>h<SrSSKJr SSKJr SSKrSSKrSSK J r SSK J r J r SSKJrJr SSKJrJrJrJr SS KJrJrJrJrJrJr SS KJr /S QrS r S r!Sr""SS5r#S/Sjr$S/Sjr%S0Sjr&S1Sjr'\"SS5S2SSSSS.Sjj5r(\"SS5S3Sj5r)\"SS5S2Sj5r*S\RVS\,S S4S!jr-S4S"jr.S#r/S5S$jr0\"S%S5S6S&j5r1S7S'jr2S8S(jr3S9S)jr4S*r5\"S+S5S:S,j5r6S-r7S;S.jr8g)r2rBc8[X5(a[[RSS95eURR nURR nURR RSnURU- nURU- nURn[X5R5n U Rn [X5R5n U Rn U[R"U RU 5U- -n US- [R "U5[R "U 5- -nU[R"U RU 5-U S-- nU[R""U5- nS[$R&R)[R*"U55-nU(aN[-5nU UlU UlUUlUUlUUlUUl[$R&UlUUU4$UU4$)a Compute the Cox test for non-nested models Parameters ---------- results_x : Result instance result instance of first model results_z : Result instance result instance of second model store : bool, default False If true, then the intermediate results are returned. Returns ------- tstat : float t statistic for the test that including the fitted values of the first model in the second model has no effect. pvalue : float two-sided pvalue for the t statistic res_store : ResultsStore, optional Intermediate results. Returned if store is True. Notes ----- Tests of non-nested hypothesis might not provide unambiguous answers. The test should be performed in both directions and it is possible that both or neither test rejects. see [1]_ for more information. Formulas from [1]_, section 8.3.4 translated to code Matches results for Example 8.3 in Greene References ---------- .. [1] Greene, W. H. Econometric Analysis. New Jersey. Prentice Hall; 5th edition. (2002). zCox comparisontestr@)r@r9 NESTED_ERRORformatr7r:r8r&ssr fittedvaluesrfitresidr'dotTlogsqrtrnormsfabsrBres_dxres_xzxc01v01qpvaluedist)r;r<storer=r>nobssigma2_xsigma2_zyhat_xrcerr_zxrderr_xzx sigma2_zxrerfrgpvalress r0rrpsLY22,,2B,CDDAA ?? & &q )D}}t#H}}t#H  # #F ^   !F \\F&n  "GmmG266&((F3d::I )rvvh'"&&*;; rnrxtstatrrrss r0rrsLY22,,.,ABBAA  # #F BOOVK0 1 5 5 7F NN1 E >>! D n 776??+  C ;r2 nonrobustcB[X5(a[[RSS95eURR nURR nURR nSnU"XEXbU5nU"XFXRU5n [R"X/SS//SQS9$)a Davidson-MacKinnon encompassing test for comparing non-nested models Parameters ---------- results_x : Result instance result instance of first model results_z : Result instance result instance of second model cov_type : str, default "nonrobust Covariance type. The default is "nonrobust` which uses the classic OLS covariance estimator. Specify one of "HC0", "HC1", "HC2", "HC3" to use White's covariance estimator. All covariance types supported by ``OLS.fit`` are accepted. cov_kwargs : dict, default None Dictionary of covariance options passed to ``OLS.fit``. See OLS.fit for more details. Returns ------- DataFrame A DataFrame with two rows and four columns. The row labeled x contains results for the null that the model contained in results_x is equivalent to the encompassing model. The results in the row labeled z correspond to the test that the model contained in results_z are equivalent to the encompassing model. The columns are the test statistic, its p-value, and the numerator and denominator degrees of freedom. The test statistic has an F distribution. The numerator degree of freedom is the number of variables in the encompassing model that are not in the x or z model. The denominator degree of freedom is the number of observations minus the number of variables in the nesting model. Notes ----- The null is that the fit produced using x is the same as the fit produced using both x and z. When testing whether x is encompassed, the model estimated is .. math:: Y = X\beta + Z_1\gamma + \epsilon where :math:`Z_1` are the columns of :math:`Z` that are not spanned by :math:`X`. The null is :math:`H_0:\gamma=0`. When testing whether z is encompassed, the roles of :math:`X` and :math:`Z` are reversed. Implementation of Davidson and MacKinnon (1993)'s