118203728504945,
                       -0.938783134717947])
    file_path = os.path.join(current_path, 'results',
                             'results_arima_forecasts_all_css.csv')
    with open(file_path, "rb") as test_data:
        arima_forecasts = np.genfromtxt(test_data, delimiter=",",
                                        skip_header=1, dtype=float)
    fc = arima_forecasts[:, 0]
    fcdyn = arima_forecasts[:, 1]
    fcdyn2 = arima_forecasts[:, 2]
    fcdyn3 = arima_forecasts[:, 3]
    fcdyn4 = arima_forecasts[:, 4]

    start, end = 1, 3
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.model.predict(params, start, end)
    #  start < p, end 0 1959q3 - 1960q1
    start, end = 2, 4
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.model.predict(params, start, end)
    #  start < p, end >0 1959q3 - 1971q4
    start, end = 2, 51
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.model.predict(params, start, end)
    #  start < p, end nobs 1959q3 - 2009q3
    start, end = 2, 202
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.model.predict(params, start, end)
    #  start < p, end >nobs 1959q3 - 2015q4
    start, end = 2, 227
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.model.predict(params, start, end)
    # start 0, end >0 1960q1 - 1971q4
    start, end = 5, 51
    fv = res1.model.predict(params, start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start 0, end nobs 1960q1 - 2009q3
    start, end = 5, 202
    fv = res1.model.predict(params, start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start 0, end >nobs 1960q1 - 2015q4
    # TODO: why detoriating precision?
    fv = res1.model.predict(params, start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >p, end >0 1965q1 - 1971q4
    start, end = 24, 51
    fv = res1.model.predict(params, start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >p, end nobs 1965q1 - 2009q3
    start, end = 24, 202
    fv = res1.model.predict(params, start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >p, end >nobs 1965q1 - 2015q4
    start, end = 24, 227
    fv = res1.model.predict(params, start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start nobs, end nobs 2009q3 - 2009q3
    start, end = 202, 202
    fv = res1.model.predict(params, start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start nobs, end >nobs 2009q3 - 2015q4
    start, end = 202, 227
    fv = res1.model.predict(params, start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >nobs, end >nobs 2009q4 - 2015q4
    start, end = 203, 227
    fv = res1.model.predict(params, start, end, typ='levels')
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # defaults
    start, end = None, None
    fv = res1.model.predict(params, start, end, typ='levels')
    assert_almost_equal(fv, fc[5:203], DECIMAL_4)

    # Dynamic

    # start < p, end <p 1959q2 - 1959q4
    start, end = 1, 3
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    # start < p, end 0 1959q3 - 1960q1
    start, end = 2, 4
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    #  start < p, end >0 1959q3 - 1971q4
    start, end = 2, 51
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    #  start < p, end nobs 1959q3 - 2009q3
    start, end = 2, 202
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    #  start < p, end >nobs 1959q3 - 2015q4
    start, end = 2, 227
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    # start 0, end >0 1960q1 - 1971q4
    start, end = 5, 51
    fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4)
    # start 0, end nobs 1960q1 - 2009q3
    start, end = 5, 202
    fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4)
    # start 0, end >nobs 1960q1 - 2015q4
    start, end = 5, 227
    fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4)
    # start >p, end >0 1965q1 - 1971q4
    start, end = 24, 51
    fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4)
    # start >p, end nobs 1965q1 - 2009q3
    start, end = 24, 202
    fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4)
    # start >p, end >nobs 1965q1 - 2015q4
    start, end = 24, 227
    fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4)
    # start nobs, end nobs 2009q3 - 2009q3
    start, end = 202, 202
    fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn3[start:end + 1], DECIMAL_4)
    # start nobs, end >nobs 2009q3 - 2015q4
    start, end = 202, 227
    fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
    # start >nobs, end >nobs 2009q4 - 2015q4
    start, end = 203, 227
    fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn4[start:end + 1], DECIMAL_4)
    # defaults
    start, end = None, None
    fv = res1.model.predict(params, start, end, dynamic=True, typ='levels')
    assert_almost_equal(fv, fcdyn[5:203], DECIMAL_4)


def test_arima_predict_css_diffs():
    cpi = load_macrodata_pandas().data['cpi'].values
    # NOTE: Doing no-constant for now to kick the conditional exogenous
    # issue 274 down the road
    # go ahead and git the model to set up necessary variables
    res1 = ARIMA(cpi, (4, 1, 1)).fit(disp=-1, method="css",
                                     trend="c")
    # but use gretl parameters to predict to avoid precision problems
    params = np.array([0.78349893861244,
                       -0.533444105973324,
                       0.321103691668809,
                       0.264012463189186,
                       0.107888256920655,
                       0.920132542916995])
    # we report mean, should we report constant?
    params[0] = params[0] / (1 - params[1:5].sum())
    file_path = os.path.join(current_path, 'results',
                             'results_arima_forecasts_all_css_diff.csv')
    with open(file_path, "rb") as test_data:
        arima_forecasts = np.genfromtxt(test_data, delimiter=",",
                                        skip_header=1, dtype=float)
    fc = arima_forecasts[:, 0]
    fcdyn = arima_forecasts[:, 1]
    fcdyn2 = arima_forecasts[:, 2]
    fcdyn3 = arima_forecasts[:, 3]
    fcdyn4 = arima_forecasts[:, 4]

    start, end = 1, 3
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.model.predict(params, start, end)
    #  start < p, end 0 1959q3 - 1960q1
    start, end = 2, 4
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.model.predict(params, start, end)
    #  start < p, end >0 1959q3 - 1971q4
    start, end = 2, 51
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.model.predict(params, start, end)
    #  start < p, end nobs 1959q3 - 2009q3
    start, end = 2, 202
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.model.predict(params, start, end)
    #  start < p, end >nobs 1959q3 - 2015q4
    start, end = 2, 227
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.model.predict(params, start, end)
    # start 0, end >0 1960q1 - 1971q4
    start, end = 5, 51
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start 0, end nobs 1960q1 - 2009q3
    start, end = 5, 202
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start 0, end >nobs 1960q1 - 2015q4
    # TODO: why detoriating precision?
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >p, end >0 1965q1 - 1971q4
    start, end = 24, 51
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >p, end nobs 1965q1 - 2009q3
    start, end = 24, 202
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >p, end >nobs 1965q1 - 2015q4
    start, end = 24, 227
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start nobs, end nobs 2009q3 - 2009q3
    start, end = 202, 202
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start nobs, end >nobs 2009q3 - 2015q4
    start, end = 202, 227
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >nobs, end >nobs 2009q4 - 2015q4
    start, end = 203, 227
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # defaults
    start, end = None, None
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[5:203], DECIMAL_4)

