コード例 #1
0
ファイル: test_sandwich.py プロジェクト: zzzz123321/pygwr
def test_hac_simple():

    from gwstatsmodels.datasets import macrodata
    d2 = macrodata.load().data
    g_gdp = 400 * np.diff(np.log(d2['realgdp']))
    g_inv = 400 * np.diff(np.log(d2['realinv']))
    exogg = add_constant(np.c_[g_gdp, d2['realint'][:-1]], prepend=True)
    res_olsg = OLS(g_inv, exogg).fit()

    #> NeweyWest(fm, lag = 4, prewhite = FALSE, sandwich = TRUE, verbose=TRUE, adjust=TRUE)
    #Lag truncation parameter chosen: 4
    #                     (Intercept)                   ggdp                  lint
    cov1_r = [
        [1.40643899878678802, -0.3180328707083329709, -0.060621111216488610],
        [-0.31803287070833292, 0.1097308348999818661, 0.000395311760301478],
        [-0.06062111121648865, 0.0003953117603014895, 0.087511528912470993]
    ]

    #> NeweyWest(fm, lag = 4, prewhite = FALSE, sandwich = TRUE, verbose=TRUE, adjust=FALSE)
    #Lag truncation parameter chosen: 4
    #                    (Intercept)                  ggdp                  lint
    cov2_r = [
        [1.3855512908840137, -0.313309610252268500, -0.059720797683570477],
        [-0.3133096102522685, 0.108101169035130618, 0.000389440793564339],
        [-0.0597207976835705, 0.000389440793564336, 0.086211852740503622]
    ]

    cov1, se1 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=True)
    cov2, se2 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=False)
    assert_almost_equal(cov1, cov1_r, decimal=14)
    assert_almost_equal(cov2, cov2_r, decimal=14)
コード例 #2
0
ファイル: test_sandwich.py プロジェクト: bolliger32/pygwr
def test_hac_simple():

    from gwstatsmodels.datasets import macrodata

    d2 = macrodata.load().data
    g_gdp = 400 * np.diff(np.log(d2["realgdp"]))
    g_inv = 400 * np.diff(np.log(d2["realinv"]))
    exogg = add_constant(np.c_[g_gdp, d2["realint"][:-1]], prepend=True)
    res_olsg = OLS(g_inv, exogg).fit()

    # > NeweyWest(fm, lag = 4, prewhite = FALSE, sandwich = TRUE, verbose=TRUE, adjust=TRUE)
    # Lag truncation parameter chosen: 4
    #                     (Intercept)                   ggdp                  lint
    cov1_r = [
        [1.40643899878678802, -0.3180328707083329709, -0.060621111216488610],
        [-0.31803287070833292, 0.1097308348999818661, 0.000395311760301478],
        [-0.06062111121648865, 0.0003953117603014895, 0.087511528912470993],
    ]

    # > NeweyWest(fm, lag = 4, prewhite = FALSE, sandwich = TRUE, verbose=TRUE, adjust=FALSE)
    # Lag truncation parameter chosen: 4
    #                    (Intercept)                  ggdp                  lint
    cov2_r = [
        [1.3855512908840137, -0.313309610252268500, -0.059720797683570477],
        [-0.3133096102522685, 0.108101169035130618, 0.000389440793564339],
        [-0.0597207976835705, 0.000389440793564336, 0.086211852740503622],
    ]

    cov1, se1 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=True)
    cov2, se2 = sw.cov_hac_simple(res_olsg, nlags=4, use_correction=False)
    assert_almost_equal(cov1, cov1_r, decimal=14)
    assert_almost_equal(cov2, cov2_r, decimal=14)
コード例 #3
0
    def test_hac(self):
        res = self.res
        #> nw = NeweyWest(fm, lag = 4, prewhite = FALSE, verbose=TRUE)
        #> nw2 = NeweyWest(fm, lag=10, prewhite = FALSE, verbose=TRUE)

        #> mkarray(nw, "cov_hac_4")
        cov_hac_4 = np.array([1.385551290884014, -0.3133096102522685,
            -0.0597207976835705, -0.3133096102522685, 0.1081011690351306,
            0.000389440793564336, -0.0597207976835705, 0.000389440793564339,
            0.0862118527405036]).reshape(3,3, order='F')

        #> mkarray(nw2, "cov_hac_10")
        cov_hac_10 = np.array([1.257386180080192, -0.2871560199899846,
            -0.03958300024627573, -0.2871560199899845, 0.1049107028987101,
            0.0003896205316866944, -0.03958300024627578, 0.0003896205316866961,
            0.0985539340694839]).reshape(3,3, order='F')

        cov, bse_hac = sw.cov_hac_simple(res, nlags=4, use_correction=False)
        assert_almost_equal(cov, cov_hac_4, decimal=14)
        assert_almost_equal(bse_hac, np.sqrt(np.diag(cov)), decimal=14)

        cov, bse_hac = sw.cov_hac_simple(res, nlags=10, use_correction=False)
        assert_almost_equal(cov, cov_hac_10, decimal=14)
        assert_almost_equal(bse_hac, np.sqrt(np.diag(cov)), decimal=14)
コード例 #4
0
    def test_all(self):

        d = macrodata.load().data
        #import datasetswsm.greene as g
        #d = g.load('5-1')

        #growth rates
        gs_l_realinv = 400 * np.diff(np.log(d['realinv']))
        gs_l_realgdp = 400 * np.diff(np.log(d['realgdp']))