encompassing test. Performs two Wald tests where models x and z are compared to a model that nests the two. The Wald tests are performed by using an OLS regression. zTesting encompassingrRcBX![RRXSS9S-- n[RRU5upgn[R"[R 5R n URSSS9[UR5-U -n [R"U5U :n XXSS2U 4-n [R"X/5n U RSnU RSn[X 5RX4S9n[R"X45n[R"U5USS2U*S24'URUSSS9nUR UR"nn[%UR&5[%UR(5nnUUUU4$) Nr$rT)axiskeepdimsr#)cov_typecov_kwdsuse_fscalar)r'r(r)svdfinfodoubleepsmaxr&rbhstackrrZzeroseye wald_test statisticrhintdf_numdf_denom)r8abcov_estrr/usvrtolnon_zeroaugaug_regk_akrsr_matrixrSstatrhrrs r0 _test_nested*compare_encompassing.._test_nested-sTbiiooa$o7:::))--$ahhryy!%%eede+c#))n)rrhrr)indexcolumns) r@r9rVrWr7r8r:pd DataFrame) r;r<r cov_kwargsr|r=r>rx_nestedz_nesteds r0compare_encompassingrslY22,,2H,IJJAAA.&A!z:HA!z:H <<,"Cj H JJr2c SSKJn [US5n[USSS9n[USSS9nUbUS ::a [ S 5eUS:a [ S 5eUR SnU(GaUS - n U"X SS 9n U(dFXS --[ R"U S U S -S -U[ R"S U S -5- - 5-n O"U[ R"U S U S -S -5-n Sn [ R"U [ R"U5-5n [ R"U 5R5[ R"U5-nX::a2U [ R"S U5[ R"U5-- n OU S [ R"S U5-- n [ R"U 5n[S U5n[US5n[ R"S US -5nOUb.[ R"S [US-S U-5S -[S9nOiUc+[ R"S [US-S5S -[S9nO;[!U["5(d&[US5n[ R"S US -5n[USSS9nUR5n U"X SS 9n U S U S -S -U[ R"S U S -5- - nXS --[ R"U5US - -nX- n[ R$"U[ R&5nUS:n[(R*R-UUUU5UU'U(d[.R0"UUS.US9$U[ R"U S U S -S -5US - -n[ R$"U[ R&5n[(R*R-UUUU5UU'[.R0"UUUUS.US9$)aj Ljung-Box test of autocorrelation in residuals. Parameters ---------- x : array_like The data series. The data is demeaned before the test statistic is computed. lags : {int, array_like}, default None If lags is an integer then this is taken to be the largest lag that is included, the test result is reported for all smaller lag length. If lags is a list or array, then all lags are included up to the largest lag in the list, however only the tests for the lags in the list are reported. If lags is None, then the default maxlag is min(10, nobs // 5). The default number of lags changes if period is set. boxpierce : bool, default False If true, then additional to the results of the Ljung-Box test also the Box-Pierce test results are returned. model_df : int, default 0 Number of degrees of freedom consumed by the model. In an ARMA model, this value is usually p+q where p is the AR order and q is the MA order. This value is subtracted from the degrees-of-freedom used in the test so that the adjusted dof for the statistics are lags - model_df. If lags - model_df <= 0, then NaN is returned. period : int, default None The period of a Seasonal time series. Used to compute the max lag for seasonal data which uses min(2*period, nobs // 5) if set. If None, then the default rule is used to set the number of lags. When set, must be >= 2. auto_lag : bool, default False Flag indicating whether to automatically determine the optimal lag length based on threshold of maximum correlation value. Returns ------- DataFrame Frame with columns: * lb_stat - The Ljung-Box test statistic. * lb_pvalue - The p-value based on chi-square distribution. The p-value is computed as 1 - chi2.cdf(lb_stat, dof) where dof is lag - model_df. If lag - model_df <= 0, then NaN is returned for the pvalue. * bp_stat - The Box-Pierce test statistic. * bp_pvalue - The p-value based for Box-Pierce test on chi-square distribution. The p-value is computed as 1 - chi2.cdf(bp_stat, dof) where dof is lag - model_df. If lag - model_df <= 0, then NaN is returned for the pvalue. See Also -------- statsmodels.regression.linear_model.OLS.fit Regression model fitting. statsmodels.regression.linear_model.RegressionResults Results from linear regression models. statsmodels.stats.stattools.q_stat Ljung-Box test statistic computed from estimated autocorrelations. Notes ----- Ljung-Box and Box-Pierce statistic differ in their scaling of the autocorrelation function. Ljung-Box test is has better finite-sample properties. References ---------- .. [*] Green, W. "Econometric Analysis," 5th ed., Pearson, 2003. .. [*] J. Carlos Escanciano, Ignacio N. Lobato "An automatic Portmanteau test for serial correlation"., Volume 151, 2009. Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.sunspots.load_pandas().data >>> res = sm.tsa.ARMA(data["SUNACTIVITY"], (1,1)).fit(disp=-1) >>> sm.stats.acorr_ljungbox(res.resid, lags=[10], return_df=True) lb_stat lb_pvalue 10 214.106992 1.827374e-40 r)acfr=periodToptionalmodel_dfFr#zperiod must be >= 2zmodel_df must be >= 0)nlagsfftrUg333333@lagsdtype r)lb_stat lb_pvalue)r)rrbp_stat bp_pvalue)statsmodels.tsa.stattoolsrrrr9r&r'cumsumaranger_r^rbrargmaxminrr4r full_likenanrchi2rarr)r=r boxpiercerr return_dfauto_lagrrkmaxlagsacfq_sacfrg thresholdthreshold_metricsacf2 qljungboxadj_lagsrrloc qboxpiercepvalbps r0rrGsj.1cA fh 6F*u=H fk.//!|011 771:D1.Qh'iiQvz 2a 7#'"))Avz*B#B!DEEFBIId1VaZ&8A&=>>F GGAt ,- 66$<++- =  )ryyD1BFF4L@AFq299Q#556Fyy 1d|f%yyD1H%  yyC 1v:6:#F yyC 2.2#> h ' 'f%yyD1H% dF% 0D XXZF qE *D 6A: ! #tbii6A:.F'F GEq!BIIe$4TAX$>>IH << 266 *D Q,C inhsm= 2. ddof : int, default 0 The number of degrees of freedom consumed by the model used to produce resid. The default value is 0. cov_type : str, default "nonrobust" Covariance type. The default is "nonrobust` which uses the classic OLS covariance estimator. Specify one of "HC0", "HC1", "HC2", "HC3" to use White's covariance estimator. All covariance types supported by ``OLS.fit`` are accepted. cov_kwargs : dict, default None Dictionary of covariance options passed to ``OLS.fit``. See OLS.fit for more details. Returns ------- lm : float Lagrange multiplier test statistic. lmpval : float The p-value for Lagrange multiplier test. fval : float The f statistic of the F test, alternative version of the same test based on F test for the parameter restriction. fpval : float The pvalue of the F test. res_store : ResultsStore, optional Intermediate results. Only returned if store=True. See Also -------- het_arch Conditional heteroskedasticity testing. acorr_breusch_godfrey Breusch-Godfrey test for serial correlation. acorr_ljung_box Ljung-Box test for serial correlation. Notes ----- The test statistic is computed as (nobs - ddof) * r2 where r2 is the R-squared from a regression on the residual on nlags lags of the residual. r[r#ndimrNrrrrUrbothtrimrrr~FTr)rrrr&rrr'r+onesrBrrZfloatfvaluef_pvaluersquaredrrrarrrrrrhresolsusedlag)r[rrjrrrrrkrxdallxshort res_storerrfvalfpvallmlmpvalr test_stats r0rrs@ ugA .E8Z0H!)zJ:|4J ;;q>D emTQYF + R# 5D>6 7E ;;q>D EE"''4)$e+ ,E 56]FIG q,7Q;,/ 0 4 4h@J5LF  D &// "E;kV__ ,r7+99bhh|4bffWoFG$$XU4$H 9&& 'y''( !#64 1164&&r2c[US-XUS9$)a Engle's Test for Autoregressive Conditional Heteroscedasticity (ARCH). Parameters ---------- resid : ndarray residuals from an estimation, or time series nlags : int, default None Highest lag to use. store : bool, default False If true then the intermediate results are also returned ddof : int, default 0 If the residuals are from a regression, or ARMA estimation, then there are recommendations to correct the degrees of freedom by the number of parameters that have been estimated, for example ddof=p+q for an ARMA(p,q). Returns ------- lm : float Lagrange multiplier test statistic lmpval : float p-value for Lagrange multiplier test fval : float fstatistic for F test, alternative version of the same test based on F test for the parameter restriction fpval : float pvalue for F test res_store : ResultsStore, optional Intermediate results. Returned if store is True. Notes ----- verified against R:FinTS::ArchTest rU)rrjr)r)r[rrjrs r0rrKsJ EQJet DDr2resultsrsc,[R"UR5R5nURS:wa [ S5eUR RnURSnUc[SUS-5n[R"[R"U5U45n[USS2S4USS9nURSn[R[R"US45U4nX5*SnUcUnO[R"XF45nURSn [!Xx5R#5n U R%[R&"XX- 55n U R(n U R*n [-[R"U 55n [-[R"U 55n XZR.