    # Dynamic

    # start < p, end <p 1959q2 - 1959q4
    start, end = 1, 3
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    # start < p, end 0 1959q3 - 1960q1
    start, end = 2, 4
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    #  start < p, end >0 1959q3 - 1971q4
    start, end = 2, 51
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    #  start < p, end nobs 1959q3 - 2009q3
    start, end = 2, 202
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    #  start < p, end >nobs 1959q3 - 2015q4
    start, end = 2, 227
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    # start 0, end >0 1960q1 - 1971q4
    start, end = 5, 51
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4)
    # start 0, end nobs 1960q1 - 2009q3
    start, end = 5, 202
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4)
    # start 0, end >nobs 1960q1 - 2015q4
    start, end = 5, 227
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4)
    # start >p, end >0 1965q1 - 1971q4
    start, end = 24, 51
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4)
    # start >p, end nobs 1965q1 - 2009q3
    start, end = 24, 202
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4)
    # start >p, end >nobs 1965q1 - 2015q4
    start, end = 24, 227
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4)
    # start nobs, end nobs 2009q3 - 2009q3
    start, end = 202, 202
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn3[start:end + 1], DECIMAL_4)
    # start nobs, end >nobs 2009q3 - 2015q4
    start, end = 202, 227
    fv = res1.model.predict(params, start, end, dynamic=True)
    # start >nobs, end >nobs 2009q4 - 2015q4
    start, end = 203, 227
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn4[start:end + 1], DECIMAL_4)
    # defaults
    start, end = None, None
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn[5:203], DECIMAL_4)


def test_arima_predict_mle_diffs():
    cpi = load_macrodata_pandas().data['cpi'].values
    # NOTE: Doing no-constant for now to kick the conditional exogenous
    # issue 274 down the road
    # go ahead and git the model to set up necessary variables
    res1 = ARIMA(cpi, (4, 1, 1)).fit(disp=-1, trend="c")
    # but use gretl parameters to predict to avoid precision problems
    params = np.array([0.926875951549299,
                       -0.555862621524846,
                       0.320865492764400,
                       0.252253019082800,
                       0.113624958031799,
                       0.939144026934634])
    file_path = os.path.join(current_path, 'results',
                             'results_arima_forecasts_all_mle_diff.csv')
    with open(file_path, "rb") as test_data:
        arima_forecasts = np.genfromtxt(test_data, delimiter=",",
                                        skip_header=1, dtype=float)
    fc = arima_forecasts[:, 0]
    fcdyn = arima_forecasts[:, 1]
    fcdyn2 = arima_forecasts[:, 2]
    fcdyn3 = arima_forecasts[:, 3]
    fcdyn4 = arima_forecasts[:, 4]

    start, end = 1, 3
    res1.model.predict(params, start, end)
    #  start < p, end 0 1959q3 - 1960q1
    start, end = 2, 4
    res1.model.predict(params, start, end)
    #  start < p, end >0 1959q3 - 1971q4
    start, end = 2, 51
    res1.model.predict(params, start, end)
    #  start < p, end nobs 1959q3 - 2009q3
    start, end = 2, 202
    res1.model.predict(params, start, end)
    #  start < p, end >nobs 1959q3 - 2015q4
    start, end = 2, 227
    res1.model.predict(params, start, end)
    # start 0, end >0 1960q1 - 1971q4
    start, end = 5, 51
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start 0, end nobs 1960q1 - 2009q3
    start, end = 5, 202
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start 0, end >nobs 1960q1 - 2015q4
    # TODO: why detoriating precision?
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >p, end >0 1965q1 - 1971q4
    start, end = 24, 51
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >p, end nobs 1965q1 - 2009q3
    start, end = 24, 202
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >p, end >nobs 1965q1 - 2015q4
    start, end = 24, 227
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start nobs, end nobs 2009q3 - 2009q3
    start, end = 202, 202
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start nobs, end >nobs 2009q3 - 2015q4
    start, end = 202, 227
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # start >nobs, end >nobs 2009q4 - 2015q4
    start, end = 203, 227
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[start:end + 1], DECIMAL_4)
    # defaults
    start, end = None, None
    fv = res1.model.predict(params, start, end)
    assert_almost_equal(fv, fc[1:203], DECIMAL_4)

    # Dynamic

    # NOTE: should raise
    # start < p, end <p 1959q2 - 1959q4
    start, end = 1, 3
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    # start < p, end 0 1959q3 - 1960q1
    start, end = 2, 4
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    #  start < p, end >0 1959q3 - 1971q4
    start, end = 2, 51
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    #  start < p, end nobs 1959q3 - 2009q3
    start, end = 2, 202
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    #  start < p, end >nobs 1959q3 - 2015q4
    start, end = 2, 227
    with pytest.raises(ValueError, match='Start must be >= k_ar'):
        res1.predict(start, end, dynamic=True)
    # start 0, end >0 1960q1 - 1971q4
    start, end = 5, 51
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4)
    # start 0, end nobs 1960q1 - 2009q3
    start, end = 5, 202
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4)
    # start 0, end >nobs 1960q1 - 2015q4
    start, end = 5, 227
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn[start:end + 1], DECIMAL_4)
    # start >p, end >0 1965q1 - 1971q4
    start, end = 24, 51
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4)
    # start >p, end nobs 1965q1 - 2009q3
    start, end = 24, 202
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4)
    # start >p, end >nobs 1965q1 - 2015q4
    start, end = 24, 227
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn2[start:end + 1], DECIMAL_4)
    # start nobs, end nobs 2009q3 - 2009q3
    start, end = 202, 202
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn3[start:end + 1], DECIMAL_4)
    # start nobs, end >nobs 2009q3 - 2015q4
    start, end = 202, 227
    fv = res1.model.predict(params, start, end, dynamic=True)
    # start >nobs, end >nobs 2009q4 - 2015q4
    start, end = 203, 227
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn4[start:end + 1], DECIMAL_4)
    # defaults
    start, end = None, None
    fv = res1.model.predict(params, start, end, dynamic=True)
    assert_almost_equal(fv, fcdyn[5:203], DECIMAL_4)


def test_arima_wrapper():
    cpi = load_macrodata_pandas().data['cpi']
    cpi.index = pd.Index(cpi_dates)
    res = ARIMA(cpi, (4, 1, 1), freq='Q').fit(disp=-1)
    assert_equal(res.params.index,
                 pd.Index(['const', 'ar.L1.D.cpi', 'ar.L2.D.cpi',
                           'ar.L3.D.cpi', 'ar.L4.D.cpi',
                           'ma.L1.D.cpi']))
    assert_equal(res.model.endog_names, 'D.cpi')


@pytest.mark.smoke
def test_1dexog():
    # smoke test, this will raise an error if broken
    dta = load_macrodata_pandas().data
    endog = dta['realcons'].values
    exog = dta['m1'].values.squeeze()
    with warnings.catch_warnings():
        warnings.simplefilter("ignore")
        mod = ARMA(endog, (1, 1), exog).fit(disp=-1)
        mod.predict(193, 203, exog[-10:])

        # check for dynamic is true and pandas Series  see #2589
        mod.predict(193, 202, exog[-10:], dynamic=True)

        dta.index = pd.Index(cpi_dates)
        mod = ARMA(dta['realcons'], (1, 1), dta['m1']).fit(disp=-1)
        mod.predict(dta.index[-10], dta.index[-1], exog=dta['m1'][-10:],
                    dynamic=True)

        mod = ARMA(dta['realcons'], (1, 1), dta['m1']).fit(trend='nc', disp=-1)
        mod.predict(dta.index[-10], dta.index[-1], exog=dta['m1'][-10:],
                    dynamic=True)


def test_arima_predict_bug():
    # predict_start_date was not getting set on start = None
    from statsmodels.datasets import sunspots
    dta = sunspots.load_pandas().data.SUNACTIVITY
    dta.index = pd.date_range(start='1700', end='2009', freq='A')[:309]
    arma_mod20 = ARMA(dta, (2, 0)).fit(disp=-1)
    arma_mod20.predict(None, None)