        #simple diff, not growthrate, I want heteroscedasticity later for testing
        endogd = np.diff(d['realinv'])
        exogd = add_constant(np.c_[np.diff(d['realgdp']), d['realint'][:-1]],
                             prepend=True)

        endogg = gs_l_realinv
        exogg = add_constant(np.c_[gs_l_realgdp, d['realint'][:-1]],
                             prepend=True)

        res_ols = OLS(endogg, exogg).fit()
        #print res_ols.params

        mod_g1 = GLSAR(endogg, exogg, rho=-0.108136)
        res_g1 = mod_g1.fit()
        #print res_g1.params

        mod_g2 = GLSAR(endogg, exogg, rho=-0.108136)  #-0.1335859) from R
        res_g2 = mod_g2.iterative_fit(maxiter=5)
        #print res_g2.params

        rho = -0.108136

        #                 coefficient   std. error   t-ratio    p-value 95% CONFIDENCE INTERVAL
        partable = np.array([
            [-9.50990, 0.990456, -9.602, 3.65e-018, -11.4631, -7.55670],  # ***
            [4.37040, 0.208146, 21.00, 2.93e-052, 3.95993, 4.78086],  # ***
            [-0.579253, 0.268009, -2.161, 0.0319, -1.10777, -0.0507346]
        ])  #    **

        #Statistics based on the rho-differenced data:

        result_gretl_g1 = dict(endog_mean=("Mean dependent var", 3.113973),
                               endog_std=("S.D. dependent var", 18.67447),
                               ssr=("Sum squared resid", 22530.90),
                               mse_resid_sqrt=("S.E. of regression", 10.66735),
                               rsquared=("R-squared", 0.676973),
                               rsquared_adj=("Adjusted R-squared", 0.673710),
                               fvalue=("F(2, 198)", 221.0475),
                               f_pvalue=("P-value(F)", 3.56e-51),
                               resid_acf1=("rho", -0.003481),
                               dw=("Durbin-Watson", 1.993858))

        #fstatistic, p-value, df1, df2
        reset_2_3 = [5.219019, 0.00619, 2, 197, "f"]
        reset_2 = [7.268492, 0.00762, 1, 198, "f"]
        reset_3 = [5.248951, 0.023, 1, 198, "f"]
        #LM-statistic, p-value, df
        arch_4 = [7.30776, 0.120491, 4, "chi2"]

        #multicollinearity
        vif = [1.002, 1.002]
        cond_1norm = 6862.0664
        determinant = 1.0296049e+009
        reciprocal_condition_number = 0.013819244

        #Chi-square(2): test-statistic, pvalue, df
        normality = [20.2792, 3.94837e-005, 2]

        #tests
        res = res_g1  #with rho from Gretl

        #basic

        assert_almost_equal(res.params, partable[:, 0], 4)
        assert_almost_equal(res.bse, partable[:, 1], 6)
        assert_almost_equal(res.tvalues, partable[:, 2], 2)

        assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2)
        #assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl
        #assert_almost_equal(res.rsquared, result_gretl_g1['rsquared'][1], decimal=7) #FAIL
        #assert_almost_equal(res.rsquared_adj, result_gretl_g1['rsquared_adj'][1], decimal=7) #FAIL
        assert_almost_equal(np.sqrt(res.mse_resid),
                            result_gretl_g1['mse_resid_sqrt'][1],
                            decimal=5)
        assert_almost_equal(res.fvalue,
                            result_gretl_g1['fvalue'][1],
                            decimal=4)
        assert_approx_equal(res.f_pvalue,
                            result_gretl_g1['f_pvalue'][1],
                            significant=2)
        #assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO

        #arch
        #sm_arch = smsdia.acorr_lm(res.wresid**2, maxlag=4, autolag=None)
        sm_arch = smsdia.het_arch(res.wresid, maxlag=4)
        assert_almost_equal(sm_arch[0], arch_4[0], decimal=4)
        assert_almost_equal(sm_arch[1], arch_4[1], decimal=6)

        #tests
        res = res_g2  #with estimated rho

        #estimated lag coefficient
        assert_almost_equal(res.model.rho, rho, decimal=3)

        #basic
        assert_almost_equal(res.params, partable[:, 0], 4)
        assert_almost_equal(res.bse, partable[:, 1], 3)
        assert_almost_equal(res.tvalues, partable[:, 2], 2)

        assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2)
        #assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl
        #assert_almost_equal(res.rsquared, result_gretl_g1['rsquared'][1], decimal=7) #FAIL
        #assert_almost_equal(res.rsquared_adj, result_gretl_g1['rsquared_adj'][1], decimal=7) #FAIL
        assert_almost_equal(np.sqrt(res.mse_resid),
                            result_gretl_g1['mse_resid_sqrt'][1],
                            decimal=5)
        assert_almost_equal(res.fvalue,
                            result_gretl_g1['fvalue'][1],
                            decimal=0)
        assert_almost_equal(res.f_pvalue,
                            result_gretl_g1['f_pvalue'][1],
                            decimal=6)
        #assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO

        c = oi.reset_ramsey(res, degree=2)
        compare_ftest(c, reset_2, decimal=(2, 4))
        c = oi.reset_ramsey(res, degree=3)
        compare_ftest(c, reset_2_3, decimal=(2, 4))

        #arch
        #sm_arch = smsdia.acorr_lm(res.wresid**2, maxlag=4, autolag=None)
        sm_arch = smsdia.het_arch(res.wresid, maxlag=4)
        assert_almost_equal(sm_arch[0], arch_4[0], decimal=1)
        assert_almost_equal(sm_arch[1], arch_4[1], decimal=2)
        '''
        Performing iterative calculation of rho...