    # test prediction with time stamp, see #2587
    predict = arma_mod20.predict(dta.index[-20], dta.index[-1])
    assert predict.index.equals(dta.index[-20:])
    predict = arma_mod20.predict(dta.index[-20], dta.index[-1], dynamic=True)
    assert predict.index.equals(dta.index[-20:])
    # partially out of sample
    predict_dates = pd.date_range(start='2000', end='2015', freq='A')
    predict = arma_mod20.predict(predict_dates[0], predict_dates[-1])
    assert predict.index.equals(predict_dates)


def test_arima_predict_q2():
    # bug with q > 1 for arima predict
    inv = load_macrodata_pandas().data['realinv'].values
    arima_mod = ARIMA(np.log(inv), (1, 1, 2)).fit(start_params=[0, 0, 0, 0],
                                                  disp=-1)
    fc, stderr, conf_int = arima_mod.forecast(5)
    # values copy-pasted from gretl
    assert_almost_equal(fc,
                        [7.306320, 7.313825, 7.321749, 7.329827, 7.337962],
                        5)


def test_arima_predict_pandas_nofreq():
    # this is issue 712
    dates = ["2010-01-04", "2010-01-05", "2010-01-06", "2010-01-07",
             "2010-01-08", "2010-01-11", "2010-01-12", "2010-01-11",
             "2010-01-12", "2010-01-13", "2010-01-17"]
    close = [626.75, 623.99, 608.26, 594.1, 602.02, 601.11, 590.48, 587.09,
             589.85, 580.0, 587.62]
    data = pd.DataFrame(close, index=DatetimeIndex(dates), columns=["close"])

    # TODO: fix this names bug for non-string names names
    with pytest.warns(ValueWarning, match="it has no associated frequency"):
        arma = ARMA(data, order=(1, 0)).fit(disp=-1)

    # first check that in-sample prediction works
    predict = arma.predict()

    assert predict.index.equals(data.index)

    # check that this raises an exception when date not on index
    assert_raises(KeyError, arma.predict, start="2010-1-9", end=10)
    assert_raises(KeyError, arma.predict, start="2010-1-9", end="2010-1-17")

    # raise because end not on index
    assert_raises(KeyError, arma.predict, start="2010-1-4", end="2010-1-10")
    # raise because end not on index
    assert_raises(KeyError, arma.predict, start=3, end="2010-1-10")

    predict = arma.predict(start="2010-1-7", end=10)  # should be of length 10
    assert len(predict) == 8
    assert predict.index.equals(data.index[3:10 + 1])

    with pytest.warns(ValueWarning, match="No supported index is available"):
        predict = arma.predict(start="2010-1-7", end=14)

    assert predict.index.equals(pd.Index(lrange(3, 15)))

    with pytest.warns(ValueWarning, match="No supported index is available"):
        predict = arma.predict(start=3, end=14)

    assert predict.index.equals(pd.Index(lrange(3, 15)))

    # end can be a date if it's in the sample and on the index
    # predict dates is just a slice of the dates index then
    predict = arma.predict(start="2010-1-6", end="2010-1-13")
    assert predict.index.equals(data.index[2:10])
    predict = arma.predict(start=2, end="2010-1-13")
    assert predict.index.equals(data.index[2:10])


def test_arima_predict_exog():
    # check 625 and 626
    # from statsmodels.tsa.arima_process import arma_generate_sample
    # arparams = np.array([1, -.45, .25])
    # maparams = np.array([1, .15])
    # nobs = 100
    # np.random.seed(123)
    # y = arma_generate_sample(arparams, maparams, nobs, burnin=100)

    #  make an exogenous trend
    # X = np.array(lrange(nobs)) / 20.0
    #  add a constant
    # y += 2.5

    from pandas import read_csv
    file_name = "/results/results_arima_exog_forecasts_mle.csv"
    arima_forecasts = read_csv(current_path + file_name)
    y = arima_forecasts["y"].dropna()
    X = np.arange(len(y) + 25) / 20.
    predict_expected = arima_forecasts["predict"]
    arma_res = ARMA(y.values, order=(2, 1), exog=X[:100]).fit(trend="c",
                                                              disp=-1)
    # params from gretl
    params = np.array([2.786912485145725, -0.122650190196475,
                       0.533223846028938, -0.319344321763337,
                       0.132883233000064])
    assert_almost_equal(arma_res.params, params, 5)
    # no exog for in-sample
    predict = arma_res.predict()
    assert_almost_equal(predict, predict_expected.values[:100], 5)

    # check 626
    assert len(arma_res.model.exog_names) == 5

    # exog for out-of-sample and in-sample dynamic
    predict = arma_res.model.predict(params, end=124, exog=X[100:])
    assert_almost_equal(predict, predict_expected.values, 6)

    # conditional sum of squares
    # arima_forecasts = read_csv(current_path + "/results/"
    #                        "results_arima_exog_forecasts_css.csv")
    # predict_expected = arima_forecasts["predict"].dropna()
    # arma_res = ARMA(y.values, order=(2,1), exog=X[:100]).fit(trend="c",
    #                                                         method="css",
    #                                                         disp=-1)

    # params = np.array([2.152350033809826, -0.103602399018814,
    #                   0.566716580421188, -0.326208009247944,
    #                   0.102142932143421])
    # predict = arma_res.model.predict(params)
    #  in-sample
    # assert_almost_equal(predict, predict_expected.values[:98], 6)

    # predict = arma_res.model.predict(params, end=124, exog=X[100:])
    #  exog for out-of-sample and in-sample dynamic
    # assert_almost_equal(predict, predict_expected.values, 3)


@pytest.mark.smoke
def test_arima_no_diff():
    # GH#736
    # smoke test, predict will break if we have ARIMAResults but
    # ARMA model, need ARIMA(p, 0, q) to return an ARMA in init.
    ar = [1, -.75, .15, .35]
    ma = [1, .25, .9]
    np.random.seed(12345)
    y = arma_generate_sample(ar, ma, 100)
    mod = ARIMA(y, (3, 0, 2))
    assert type(mod) is ARMA
    res = mod.fit(disp=-1)
    # smoke test just to be sure
    res.predict()


@pytest.mark.smoke
def test_arima_predict_noma():
    # GH#657
    ar = [1, .75]
    ma = [1]
    np.random.seed(12345)
    data = arma_generate_sample(ar, ma, 100)
    arma = ARMA(data, order=(0, 1))
    arma_res = arma.fit(disp=-1)
    arma_res.forecast(1)


def test_arimax():
    dta = load_macrodata_pandas().data
    dta.index = cpi_dates
    dta = dta[["realdpi", "m1", "realgdp"]]
    y = dta.pop("realdpi")

    # 1 exog
    # X = dta.iloc[1:]["m1"]
    # res = ARIMA(y, (2, 1, 1), X).fit(disp=-1)
    # params = [23.902305009084373, 0.024650911502790, -0.162140641341602,
    #          0.165262136028113, -0.066667022903974]
    # assert_almost_equal(res.params.values, params, 6)

    # 2 exog
    X = dta
    res = ARIMA(y, (2, 1, 1), X).fit(disp=False, solver="nm", maxiter=1000,
                                     ftol=1e-12, xtol=1e-12)

    # from gretl
    # params = [13.113976653926638, -0.003792125069387,  0.004123504809217,
    #          -0.199213760940898,  0.151563643588008, -0.033088661096699]
    # from stata using double
    stata_llf = -1076.108614859121
    params = [13.1259220104, -0.00376814509403812, 0.00411970083135622,
              -0.19921477896158524, 0.15154396192855729, -0.03308400760360837]
    # we can get close
    assert_almost_equal(res.params.values, params, 4)

    # This shows that it's an optimizer problem and not a problem in the code
    assert_almost_equal(res.model.loglike(np.array(params)), stata_llf, 6)

    X = dta.diff()
    X.iloc[0] = 0
    res = ARIMA(y, (2, 1, 1), X).fit(disp=False)

    # gretl will not estimate this - looks like maybe a bug on their part,
    # but we can just fine, we're close to Stata's answer
    # from Stata
    params = [19.5656863783347, 0.32653841355833396198,
              0.36286527042965188716, -1.01133792126884,
              -0.15722368379307766206, 0.69359822544092153418]

    assert_almost_equal(res.params.values, params, 3)


def test_bad_start_params():
    endog = np.array([
        820.69093, 781.0103028, 785.8786988, 767.64282267,
        778.9837648, 824.6595702, 813.01877867, 751.65598567,
        753.431091, 746.920813, 795.6201904, 772.65732833,
        793.4486454, 868.8457766, 823.07226547, 783.09067747,
        791.50723847, 770.93086347, 835.34157333, 810.64147947,
        738.36071367, 776.49038513, 822.93272333, 815.26461227,
        773.70552987, 777.3726522, 811.83444853, 840.95489133,
        777.51031933, 745.90077307, 806.95113093, 805.77521973,
        756.70927733, 749.89091773, 1694.2266924, 2398.4802244,
        1434.6728516, 909.73940427, 929.01291907, 769.07561453,
        801.1112548, 796.16163313, 817.2496376, 857.73046447,
        838.849345, 761.92338873, 731.7842242, 770.4641844])

    mod = ARMA(endog, (15, 0))
    with pytest.raises(ValueError, match="pass your own start_params"):
        with pytest.warns(RuntimeWarning, match="encountered in sqrt"):
            # numpy warns "invalid value encountered in sqrt"
            mod.fit()

    inv = load_macrodata_pandas().data['realinv'].values
    arima_mod = ARIMA(np.log(inv), (1, 1, 2))
    with pytest.raises(ValueError):
        arima_mod.fit()


def test_arima_small_data_bug():
    # Issue 1038, too few observations with given order
    import statsmodels.api as sm

    vals = [96.2, 98.3, 99.1, 95.5, 94.0, 87.1, 87.9, 86.7402777504474]

    dr = pd.date_range("1990", periods=len(vals), freq='Q')
    ts = pd.Series(vals, index=dr)
    df = pd.DataFrame(ts)
    mod = sm.tsa.ARIMA(df, (2, 0, 2))
    assert_raises(ValueError, mod.fit)


@pytest.mark.smoke
def test_arima_dataframe_integer_name():
    # Smoke Test for Issue GH#1038
    import statsmodels.api as sm

    vals = [96.2, 98.3, 99.1, 95.5, 94.0, 87.1, 87.9, 86.7402777504474,
            94.0, 96.5, 93.3, 97.5, 96.3, 92.]

    dr = pd.date_range("1990", periods=len(vals), freq='Q')
    ts = pd.Series(vals, index=dr)
    df = pd.DataFrame(ts)
    sm.tsa.ARIMA(df, (2, 0, 2))


def test_arima_exog_predict_1d():
    # test 1067
    np.random.seed(12345)
    y = np.random.random(100)
    x = np.random.random(100)
    mod = ARMA(y, (2, 1), x).fit(disp=-1)
    newx = np.random.random(10)
    mod.forecast(steps=10, alpha=0.05, exog=newx)

    with pytest.raises(ValueError):
        mod.forecast(steps=10, alpha=0.05, exog=newx[:5])

    with pytest.raises(ValueError):
        mod.forecast(steps=10, alpha=0.05)

    too_many = pd.DataFrame(np.zeros((10, 2)),
                            columns=['x1', 'x2'])
    with pytest.raises(ValueError):
        mod.forecast(steps=10, alpha=0.05, exog=too_many)


def test_arima_1123():
    # test ARMAX predict when trend is none
    np.random.seed(12345)
    arparams = np.array([.75, -.25])
    maparams = np.array([.65, .35])

    nobs = 20
    np.random.seed(12345)
    y = arma_generate_sample(arparams, maparams, nobs)

    X = np.random.randn(nobs)
    y += 5 * X
    mod = ARMA(y[:-1], order=(1, 0), exog=X[:-1])
    res = mod.fit(trend='nc', disp=False)
    fc = res.forecast(exog=X[-1:])
    # results from gretl
    assert_almost_equal(fc[0], 2.200393, 6)
    assert_almost_equal(fc[1], 1.030743, 6)
    assert_almost_equal(fc[2][0, 0], 0.180175, 6)
    assert_almost_equal(fc[2][0, 1], 4.220611, 6)

    mod = ARMA(y[:-1], order=(1, 1), exog=X[:-1])
    res = mod.fit(trend='nc', disp=False)
    fc = res.forecast(exog=X[-1:])
    assert_almost_equal(fc[0], 2.765688, 6)
    assert_almost_equal(fc[1], 0.835048, 6)
    assert_almost_equal(fc[2][0, 0], 1.129023, 6)
    assert_almost_equal(fc[2][0, 1], 4.402353, 6)

    # make sure this works to. code looked fishy.
    mod = ARMA(y[:-1], order=(1, 0), exog=X[:-1])
    res = mod.fit(trend='c', disp=False)
    fc = res.forecast(exog=X[-1:])
    assert_almost_equal(fc[0], 2.481219, 6)
    assert_almost_equal(fc[1], 0.968759, 6)
    assert_almost_equal(fc[2][0], [0.582485, 4.379952], 6)


def test_small_data():
    # 1146
    y = [-1214.360173, -1848.209905, -2100.918158, -3647.483678, -4711.186773]

    # refuse to estimate these
    assert_raises(ValueError, ARIMA, y, (2, 0, 3))
    assert_raises(ValueError, ARIMA, y, (1, 1, 3))
    mod = ARIMA(y, (1, 0, 3))
    assert_raises(ValueError, mod.fit, trend="c")

    # try to estimate these...leave it up to the user to check for garbage
    # and be clear, these are garbage parameters.
    # X-12 arima will estimate, gretl refuses to estimate likely a problem
    # in start params regression.
    mod.fit(trend="nc", disp=0, start_params=[.1, .1, .1, .1])
    mod = ARIMA(y, (1, 0, 2))
    import warnings
    with warnings.catch_warnings():
        warnings.simplefilter("ignore")
        mod.fit(disp=0, start_params=[np.mean(y), .1, .1, .1])


class TestARMA00(object):

    @classmethod
    def setup_class(cls):
        from statsmodels.datasets.sunspots import load_pandas

        sunspots = load_pandas().data['SUNACTIVITY'].values
        cls.y = y = sunspots
        cls.arma_00_model = ARMA(y, order=(0, 0))
        cls.arma_00_res = cls.arma_00_model.fit(disp=-1)

    def test_parameters(self):
        params = self.arma_00_res.params
        assert_almost_equal(self.y.mean(), params)

    def test_predictions(self):
        predictions = self.arma_00_res.predict()
        assert_almost_equal(self.y.mean() * np.ones_like(predictions),
                            predictions)

    def test_arroots(self):
        # regression test; older implementation of arroots returned None
        # instead of en empty array
        roots = self.arma_00_res.arroots
        assert_equal(roots.size, 0)

    def test_maroots(self):
        # regression test; older implementation of arroots returned None
        # instead of en empty array
        roots = self.arma_00_res.maroots
        assert_equal(roots.size, 0)