                         ITER       RHO        ESS
                           1     -0.10734   22530.9
                           2     -0.10814   22530.9

        Model 4: Cochrane-Orcutt, using observations 1959:3-2009:3 (T = 201)
        Dependent variable: ds_l_realinv
        rho = -0.108136

                         coefficient   std. error   t-ratio    p-value
          -------------------------------------------------------------
          const           -9.50990      0.990456    -9.602    3.65e-018 ***
          ds_l_realgdp     4.37040      0.208146    21.00     2.93e-052 ***
          realint_1       -0.579253     0.268009    -2.161    0.0319    **

        Statistics based on the rho-differenced data:

        Mean dependent var   3.113973   S.D. dependent var   18.67447
        Sum squared resid    22530.90   S.E. of regression   10.66735
        R-squared            0.676973   Adjusted R-squared   0.673710
        F(2, 198)            221.0475   P-value(F)           3.56e-51
        rho                 -0.003481   Durbin-Watson        1.993858
        '''
        '''
        RESET test for specification (squares and cubes)
        Test statistic: F = 5.219019,
        with p-value = P(F(2,197) > 5.21902) = 0.00619

        RESET test for specification (squares only)
        Test statistic: F = 7.268492,
        with p-value = P(F(1,198) > 7.26849) = 0.00762

        RESET test for specification (cubes only)
        Test statistic: F = 5.248951,
        with p-value = P(F(1,198) > 5.24895) = 0.023:
        '''
        '''
        Test for ARCH of order 4

                     coefficient   std. error   t-ratio   p-value
          --------------------------------------------------------
          alpha(0)   97.0386       20.3234       4.775    3.56e-06 ***
          alpha(1)    0.176114      0.0714698    2.464    0.0146   **
          alpha(2)   -0.0488339     0.0724981   -0.6736   0.5014
          alpha(3)   -0.0705413     0.0737058   -0.9571   0.3397
          alpha(4)    0.0384531     0.0725763    0.5298   0.5968

          Null hypothesis: no ARCH effect is present
          Test statistic: LM = 7.30776
          with p-value = P(Chi-square(4) > 7.30776) = 0.120491:
        '''
        '''
        Variance Inflation Factors

        Minimum possible value = 1.0
        Values > 10.0 may indicate a collinearity problem

           ds_l_realgdp    1.002
              realint_1    1.002

        VIF(j) = 1/(1 - R(j)^2), where R(j) is the multiple correlation coefficient
        between variable j and the other independent variables

        Properties of matrix X'X:

         1-norm = 6862.0664
         Determinant = 1.0296049e+009
         Reciprocal condition number = 0.013819244
        '''
        '''
        Test for ARCH of order 4 -
          Null hypothesis: no ARCH effect is present
          Test statistic: LM = 7.30776
          with p-value = P(Chi-square(4) > 7.30776) = 0.120491

        Test of common factor restriction -
          Null hypothesis: restriction is acceptable
          Test statistic: F(2, 195) = 0.426391
          with p-value = P(F(2, 195) > 0.426391) = 0.653468

        Test for normality of residual -
          Null hypothesis: error is normally distributed
          Test statistic: Chi-square(2) = 20.2792
          with p-value = 3.94837e-005:
        '''

        #no idea what this is
        '''
        Augmented regression for common factor test
        OLS, using observations 1959:3-2009:3 (T = 201)
        Dependent variable: ds_l_realinv

                           coefficient   std. error   t-ratio    p-value
          ---------------------------------------------------------------
          const            -10.9481      1.35807      -8.062    7.44e-014 ***
          ds_l_realgdp       4.28893     0.229459     18.69     2.40e-045 ***
          realint_1         -0.662644    0.334872     -1.979    0.0492    **
          ds_l_realinv_1    -0.108892    0.0715042    -1.523    0.1294
          ds_l_realgdp_1     0.660443    0.390372      1.692    0.0923    *
          realint_2          0.0769695   0.341527      0.2254   0.8219

          Sum of squared residuals = 22432.8

        Test of common factor restriction

          Test statistic: F(2, 195) = 0.426391, with p-value = 0.653468
        '''

        ################ with OLS, HAC errors

        #Model 5: OLS, using observations 1959:2-2009:3 (T = 202)
        #Dependent variable: ds_l_realinv
        #HAC standard errors, bandwidth 4 (Bartlett kernel)