    @pytest.mark.skip("This test is invalid since the ICs differ due to "
                      "df_model differences between OLS and ARIMA")
    def test_information_criteria(self):
        res = self.arma_00_res
        y = self.y
        ols_res = OLS(y, np.ones_like(y)).fit(disp=-1)
        ols_ic = np.array([ols_res.aic, ols_res.bic])
        arma_ic = np.array([res.aic, res.bic])
        assert_almost_equal(ols_ic, arma_ic, DECIMAL_4)

    def test_arma_00_nc(self):
        arma_00 = ARMA(self.y, order=(0, 0))
        assert_raises(ValueError, arma_00.fit, trend='nc', disp=-1)

    def test_css(self):
        arma = ARMA(self.y, order=(0, 0))
        fit = arma.fit(method='css', disp=-1)
        predictions = fit.predict()
        assert_almost_equal(self.y.mean() * np.ones_like(predictions),
                            predictions)

    def test_arima(self):
        yi = np.cumsum(self.y)
        arima = ARIMA(yi, order=(0, 1, 0))
        fit = arima.fit(disp=-1)
        assert_almost_equal(np.diff(yi).mean(), fit.params, DECIMAL_4)

    def test_arma_ols(self):
        y = self.y
        y_lead = y[1:]
        y_lag = y[:-1]
        T = y_lag.shape[0]
        X = np.hstack((np.ones((T, 1)), y_lag[:, None]))
        ols_res = OLS(y_lead, X).fit()
        arma_res = ARMA(y_lead, order=(0, 0), exog=y_lag).fit(trend='c',
                                                              disp=-1)
        assert_almost_equal(ols_res.params, arma_res.params)

    def test_arma_exog_no_constant(self):
        y = self.y
        y_lead = y[1:]
        y_lag = y[:-1]
        X = y_lag[:, None]
        ols_res = OLS(y_lead, X).fit()
        arma_res = ARMA(y_lead, order=(0, 0), exog=y_lag).fit(trend='nc',
                                                              disp=-1)
        assert_almost_equal(ols_res.params, arma_res.params)


def test_arima_dates_startatend():
    # bug
    np.random.seed(18)
    x = pd.Series(np.random.random(36),
                  index=pd.date_range(start='1/1/1990',
                                      periods=36, freq='M'))
    res = ARIMA(x, (1, 0, 0)).fit(disp=0)
    pred = res.predict(start=len(x), end=len(x))
    assert pred.index[0] == x.index.shift(1)[-1]
    fc = res.forecast()[0]
    assert_almost_equal(pred.values[0], fc)


def test_arma_missing():
    from statsmodels.tools.sm_exceptions import MissingDataError
    # bug 1343
    y = np.random.random(40)
    y[-1] = np.nan
    assert_raises(MissingDataError, ARMA, y, (1, 0), missing='raise')


@pytest.mark.matplotlib
def test_plot_predict(close_figures):
    from statsmodels.datasets.sunspots import load_pandas

    dta = load_pandas().data[['SUNACTIVITY']]
    dta.index = date_range(start='1700', end='2009', freq='A')[:309]
    res = ARMA(dta, (3, 0)).fit(disp=-1)
    res.plot_predict('1990', '2012', dynamic=True, plot_insample=False)
    res.plot_predict('1990', '2012', dynamic=True, plot_insample=True)

    res = ARIMA(dta, (3, 1, 0)).fit(disp=-1)
    res.plot_predict('1990', '2012', dynamic=True, plot_insample=False)
    res.plot_predict('1990', '2012', dynamic=True, plot_insample=True)


def test_arima_diff2():
    dta = load_macrodata_pandas().data['cpi']
    dta.index = cpi_dates
    mod = ARIMA(dta, (3, 2, 1)).fit(disp=-1)
    fc, fcerr, conf_int = mod.forecast(10)
    # forecasts from gretl
    conf_int_res = [(216.139, 219.231),
                    (216.472, 221.520),
                    (217.064, 223.649),
                    (217.586, 225.727),
                    (218.119, 227.770),
                    (218.703, 229.784),
                    (219.306, 231.777),
                    (219.924, 233.759),
                    (220.559, 235.735),
                    (221.206, 237.709)]

    fc_res = [217.685, 218.996, 220.356, 221.656, 222.945, 224.243, 225.541,
              226.841, 228.147, 229.457]
    fcerr_res = [0.7888, 1.2878, 1.6798, 2.0768, 2.4620, 2.8269, 3.1816,
                 3.52950, 3.8715, 4.2099]

    assert_almost_equal(fc, fc_res, 3)
    assert_almost_equal(fcerr, fcerr_res, 3)
    assert_almost_equal(conf_int, conf_int_res, 3)

    predicted = mod.predict('2008Q1', '2012Q1', typ='levels')

    predicted_res = [214.464, 215.478, 221.277, 217.453, 212.419, 213.530,
                     215.087, 217.685, 218.996, 220.356, 221.656,
                     222.945, 224.243, 225.541, 226.841, 228.147,
                     229.457]
    assert_almost_equal(predicted, predicted_res, 3)


def test_arima111_predict_exog_2127():
    # regression test for issue #2127
    ef = [0.03005, 0.03917, 0.02828, 0.03644, 0.03379, 0.02744,
          0.03343, 0.02621, 0.03050, 0.02455, 0.03261, 0.03507,
          0.02734, 0.05373, 0.02677, 0.03443, 0.03331, 0.02741,
          0.03709, 0.02113, 0.03343, 0.02011, 0.03675, 0.03077,
          0.02201, 0.04844, 0.05518, 0.03765, 0.05433, 0.03049,
          0.04829, 0.02936, 0.04421, 0.02457, 0.04007, 0.03009,
          0.04504, 0.05041, 0.03651, 0.02719, 0.04383, 0.02887,
          0.03440, 0.03348, 0.02364, 0.03496, 0.02549, 0.03284,
          0.03523, 0.02579, 0.03080, 0.01784, 0.03237, 0.02078,
          0.03508, 0.03062, 0.02006, 0.02341, 0.02223, 0.03145,
          0.03081, 0.02520, 0.02683, 0.01720, 0.02225, 0.01579,
          0.02237, 0.02295, 0.01830, 0.02356, 0.02051, 0.02932,
          0.03025, 0.02390, 0.02635, 0.01863, 0.02994, 0.01762,
          0.02837, 0.02421, 0.01951, 0.02149, 0.02079, 0.02528,
          0.02575, 0.01634, 0.02563, 0.01719, 0.02915, 0.01724,
          0.02804, 0.02750, 0.02099, 0.02522, 0.02422, 0.03254,
          0.02095, 0.03241, 0.01867, 0.03998, 0.02212, 0.03034,
          0.03419, 0.01866, 0.02623, 0.02052]
    ue = [4.9, 5.0, 5.0, 5.0, 4.9, 4.7, 4.8, 4.7, 4.7,
          4.6, 4.6, 4.7, 4.7, 4.5, 4.4, 4.5, 4.4, 4.6,
          4.5, 4.4, 4.5, 4.4, 4.6, 4.7, 4.6, 4.7, 4.7,
          4.7, 5.0, 5.0, 4.9, 5.1, 5.0, 5.4, 5.6, 5.8,
          6.1, 6.1, 6.5, 6.8, 7.3, 7.8, 8.3, 8.7, 9.0,
          9.4, 9.5, 9.5, 9.6, 9.8, 10., 9.9, 9.9, 9.7,
          9.8, 9.9, 9.9, 9.6, 9.4, 9.5, 9.5, 9.5, 9.5,
          9.8, 9.4, 9.1, 9.0, 9.0, 9.1, 9.0, 9.1, 9.0,
          9.0, 9.0, 8.8, 8.6, 8.5, 8.2, 8.3, 8.2, 8.2,
          8.2, 8.2, 8.2, 8.1, 7.8, 7.8, 7.8, 7.9, 7.9,
          7.7, 7.5, 7.5, 7.5, 7.5, 7.3, 7.2, 7.2, 7.2,
          7.0, 6.7, 6.6, 6.7, 6.7, 6.3, 6.3]

    ue = np.array(ue) / 100
    model = ARIMA(ef, (1, 1, 1), exog=ue)
    res = model.fit(transparams=False, pgtol=1e-8, iprint=0, disp=0)
    assert_equal(res.mle_retvals['warnflag'], 0)
    predicts = res.predict(start=len(ef), end=len(ef) + 10,
                           exog=ue[-11:], typ='levels')

    # regression test, not verified numbers
    predicts_res = np.array([
        0.02591095, 0.02321325, 0.02436579, 0.02368759, 0.02389753,
        0.02372, 0.0237481, 0.0236738, 0.023644, 0.0236283,
        0.02362267])

    assert_allclose(predicts, predicts_res, atol=5e-6)

    # Smoke check of forecast with exog in ARIMA
    res.forecast(steps=10, exog=np.empty(10))

    with pytest.raises(ValueError):
        res.forecast(steps=10)
    with pytest.raises(ValueError):
        res.forecast(steps=10, exog=np.empty((10, 2)))
    with pytest.raises(ValueError):
        res.forecast(steps=10, exog=np.empty(100))


def test_arima_exog_predict():
    # test forecasting and dynamic prediction with exog against Stata

    dta = load_macrodata_pandas().data
    cpi_dates = period_range(start='1959Q1', end='2009Q3', freq='Q')
    dta.index = cpi_dates

    data = dta
    data['loginv'] = np.log(data['realinv'])
    data['loggdp'] = np.log(data['realgdp'])
    data['logcons'] = np.log(data['realcons'])

    forecast_period = period_range(start='2008Q2', end='2009Q4', freq='Q')
    end = forecast_period[0]
    data_sample = data.loc[dta.index < end]

    exog_full = data[['loggdp', 'logcons']]

    # pandas

    mod = ARIMA(data_sample['loginv'], (1, 0, 1),
                exog=data_sample[['loggdp', 'logcons']])
    with warnings.catch_warnings():
        warnings.simplefilter("ignore")
        res = mod.fit(disp=0, solver='bfgs', maxiter=5000)

    predicted_arma_fp = res.predict(start=197, end=202,
                                    exog=exog_full.values[197:]).values
    predicted_arma_dp = res.predict(start=193, end=202,
                                    exog=exog_full[197:], dynamic=True)

    # numpy
    mod2 = ARIMA(np.asarray(data_sample['loginv']), (1, 0, 1),
                 exog=np.asarray(data_sample[['loggdp', 'logcons']]))
    res2 = mod2.fit(start_params=res.params, disp=0,
                    solver='bfgs', maxiter=5000)

    exog_full = data[['loggdp', 'logcons']]
    predicted_arma_f = res2.predict(start=197, end=202,
                                    exog=exog_full.values[197:])
    predicted_arma_d = res2.predict(start=193, end=202,
                                    exog=exog_full[197:], dynamic=True)

    endog_scale = 100
    ex_scale = 1000
    # ARIMA(1, 1, 1)
    ex = ex_scale * np.asarray(data_sample[['loggdp', 'logcons']].diff())
    # The first observation is not (supposed to be) used,
    # but I get a Lapack problem
    # Intel MKL ERROR: Parameter 5 was incorrect on entry to DLASCL.
    ex[0] = 0
    mod111 = ARIMA(100 * np.asarray(data_sample['loginv']), (1, 1, 1),
                   # Stata differences also the exog
                   exog=ex)
    sv = [-0.94771574, 0.5869353, -0.32651653, 0.78066562, -0.68747501]
    res111 = mod111.fit(start_params=sv, disp=0, solver='bfgs', maxiter=5000)
    exog_full_d = ex_scale * data[['loggdp', 'logcons']].diff()
    res111.predict(start=197, end=202, exog=exog_full_d.values[197:])

    predicted_arima_f = res111.predict(start=196, end=202,
                                       exog=exog_full_d.values[197:],
                                       typ='levels')
    predicted_arima_d = res111.predict(start=193, end=202,
                                       exog=exog_full_d.values[197:],
                                       typ='levels', dynamic=True)

    res_f101 = np.array(
        [7.73975859954, 7.71660108543, 7.69808978329, 7.70872117504,
         7.65183927580, 7.69784279784, 7.70290907856, 7.69237782644,
         7.65017785174, 7.66061689028, 7.65980022857, 7.61505314129,
         7.51697158428, 7.51657606630, 7.5271053284])
    res_f111 = np.array(
        [7.74460013693, 7.71958207517, 7.69629561172, 7.71208186737,
         7.65758850178, 7.69223472572, 7.70411775588, 7.68896109499,
         7.64016249001, 7.64871881901, 7.62550283402, 7.55814609462,
         7.44431310053, 7.42963968062, 7.43554675427])
    res_d111 = np.array(
        [7.74460013693, 7.71958207517, 7.69629561172, 7.71208186737,
         7.65758850178, 7.69223472572, 7.71870821151, 7.72994302150,
         7.71439447355, 7.72544001101, 7.70521902623, 7.64020040524,
         7.52819271910, 7.51494426940, 7.52196378005])
    res_d101 = np.array(
        [7.73975859954, 7.71660108543, 7.69808978329, 7.70872117504,
         7.65183927580, 7.69784279784, 7.72522142662, 7.73962377858,
         7.73245950636, 7.74935432862, 7.74449584691, 7.69589103679,
         7.59412746880, 7.59021764836, 7.59739267775])

    # Relax tolerance on OSX due to frequent small failures
    # GH 4657
    tol = 1e-3 if PLATFORM_OSX or PLATFORM_WIN else 1e-4
    assert_allclose(predicted_arma_dp,
                    res_d101[-len(predicted_arma_d):], rtol=tol, atol=tol)
    assert_allclose(predicted_arma_fp,
                    res_f101[-len(predicted_arma_f):], rtol=tol, atol=tol)
    assert_allclose(predicted_arma_d,
                    res_d101[-len(predicted_arma_d):], rtol=tol, atol=tol)
    assert_allclose(predicted_arma_f,
                    res_f101[-len(predicted_arma_f):], rtol=tol, atol=tol)
    assert_allclose(predicted_arima_d / endog_scale,
                    res_d111[-len(predicted_arima_d):], rtol=tol, atol=tol)
    assert_allclose(predicted_arima_f / endog_scale,
                    res_f111[-len(predicted_arima_f):], rtol=tol, atol=tol)

    # test for forecast with 0 ar fix in #2457 numbers again from Stata

    res_f002 = np.array(
        [7.70178181209, 7.67445481224, 7.67153737650, 7.67729153190,
         7.61173201163, 7.67913499878, 7.67276092120, 7.66275451925,
         7.65199799315, 7.65149983741, 7.65554131408, 7.62213286298,
         7.53795983357, 7.53626130154, 7.54539963934])
    res_d002 = np.array(
        [7.70178181209, 7.67445481224, 7.67153737650, 7.67729153190,
         7.61173201163, 7.67913499878, 7.67306697759, 7.65287924998,
         7.64904451605, 7.66580449603, 7.66252081172, 7.62213286298,
         7.53795983357, 7.53626130154, 7.54539963934])

    mod_002 = ARIMA(np.asarray(data_sample['loginv']), (0, 0, 2),
                    exog=np.asarray(data_sample[['loggdp', 'logcons']]))

    # does not converge with default starting values
    start_params = np.concatenate((res.params[[0, 1, 2, 4]], [0]))
    res_002 = mod_002.fit(start_params=start_params, disp=0,
                          solver='bfgs', maxiter=5000)

    # forecast
    fpredict_002 = res_002.predict(start=197, end=202,
                                   exog=exog_full.values[197:])
    forecast_002 = res_002.forecast(steps=len(exog_full.values[197:]),
                                    exog=exog_full.values[197:])
    # TODO: Checking other results
    forecast_002 = forecast_002[0]
    assert_allclose(fpredict_002, res_f002[-len(fpredict_002):],
                    rtol=tol, atol=tol / 100.0)
    assert_allclose(forecast_002, res_f002[-len(forecast_002):],
                    rtol=tol, atol=tol / 100.0)