        #coefficient   std. error   t-ratio    p-value 95% CONFIDENCE INTERVAL
        #for confidence interval t(199, 0.025) = 1.972

        partable = np.array([
            [-9.48167, 1.17709, -8.055, 7.17e-014, -11.8029, -7.16049],  # ***
            [4.37422, 0.328787, 13.30, 2.62e-029, 3.72587, 5.02258],  #***
            [-0.613997, 0.293619, -2.091, 0.0378, -1.19300, -0.0349939]
        ])  # **

        result_gretl_g1 = dict(endog_mean=("Mean dependent var", 3.257395),
                               endog_std=("S.D. dependent var", 18.73915),
                               ssr=("Sum squared resid", 22799.68),
                               mse_resid_sqrt=("S.E. of regression", 10.70380),
                               rsquared=("R-squared", 0.676978),
                               rsquared_adj=("Adjusted R-squared", 0.673731),
                               fvalue=("F(2, 199)", 90.79971),
                               f_pvalue=("P-value(F)", 9.53e-29),
                               llf=("Log-likelihood", -763.9752),
                               aic=("Akaike criterion", 1533.950),
                               bic=("Schwarz criterion", 1543.875),
                               hqic=("Hannan-Quinn", 1537.966),
                               resid_acf1=("rho", -0.107341),
                               dw=("Durbin-Watson", 2.213805))

        linear_logs = [1.68351, 0.430953, 2, "chi2"]
        #for logs: dropping 70 nan or incomplete observations, T=133
        #(res_ols.model.exog <=0).any(1).sum() = 69  ?not 70
        linear_squares = [7.52477, 0.0232283, 2, "chi2"]

        #Autocorrelation, Breusch-Godfrey test for autocorrelation up to order 4
        lm_acorr4 = [1.17928, 0.321197, 4, 195, "F"]
        lm2_acorr4 = [4.771043, 0.312, 4, "chi2"]
        acorr_ljungbox4 = [5.23587, 0.264, 4, "chi2"]

        #break
        cusum_Harvey_Collier = [0.494432, 0.621549, 198,
                                "t"]  #stats.t.sf(0.494432, 198)*2
        #see cusum results in files
        break_qlr = [3.01985, 0.1, 3, 196,
                     "maxF"]  #TODO check this, max at 2001:4
        break_chow = [13.1897, 0.00424384, 3, "chi2"]  # break at 1984:1

        arch_4 = [3.43473, 0.487871, 4, "chi2"]

        normality = [23.962, 0.00001, 2, "chi2"]

        het_white = [33.503723, 0.000003, 5, "chi2"]
        het_breush_pagan = [1.302014, 0.521520, 2,
                            "chi2"]  #TODO: not available
        het_breush_pagan_konker = [0.709924, 0.701200, 2, "chi2"]

        reset_2_3 = [5.219019, 0.00619, 2, 197, "f"]
        reset_2 = [7.268492, 0.00762, 1, 198, "f"]
        reset_3 = [5.248951, 0.023, 1, 198, "f"]  #not available

        cond_1norm = 5984.0525
        determinant = 7.1087467e+008
        reciprocal_condition_number = 0.013826504
        vif = [1.001, 1.001]

        names = 'date   residual        leverage       influence        DFFITS'.split(
        )
        cur_dir = os.path.abspath(os.path.dirname(__file__))
        fpath = os.path.join(cur_dir,
                             'results/leverage_influence_ols_nostars.txt')
        lev = np.genfromtxt(fpath,
                            skip_header=3,
                            skip_footer=1,
                            converters={0: lambda s: s})
        #either numpy 1.6 or python 3.2 changed behavior
        if np.isnan(lev[-1]['f1']):
            lev = np.genfromtxt(fpath,
                                skip_header=3,
                                skip_footer=2,
                                converters={0: lambda s: s})

        lev.dtype.names = names

        res = res_ols  #for easier copying

        cov_hac, bse_hac = sw.cov_hac_simple(res,
                                             nlags=4,
                                             use_correction=False)

        assert_almost_equal(res.params, partable[:, 0], 5)
        assert_almost_equal(bse_hac, partable[:, 1], 5)
        #TODO

        assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2)
        #assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl
        assert_almost_equal(res.rsquared,
                            result_gretl_g1['rsquared'][1],
                            decimal=6)  #FAIL
        assert_almost_equal(res.rsquared_adj,
                            result_gretl_g1['rsquared_adj'][1],
                            decimal=6)  #FAIL
        assert_almost_equal(np.sqrt(res.mse_resid),
                            result_gretl_g1['mse_resid_sqrt'][1],
                            decimal=5)
        #f-value is based on cov_hac I guess
        #assert_almost_equal(res.fvalue, result_gretl_g1['fvalue'][1], decimal=0) #FAIL
        #assert_approx_equal(res.f_pvalue, result_gretl_g1['f_pvalue'][1], significant=1) #FAIL
        #assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO

        c = oi.reset_ramsey(res, degree=2)
        compare_ftest(c, reset_2, decimal=(6, 5))
        c = oi.reset_ramsey(res, degree=3)
        compare_ftest(c, reset_2_3, decimal=(6, 5))

        linear_sq = smsdia.linear_lm(res.resid, res.model.exog)
        assert_almost_equal(linear_sq[0], linear_squares[0], decimal=6)
        assert_almost_equal(linear_sq[1], linear_squares[1], decimal=7)

        hbpk = smsdia.het_breushpagan(res.resid, res.model.exog)
        assert_almost_equal(hbpk[0], het_breush_pagan_konker[0], decimal=6)
        assert_almost_equal(hbpk[1], het_breush_pagan_konker[1], decimal=6)

        hw = smsdia.het_white(res.resid, res.model.exog)
        assert_almost_equal(hw[:2], het_white[:2], 6)

        #arch
        #sm_arch = smsdia.acorr_lm(res.resid**2, maxlag=4, autolag=None)
        sm_arch = smsdia.het_arch(res.resid, maxlag=4)
        assert_almost_equal(sm_arch[0], arch_4[0], decimal=5)
        assert_almost_equal(sm_arch[1], arch_4[1], decimal=6)

        vif2 = [
            oi.variance_inflation_factor(res.model.exog, k) for k in [1, 2]
        ]

        infl = oi.OLSInfluence(res_ols)
        #print np.max(np.abs(lev['DFFITS'] - infl.dffits[0]))
        #print np.max(np.abs(lev['leverage'] - infl.hat_matrix_diag))
        #print np.max(np.abs(lev['influence'] - infl.influence))  #just added this based on Gretl

        #just rough test, low decimal in Gretl output,
        assert_almost_equal(lev['residual'], res.resid, decimal=3)
        assert_almost_equal(lev['DFFITS'], infl.dffits[0], decimal=3)
        assert_almost_equal(lev['leverage'], infl.hat_matrix_diag, decimal=3)
        assert_almost_equal(lev['influence'], infl.influence, decimal=4)
コード例 #5
0
ファイル: ex_sandwich.py プロジェクト: bolliger32/pygwr
params_true = np.ones(kvars)
y_true = np.dot(exog, params_true)
sigma = 0.1 + np.exp(exog[:, -1])
endog = y_true + sigma * np.random.randn(nobs)

self = sm.OLS(endog, exog).fit()

print self.HC3_se
print sw.se_cov(sw.cov_hc3(self))
# test standalone refactoring
assert_almost_equal(sw.se_cov(sw.cov_hc0(self)), self.HC0_se, 15)
assert_almost_equal(sw.se_cov(sw.cov_hc1(self)), self.HC1_se, 15)
assert_almost_equal(sw.se_cov(sw.cov_hc2(self)), self.HC2_se, 15)
assert_almost_equal(sw.se_cov(sw.cov_hc3(self)), self.HC3_se, 15)
print self.HC0_se
print sw.cov_hac_simple(self, nlags=0, use_correction=False)[1]
# test White as HAC with nlags=0, same as nlags=1 ?
bse_hac0 = sw.cov_hac_simple(self, nlags=0, use_correction=False)[1]
assert_almost_equal(bse_hac0, self.HC0_se, 15)
print bse_hac0
# test White as HAC with nlags=0, same as nlags=1 ?
bse_hac0c = sw.cov_hac_simple(self, nlags=0, use_correction=True)[1]
assert_almost_equal(bse_hac0c, self.HC1_se, 15)

bse_w = sw.cov_white_simple(self, use_correction=False)[1]
print bse_w
# test White
assert_almost_equal(bse_w, self.HC0_se, 15)

bse_wc = sw.cov_white_simple(self, use_correction=True)[1]
print bse_wc
コード例 #6
0
ファイル: test_glsar_gretl.py プロジェクト: bolliger32/pygwr
    def test_all(self):

        d = macrodata.load().data
        #import datasetswsm.greene as g
        #d = g.load('5-1')

        #growth rates
        gs_l_realinv = 400 * np.diff(np.log(d['realinv']))
        gs_l_realgdp = 400 * np.diff(np.log(d['realgdp']))

        #simple diff, not growthrate, I want heteroscedasticity later for testing
        endogd = np.diff(d['realinv'])
        exogd = add_constant(np.c_[np.diff(d['realgdp']), d['realint'][:-1]],
                            prepend=True)

        endogg = gs_l_realinv
        exogg = add_constant(np.c_[gs_l_realgdp, d['realint'][:-1]],prepend=True)

        res_ols = OLS(endogg, exogg).fit()
        #print res_ols.params

        mod_g1 = GLSAR(endogg, exogg, rho=-0.108136)
        res_g1 = mod_g1.fit()
        #print res_g1.params

        mod_g2 = GLSAR(endogg, exogg, rho=-0.108136)   #-0.1335859) from R
        res_g2 = mod_g2.iterative_fit(maxiter=5)
        #print res_g2.params


        rho = -0.108136

        #                 coefficient   std. error   t-ratio    p-value 95% CONFIDENCE INTERVAL
        partable = np.array([
                        [-9.50990,  0.990456, -9.602, 3.65e-018, -11.4631, -7.55670], # ***
                        [ 4.37040,  0.208146, 21.00,  2.93e-052,  3.95993, 4.78086], # ***
                        [-0.579253, 0.268009, -2.161, 0.0319, -1.10777, -0.0507346]]) #    **

        #Statistics based on the rho-differenced data:

        result_gretl_g1 = dict(
        endog_mean = ("Mean dependent var",   3.113973),
        endog_std = ("S.D. dependent var",   18.67447),
        ssr = ("Sum squared resid",    22530.90),
        mse_resid_sqrt = ("S.E. of regression",   10.66735),
        rsquared = ("R-squared",            0.676973),
        rsquared_adj = ("Adjusted R-squared",   0.673710),
        fvalue = ("F(2, 198)",            221.0475),
        f_pvalue = ("P-value(F)",           3.56e-51),
        resid_acf1 = ("rho",                 -0.003481),
        dw = ("Durbin-Watson",        1.993858))


        #fstatistic, p-value, df1, df2
        reset_2_3 = [5.219019, 0.00619, 2, 197, "f"]
        reset_2 = [7.268492, 0.00762, 1, 198, "f"]
        reset_3 = [5.248951, 0.023, 1, 198, "f"]
        #LM-statistic, p-value, df
        arch_4 = [7.30776, 0.120491, 4, "chi2"]

        #multicollinearity
        vif = [1.002, 1.002]
        cond_1norm = 6862.0664
        determinant = 1.0296049e+009
        reciprocal_condition_number = 0.013819244