    # dynamic predict
    dpredict_002 = res_002.predict(start=193, end=202,
                                   exog=exog_full.values[197:], dynamic=True)
    assert_allclose(dpredict_002, res_d002[-len(dpredict_002):],
                    rtol=tol, atol=tol / 100.0)

    # in-sample dynamic predict should not need exog, #2982
    predict_3a = res_002.predict(start=100, end=120, dynamic=True)
    predict_3b = res_002.predict(start=100, end=120,
                                 exog=exog_full.values[100:120], dynamic=True)
    assert_allclose(predict_3a, predict_3b, rtol=1e-10)

    h = len(exog_full.values[197:])
    with pytest.raises(ValueError):
        res_002.forecast(steps=h)
    with pytest.raises(ValueError):
        res_002.forecast(steps=h, exog=np.empty((h, 20)))
    with pytest.raises(ValueError):
        res_002.forecast(steps=h, exog=np.empty(20))


def test_arima_fit_multiple_calls():
    y = [-1214.360173, -1848.209905, -2100.918158, -3647.483678, -4711.186773]
    mod = ARIMA(y, (1, 0, 2))
    # Make multiple calls to fit
    with pytest.warns(HessianInversionWarning, match="no bse or cov"):
        mod.fit(disp=0, start_params=[np.mean(y), .1, .1, .1])
    assert_equal(mod.exog_names, ['const', 'ar.L1.y', 'ma.L1.y', 'ma.L2.y'])

    with pytest.warns(HessianInversionWarning, match="no bse or cov"):
        res = mod.fit(disp=0, start_params=[np.mean(y), .1, .1, .1])
    assert_equal(mod.exog_names, ['const', 'ar.L1.y', 'ma.L1.y', 'ma.L2.y'])

    # ensure summary() works  # TODO: separate and pytest.mark.smoke
    res.summary()
    res.summary2()

    # test multiple calls when there is only a constant term
    mod = ARIMA(y, (0, 0, 0))
    # Make multiple calls to fit
    mod.fit(disp=0, start_params=[np.mean(y)])
    assert_equal(mod.exog_names, ['const'])

    with pytest.raises(RuntimeError):
        mod.fit(disp=0, start_params=[np.mean(y)])


def test_long_ar_start_params():
    np.random.seed(12345)
    arparams = np.array([1, -.75, .25])
    maparams = np.array([1, .65, .35])

    nobs = 30

    np.random.seed(12345)
    y = arma_generate_sample(arparams, maparams, nobs)

    model = ARMA(y, order=(2, 2))

    model.fit(method='css', start_ar_lags=10, disp=0)

    with pytest.raises(RuntimeError):
        model.fit(method='css-mle', start_ar_lags=10, disp=0)

    with pytest.raises(RuntimeError):
        model.fit(method='mle', start_ar_lags=10, disp=0)

    with pytest.raises(RuntimeError):
        model.fit(ValueError, start_ar_lags=nobs + 5, disp=0)


def test_start_params_too_large():
    np.random.seed(12345)
    arparams = np.array([1, -.75, .25])
    maparams = np.array([1, .65, .35])

    nobs = 30

    np.random.seed(12345)
    y = arma_generate_sample(arparams, maparams, nobs)

    model = ARMA(y, order=(2, 2))
    with pytest.raises(ValueError):
        model.fit(start_ar_lags=nobs + 5, disp=0)


def test_arma_pickle():
    np.random.seed(9876565)
    x = fa.ArmaFft([1, -0.5], [1., 0.4], 40).generate_sample(nsample=200,
                                                             burnin=1000)
    mod = ARMA(x, (1, 1))
    pkl_mod = pickle.loads(pickle.dumps(mod))

    res = mod.fit(trend="c", disp=-1, solver='newton')
    pkl_res = pkl_mod.fit(trend="c", disp=-1, solver='newton')

    assert_allclose(res.params, pkl_res.params)
    assert_allclose(res.llf, pkl_res.llf)
    assert_almost_equal(res.resid, pkl_res.resid)
    assert_almost_equal(res.fittedvalues, pkl_res.fittedvalues)
    assert_almost_equal(res.pvalues, pkl_res.pvalues)


def test_arima_pickle():
    endog = y_arma[:, 6]
    mod = ARIMA(endog, (1, 1, 1))
    pkl_mod = pickle.loads(pickle.dumps(mod))

    res = mod.fit(trend="c", disp=-1, solver='newton')
    pkl_res = pkl_mod.fit(trend="c", disp=-1, solver='newton')

    assert_allclose(res.params, pkl_res.params)
    assert_allclose(res.llf, pkl_res.llf)
    assert_almost_equal(res.resid, pkl_res.resid)
    assert_almost_equal(res.fittedvalues, pkl_res.fittedvalues)
    assert_almost_equal(res.pvalues, pkl_res.pvalues)


def test_arima_not_implemented():
    formula = ' WUE ~ 1 + SFO3 '
    data = [-1214.360173, -1848.209905, -2100.918158]
    assert_raises(NotImplementedError, ARIMA.from_formula, formula, data)


def test_endog_int():
    # int endog should produce same result as float, #3504

    np.random.seed(123987)
    y = np.random.randint(0, 16, size=100)
    yf = y.astype(np.float64)

    res = AutoReg(y, 5).fit()
    resf = AutoReg(yf, 5).fit()
    assert_allclose(res.params, resf.params, atol=1e-5)
    assert_allclose(res.bse, resf.bse, atol=1e-5)

    res = ARMA(y, order=(2, 1)).fit(disp=-1)
    resf = ARMA(yf, order=(2, 1)).fit(disp=-1)
    assert_allclose(res.params, resf.params, atol=1e-5)
    assert_allclose(res.bse, resf.bse, atol=1e-5)

    res = ARIMA(y.cumsum(), order=(1, 1, 1)).fit(disp=-1)
    resf = ARIMA(yf.cumsum(), order=(1, 1, 1)).fit(disp=-1)
    assert_allclose(res.params, resf.params, rtol=1e-6, atol=1e-5)
    assert_allclose(res.bse, resf.bse, rtol=1e-6, atol=1e-5)


def test_multidim_endog(reset_randomstate):
    y = np.random.randn(1000, 2)
    with pytest.raises(ValueError):
        ARMA(y, order=(1, 1))

    y = np.random.randn(1000, 1, 2)
    with pytest.raises(ValueError):
        ARMA(y, order=(1, 1))

    y = np.random.randn(1, 1, 1000)
    with pytest.raises(ValueError):
        ARMA(y, order=(1, 1))


def test_arima_no_full_output():
    # GH 2752
    endog = y_arma[:, 6]
    mod = ARIMA(endog, (1, 0, 1))
    res = mod.fit(trend="c", disp=-1, full_output=False)
    assert res.mle_retvals is None


def test_arima_summary_no_lags(reset_randomstate):
    y_train = pd.Series(np.random.randn(1000), name='y_train')
    x_train = pd.DataFrame(np.random.randn(1000, 2), columns=['x1', 'x2'])
    res = ARIMA(endog=y_train.values, exog=x_train,
                order=(0, 1, 0)).fit(disp=-1)
    summ = res.summary().as_text()
    assert 'const ' in summ
    assert 'x1 ' in summ
    assert 'x2 ' in summ


def test_constant_column_trend():
    # GH#3343 analogous to GH#5258 for AR, when the user passes a constant exog
    #  and also passes trend="c", raise instead _make_arma_exog used to
    #  silently drop a column and return an inconsistenct k_trend value.