        #Chi-square(2): test-statistic, pvalue, df
        normality = [20.2792, 3.94837e-005, 2]

        #tests
        res = res_g1  #with rho from Gretl

        #basic

        assert_almost_equal(res.params, partable[:,0], 4)
        assert_almost_equal(res.bse, partable[:,1], 6)
        assert_almost_equal(res.tvalues, partable[:,2], 2)

        assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2)
        #assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl
        #assert_almost_equal(res.rsquared, result_gretl_g1['rsquared'][1], decimal=7) #FAIL
        #assert_almost_equal(res.rsquared_adj, result_gretl_g1['rsquared_adj'][1], decimal=7) #FAIL
        assert_almost_equal(np.sqrt(res.mse_resid), result_gretl_g1['mse_resid_sqrt'][1], decimal=5)
        assert_almost_equal(res.fvalue, result_gretl_g1['fvalue'][1], decimal=4)
        assert_approx_equal(res.f_pvalue, result_gretl_g1['f_pvalue'][1], significant=2)
        #assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO

        #arch
        #sm_arch = smsdia.acorr_lm(res.wresid**2, maxlag=4, autolag=None)
        sm_arch = smsdia.het_arch(res.wresid, maxlag=4)
        assert_almost_equal(sm_arch[0], arch_4[0], decimal=4)
        assert_almost_equal(sm_arch[1], arch_4[1], decimal=6)

        #tests
        res = res_g2 #with estimated rho

        #estimated lag coefficient
        assert_almost_equal(res.model.rho, rho, decimal=3)

        #basic
        assert_almost_equal(res.params, partable[:,0], 4)
        assert_almost_equal(res.bse, partable[:,1], 3)
        assert_almost_equal(res.tvalues, partable[:,2], 2)

        assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2)
        #assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl
        #assert_almost_equal(res.rsquared, result_gretl_g1['rsquared'][1], decimal=7) #FAIL
        #assert_almost_equal(res.rsquared_adj, result_gretl_g1['rsquared_adj'][1], decimal=7) #FAIL
        assert_almost_equal(np.sqrt(res.mse_resid), result_gretl_g1['mse_resid_sqrt'][1], decimal=5)
        assert_almost_equal(res.fvalue, result_gretl_g1['fvalue'][1], decimal=0)
        assert_almost_equal(res.f_pvalue, result_gretl_g1['f_pvalue'][1], decimal=6)
        #assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO



        c = oi.reset_ramsey(res, degree=2)
        compare_ftest(c, reset_2, decimal=(2,4))
        c = oi.reset_ramsey(res, degree=3)
        compare_ftest(c, reset_2_3, decimal=(2,4))

        #arch
        #sm_arch = smsdia.acorr_lm(res.wresid**2, maxlag=4, autolag=None)
        sm_arch = smsdia.het_arch(res.wresid, maxlag=4)
        assert_almost_equal(sm_arch[0], arch_4[0], decimal=1)
        assert_almost_equal(sm_arch[1], arch_4[1], decimal=2)



        '''
        Performing iterative calculation of rho...

                         ITER       RHO        ESS
                           1     -0.10734   22530.9
                           2     -0.10814   22530.9

        Model 4: Cochrane-Orcutt, using observations 1959:3-2009:3 (T = 201)
        Dependent variable: ds_l_realinv
        rho = -0.108136

                         coefficient   std. error   t-ratio    p-value
          -------------------------------------------------------------
          const           -9.50990      0.990456    -9.602    3.65e-018 ***
          ds_l_realgdp     4.37040      0.208146    21.00     2.93e-052 ***
          realint_1       -0.579253     0.268009    -2.161    0.0319    **

        Statistics based on the rho-differenced data:

        Mean dependent var   3.113973   S.D. dependent var   18.67447
        Sum squared resid    22530.90   S.E. of regression   10.66735
        R-squared            0.676973   Adjusted R-squared   0.673710
        F(2, 198)            221.0475   P-value(F)           3.56e-51
        rho                 -0.003481   Durbin-Watson        1.993858
        '''

        '''
        RESET test for specification (squares and cubes)
        Test statistic: F = 5.219019,
        with p-value = P(F(2,197) > 5.21902) = 0.00619

        RESET test for specification (squares only)
        Test statistic: F = 7.268492,
        with p-value = P(F(1,198) > 7.26849) = 0.00762

        RESET test for specification (cubes only)
        Test statistic: F = 5.248951,
        with p-value = P(F(1,198) > 5.24895) = 0.023:
        '''

        '''
        Test for ARCH of order 4

                     coefficient   std. error   t-ratio   p-value
          --------------------------------------------------------
          alpha(0)   97.0386       20.3234       4.775    3.56e-06 ***
          alpha(1)    0.176114      0.0714698    2.464    0.0146   **
          alpha(2)   -0.0488339     0.0724981   -0.6736   0.5014
          alpha(3)   -0.0705413     0.0737058   -0.9571   0.3397
          alpha(4)    0.0384531     0.0725763    0.5298   0.5968

          Null hypothesis: no ARCH effect is present
          Test statistic: LM = 7.30776
          with p-value = P(Chi-square(4) > 7.30776) = 0.120491:
        '''

        '''
        Variance Inflation Factors

        Minimum possible value = 1.0
        Values > 10.0 may indicate a collinearity problem

           ds_l_realgdp    1.002
              realint_1    1.002

        VIF(j) = 1/(1 - R(j)^2), where R(j) is the multiple correlation coefficient
        between variable j and the other independent variables

        Properties of matrix X'X:

         1-norm = 6862.0664
         Determinant = 1.0296049e+009
         Reciprocal condition number = 0.013819244
        '''
        '''
        Test for ARCH of order 4 -
          Null hypothesis: no ARCH effect is present
          Test statistic: LM = 7.30776
          with p-value = P(Chi-square(4) > 7.30776) = 0.120491

        Test of common factor restriction -
          Null hypothesis: restriction is acceptable
          Test statistic: F(2, 195) = 0.426391
          with p-value = P(F(2, 195) > 0.426391) = 0.653468

        Test for normality of residual -
          Null hypothesis: error is normally distributed
          Test statistic: Chi-square(2) = 20.2792
          with p-value = 3.94837e-005:
        '''

        #no idea what this is
        '''
        Augmented regression for common factor test
        OLS, using observations 1959:3-2009:3 (T = 201)
        Dependent variable: ds_l_realinv

                           coefficient   std. error   t-ratio    p-value
          ---------------------------------------------------------------
          const            -10.9481      1.35807      -8.062    7.44e-014 ***
          ds_l_realgdp       4.28893     0.229459     18.69     2.40e-045 ***
          realint_1         -0.662644    0.334872     -1.979    0.0492    **
          ds_l_realinv_1    -0.108892    0.0715042    -1.523    0.1294
          ds_l_realgdp_1     0.660443    0.390372      1.692    0.0923    *
          realint_2          0.0769695   0.341527      0.2254   0.8219

          Sum of squared residuals = 22432.8

        Test of common factor restriction

          Test statistic: F(2, 195) = 0.426391, with p-value = 0.653468
        '''


        ################ with OLS, HAC errors

        #Model 5: OLS, using observations 1959:2-2009:3 (T = 202)
        #Dependent variable: ds_l_realinv
        #HAC standard errors, bandwidth 4 (Bartlett kernel)

        #coefficient   std. error   t-ratio    p-value 95% CONFIDENCE INTERVAL
        #for confidence interval t(199, 0.025) = 1.972

        partable = np.array([
        [-9.48167,      1.17709,     -8.055,    7.17e-014, -11.8029, -7.16049], # ***
        [4.37422,      0.328787,    13.30,     2.62e-029, 3.72587, 5.02258], #***
        [-0.613997,     0.293619,    -2.091,    0.0378, -1.19300, -0.0349939]]) # **

        result_gretl_g1 = dict(
                    endog_mean = ("Mean dependent var",   3.257395),
                    endog_std = ("S.D. dependent var",   18.73915),
                    ssr = ("Sum squared resid",    22799.68),
                    mse_resid_sqrt = ("S.E. of regression",   10.70380),
                    rsquared = ("R-squared",            0.676978),
                    rsquared_adj = ("Adjusted R-squared",   0.673731),
                    fvalue = ("F(2, 199)",            90.79971),
                    f_pvalue = ("P-value(F)",           9.53e-29),
                    llf = ("Log-likelihood",      -763.9752),
                    aic = ("Akaike criterion",     1533.950),
                    bic = ("Schwarz criterion",    1543.875),
                    hqic = ("Hannan-Quinn",         1537.966),
                    resid_acf1 = ("rho",                 -0.107341),
                    dw = ("Durbin-Watson",        2.213805))

        linear_logs = [1.68351, 0.430953, 2, "chi2"]
        #for logs: dropping 70 nan or incomplete observations, T=133
        #(res_ols.model.exog <=0).any(1).sum() = 69  ?not 70
        linear_squares = [7.52477, 0.0232283, 2, "chi2"]

        #Autocorrelation, Breusch-Godfrey test for autocorrelation up to order 4
        lm_acorr4 = [1.17928, 0.321197, 4, 195, "F"]
        lm2_acorr4 = [4.771043, 0.312, 4, "chi2"]
        acorr_ljungbox4 = [5.23587, 0.264, 4, "chi2"]

        #break
        cusum_Harvey_Collier  = [0.494432, 0.621549, 198, "t"] #stats.t.sf(0.494432, 198)*2
        #see cusum results in files
        break_qlr = [3.01985, 0.1, 3, 196, "maxF"]  #TODO check this, max at 2001:4
        break_chow = [13.1897, 0.00424384, 3, "chi2"] # break at 1984:1

        arch_4 = [3.43473, 0.487871, 4, "chi2"]

        normality = [23.962, 0.00001, 2, "chi2"]

        het_white = [33.503723, 0.000003, 5, "chi2"]
        het_breush_pagan = [1.302014, 0.521520, 2, "chi2"]  #TODO: not available
        het_breush_pagan_konker = [0.709924, 0.701200, 2, "chi2"]


        reset_2_3 = [5.219019, 0.00619, 2, 197, "f"]
        reset_2 = [7.268492, 0.00762, 1, 198, "f"]
        reset_3 = [5.248951, 0.023, 1, 198, "f"]  #not available

        cond_1norm = 5984.0525
        determinant = 7.1087467e+008
        reciprocal_condition_number = 0.013826504
        vif = [1.001, 1.001]