    exog = np.array([0.5, 0.5, 0.5, 0.5, 0.5])
    endog = np.array([-0.011866, 0.003380, 0.015357, 0.004451, -0.020889])

    model = ARIMA(endog=endog, order=(1, 1, 0), exog=exog)

    # Fitting with a constant and constant exog raises because of colinearity
    with pytest.raises(ValueError, match="x contains a constant"):
        model.fit(trend="c", disp=-1)

    # FIXME: calling model.fit(trend="nc") raises for orthogonal reasons


def test_arima_d0_forecast(reset_randomstate):
    arparams = np.array([1, -.75])
    maparams = np.array([1, .65])
    y = arma_generate_sample(arparams, maparams, 250)
    mod = ARIMA(y, (1, 0, 1))
    assert isinstance(mod, ARMA)
    res = mod.fit(disp=-1)
    pred = res.predict(start=200, end=300)
    pred_typ = res.predict(start=200, end=300, typ='linear')
    assert_allclose(pred, pred_typ)
    pred_mod = mod.predict(res.params, start=200, end=300, typ='linear')
    assert_allclose(pred, pred_mod)


def test_predict_exog_adjust(reset_randomstate):
    df = pd.DataFrame(np.random.standard_normal((1000, 2)),
                      index=pd.date_range('31-12-2000', periods=1000),
                      columns=['y', 'x'])
    y = df.y.iloc[:750]
    x = df.x.iloc[:750]
    mod = ARMA(y, (2, 0), exog=x)
    res = mod.fit(disp=-1)
    pred_adj = res.predict(end=df.index[-1], exog=df.x)
    pred = res.predict(end=df.index[-1], exog=df.x.iloc[750:])
    assert_allclose(pred, pred_adj)


def test_predict_wrong_exog_len(reset_randomstate):
    df = pd.DataFrame(np.random.standard_normal((1000, 2)),
                      index=pd.date_range('31-12-2000', periods=1000),
                      columns=['y', 'x'])
    y = df.y.iloc[:750]
    x = df.x.iloc[:750]
    mod = ARMA(y, (2, 0), exog=x)
    res = mod.fit(disp=-1)
    with pytest.warns(SpecificationWarning, match='of observations in exog'):
        res.predict(end=df.index[-1], exog=df.x.iloc[500:])


def test_invalid_method(reset_randomstate):
    ar, ma = [1, -0.5], [1., 0.4]
    x = fa.ArmaFft(ar, ma, 40).generate_sample(nsample=1000, burnin=1000)
    mod = ARMA(x, (1, 1))
    with pytest.raises(ValueError, match='Method unknown not understood'):
        mod.fit(method='unknown')


@pytest.mark.matplotlib
def test_summary_plots_no_dates(reset_randomstate, close_figures):
    ar, ma = [1, -0.5], [1., 0.4]
    x = fa.ArmaFft(ar, ma, 40).generate_sample(nsample=1000, burnin=1000)
    res = ARMA(x, (1, 1)).fit(disp=-1)
    res.plot_predict()
    res.plot_predict(plot_insample=True)
    assert isinstance(res.summary().as_text(), str)
    assert isinstance(res.summary2().as_text(), str)


def test_predict_exog_missing():
    dta = load_macrodata_pandas().data
    res = ARMA(dta['realcons'], (1, 1), dta['m1']).fit(disp=-1)
    with pytest.raises(ValueError, match='You must provide exog for ARMAX'):
        res.predict(start=203, end=210)


def test_too_few_obs_starting_values(reset_randomstate):
    ar, ma = [1, -0.5], [1., 0.4]
    x = fa.ArmaFft(ar, ma, 40).generate_sample(nsample=5, burnin=100)
    with pytest.raises(ValueError, match='Insufficient degrees of freedom'):
        ARMA(x, (1, 6)).fit(disp=-1)


def test_repeated_fit_error(reset_randomstate):
    ar, ma = [1, -0.5], [1., 0.4]
    x = fa.ArmaFft(ar, ma, 40).generate_sample(nsample=1000, burnin=100)
    arma = ARMA(x, (1, 1))
    arma.fit(disp=-1)
    with pytest.raises(RuntimeError):
        arma.fit(trend='nc')
    with pytest.raises(RuntimeError):
        arma.fit(method='css')


def test_predict_no_fit():
    ar, ma = [1, -0.5], [1., 0.4]
    x = fa.ArmaFft(ar, ma, 40).generate_sample(nsample=1000, burnin=100)
    arma = ARMA(x, (1, 1))
    with pytest.raises(RuntimeError, match='Model must be fit'):
        arma.predict([.1, .1])
    arima = ARIMA(x, (1, 1, 1))
    with pytest.raises(RuntimeError, match='Model must be fit'):
        arima.predict([.1, .1])


def test_arma_repeated_fit():
    ar, ma = [1, -0.5], [1., 0.4]
    x = fa.ArmaFft(ar, ma, 40).generate_sample(nsample=1000, burnin=100)
    arma = ARMA(x, (1, 1))
    res = arma.fit(trend='c', disp=-1)
    repeat = arma.fit(trend='c', disp=-1)
    rtol = 1e-4 if PLATFORM_WIN32 else 1e-7
    assert_allclose(res.params, repeat.params, rtol=rtol)
    assert isinstance(res.summary().as_text(), str)
    assert isinstance(repeat.summary().as_text(), str)


def test_arima_repeated_fit(reset_randomstate):
    ar, ma = [1, -0.5], [1., 0.4]
    n = 1000
    arma_fft = fa.ArmaFft(ar, ma, 40)
    x = 4 * np.arange(n) + arma_fft.generate_sample(nsample=n, burnin=100)
    arma = ARIMA(x, (1, 1, 1))
    res = arma.fit(trend='c', disp=-1)
    repeat = arma.fit(trend='c', disp=-1)
    tol = 1e-3 if PLATFORM_WIN32 else 1e-6
    assert_allclose(res.params, repeat.params, atol=tol, rtol=tol)
    assert isinstance(res.summary().as_text(), str)
    assert isinstance(repeat.summary().as_text(), str)


def test_arma_ttest_ftest():
    # GH947
    ar, ma = [1, -0.5], [1., 0.4]
    x = 2 + fa.ArmaFft(ar, ma, 40).generate_sample(nsample=1000, burnin=100)
    arma = ARMA(x, (1, 1))
    res = arma.fit(disp=-1)
    r = np.array([0, 1, 1])
    t_test = res.t_test(r)
    c = res.cov_params()
    v = r @ c @ r
    numerator = res.params @ r
    denom = np.sqrt(v)
    stat = numerator / denom
    assert_allclose(stat, t_test.statistic)

    f_test = res.f_test(r)
    assert_allclose(stat**2, f_test.statistic)


def test_nan_exog_arima_d1():
    # GH2746, verify raises on missing
    df = pd.DataFrame(np.random.standard_normal((1000, 2)),
                      index=pd.date_range('31-12-2000', periods=1000),
                      columns=['y', 'x'])
    y = df.y.iloc[:750]
    x = df.x.iloc[:750]
    x.iloc[0] = np.nan
    with pytest.raises(MissingDataError):
        ARIMA(y, (0, 1, 1), exog=x)


def test_arma_exog_const_trend_nc(reset_randomstate):
    x = np.ones((1000, 1))
    y = arma_generate_sample([1, -1.2, 0.5], [1, 0.7], 1000,
                             distrvs=np.random.standard_normal)
    y += 1
    res = ARMA(y, (2, 1), exog=x).fit(trend='nc', disp=-1)
    assert res.params.shape[0] == 4