        names = 'date   residual        leverage       influence        DFFITS'.split()
        cur_dir = os.path.abspath(os.path.dirname(__file__))
        fpath = os.path.join(cur_dir, 'results/leverage_influence_ols_nostars.txt')
        lev = np.genfromtxt(fpath, skip_header=3, skip_footer=1,
                            converters={0:lambda s: s})
        #either numpy 1.6 or python 3.2 changed behavior
        if np.isnan(lev[-1]['f1']):
            lev = np.genfromtxt(fpath, skip_header=3, skip_footer=2,
                                converters={0:lambda s: s})

        lev.dtype.names = names

        res = res_ols #for easier copying

        cov_hac, bse_hac = sw.cov_hac_simple(res, nlags=4, use_correction=False)

        assert_almost_equal(res.params, partable[:,0], 5)
        assert_almost_equal(bse_hac, partable[:,1], 5)
        #TODO

        assert_almost_equal(res.ssr, result_gretl_g1['ssr'][1], decimal=2)
        #assert_almost_equal(res.llf, result_gretl_g1['llf'][1], decimal=7) #not in gretl
        assert_almost_equal(res.rsquared, result_gretl_g1['rsquared'][1], decimal=6) #FAIL
        assert_almost_equal(res.rsquared_adj, result_gretl_g1['rsquared_adj'][1], decimal=6) #FAIL
        assert_almost_equal(np.sqrt(res.mse_resid), result_gretl_g1['mse_resid_sqrt'][1], decimal=5)
        #f-value is based on cov_hac I guess
        #assert_almost_equal(res.fvalue, result_gretl_g1['fvalue'][1], decimal=0) #FAIL
        #assert_approx_equal(res.f_pvalue, result_gretl_g1['f_pvalue'][1], significant=1) #FAIL
        #assert_almost_equal(res.durbin_watson, result_gretl_g1['dw'][1], decimal=7) #TODO


        c = oi.reset_ramsey(res, degree=2)
        compare_ftest(c, reset_2, decimal=(6,5))
        c = oi.reset_ramsey(res, degree=3)
        compare_ftest(c, reset_2_3, decimal=(6,5))

        linear_sq = smsdia.linear_lm(res.resid, res.model.exog)
        assert_almost_equal(linear_sq[0], linear_squares[0], decimal=6)
        assert_almost_equal(linear_sq[1], linear_squares[1], decimal=7)

        hbpk = smsdia.het_breushpagan(res.resid, res.model.exog)
        assert_almost_equal(hbpk[0], het_breush_pagan_konker[0], decimal=6)
        assert_almost_equal(hbpk[1], het_breush_pagan_konker[1], decimal=6)

        hw = smsdia.het_white(res.resid, res.model.exog)
        assert_almost_equal(hw[:2], het_white[:2], 6)

        #arch
        #sm_arch = smsdia.acorr_lm(res.resid**2, maxlag=4, autolag=None)
        sm_arch = smsdia.het_arch(res.resid, maxlag=4)
        assert_almost_equal(sm_arch[0], arch_4[0], decimal=5)
        assert_almost_equal(sm_arch[1], arch_4[1], decimal=6)

        vif2 = [oi.variance_inflation_factor(res.model.exog, k) for k in [1,2]]

        infl = oi.OLSInfluence(res_ols)
        #print np.max(np.abs(lev['DFFITS'] - infl.dffits[0]))
        #print np.max(np.abs(lev['leverage'] - infl.hat_matrix_diag))
        #print np.max(np.abs(lev['influence'] - infl.influence))  #just added this based on Gretl

        #just rough test, low decimal in Gretl output,
        assert_almost_equal(lev['residual'], res.resid, decimal=3)
        assert_almost_equal(lev['DFFITS'], infl.dffits[0], decimal=3)
        assert_almost_equal(lev['leverage'], infl.hat_matrix_diag, decimal=3)
        assert_almost_equal(lev['influence'], infl.influence, decimal=4)
コード例 #7
0
params_true = np.ones(kvars)
y_true = np.dot(exog, params_true)
sigma = 0.1 + np.exp(exog[:,-1])
endog = y_true + sigma * np.random.randn(nobs)

self = sm.OLS(endog, exog).fit()

print self.HC3_se
print sw.se_cov(sw.cov_hc3(self))
#test standalone refactoring
assert_almost_equal(sw.se_cov(sw.cov_hc0(self)), self.HC0_se, 15)
assert_almost_equal(sw.se_cov(sw.cov_hc1(self)), self.HC1_se, 15)
assert_almost_equal(sw.se_cov(sw.cov_hc2(self)), self.HC2_se, 15)
assert_almost_equal(sw.se_cov(sw.cov_hc3(self)), self.HC3_se, 15)
print self.HC0_se
print sw.cov_hac_simple(self, nlags=0, use_correction=False)[1]
#test White as HAC with nlags=0, same as nlags=1 ?
bse_hac0 = sw.cov_hac_simple(self, nlags=0, use_correction=False)[1]
assert_almost_equal(bse_hac0, self.HC0_se, 15)
print bse_hac0
#test White as HAC with nlags=0, same as nlags=1 ?
bse_hac0c = sw.cov_hac_simple(self, nlags=0, use_correction=True)[1]
assert_almost_equal(bse_hac0c, self.HC1_se, 15)

bse_w = sw.cov_white_simple(self, use_correction=False)[1]
print bse_w
#test White
assert_almost_equal(bse_w, self.HC0_se, 15)

bse_wc = sw.cov_white_simple(self, use_correction=True)[1]
print bse_wc