-n[0R2R5X5nU(a[75nU UlUUlXXU4$XX4$) av Breusch-Godfrey Lagrange Multiplier tests for residual autocorrelation. Parameters ---------- res : RegressionResults Estimation results for which the residuals are tested for serial correlation. nlags : int, optional Number of lags to include in the auxiliary regression. (nlags is highest lag). store : bool, default False If store is true, then an additional class instance that contains intermediate results is returned. Returns ------- lm : float Lagrange multiplier test statistic. lmpval : float The p-value for Lagrange multiplier test. fval : float The value of the f statistic for F test, alternative version of the same test based on F test for the parameter restriction. fpval : float The pvalue for F test. res_store : ResultsStore A class instance that holds intermediate results. Only returned if store=True. Notes ----- BG adds lags of residual to exog in the design matrix for the auxiliary regression with residuals as endog. See [1]_, section 12.7.1. References ---------- .. [1] Greene, W. H. Econometric Analysis. New Jersey. Prentice Hall; 5th edition. (2002). r#zFModel resid must be a 1d array. Cannot be used on multivariate models.rNrrrr)r'asarrayr[squeezerr9r7r:r&r concatenaterrr+rrurrZf_testrrrhrrrrrarBrr)rsrrjr=exog_oldrkrrr:k_varsrftrrrrrs r0rrssV 399%%'Avv{12 2yy~~H 771:D }B " +,A 1QW:u6 2E ;;q>D EE"''4)$e+ ,E uvYF01 ZZ]F   " " $F rvveV^< =B 99D IIE D! "D "**U# $E  B ZZ]]2 %F  N ! ! 4 114&&r2r= test_namereturncURSS9n[R"X RSS9- S:HUS:g-5(aURSS:a[ US35eg)z Check validity of the exogenous regressors in a heteroskedasticity test Parameters ---------- x : ndarray The exogenous regressor array test_name : str The test name for the exception rrr#rUzI test requires exog to have at least two columns where one is a constant.N)rr'anyrr&r9)r=rx_maxs r0_check_het_testrsm EEqEME FFUUUU]*q0UaZ@ A A 771:>k3 3   r2c[USSS9n[US5 [USSS9S-nU(dU[R"U5- nURupV[ XC5R 5nURnURn U(aXWR-OURS- n U [RRXS- 5X4$)u Breusch-Pagan Lagrange Multiplier test for heteroscedasticity The tests the hypothesis that the residual variance does not depend on the variables in x in the form .. :math: \sigma_i = \sigma * f(\alpha_0 + \alpha z_i) Homoscedasticity implies that :math:`\alpha=0`. Parameters ---------- resid : array_like For the Breusch-Pagan test, this should be the residual of a regression. If an array is given in exog, then the residuals are calculated by the an OLS regression or resid on exog. In this case resid should contain the dependent variable. Exog can be the same as x. exog_het : array_like This contains variables suspected of being related to heteroscedasticity in resid. robust : bool, default True Flag indicating whether to use the Koenker version of the test (default) which assumes independent and identically distributed error terms, or the original Breusch-Pagan version which assumes residuals are normally distributed. Returns ------- lm : float lagrange multiplier statistic lm_pvalue : float p-value of lagrange multiplier test fvalue : float f-statistic of the hypothesis that the error variance does not depend on x f_pvalue : float p-value for the f-statistic Notes ----- Assumes x contains constant (for counting dof and calculation of R^2). In the general description of LM test, Greene mentions that this test exaggerates the significance of results in small or moderately large samples. In this case the F-statistic is preferable. **Verification** Chisquare test statistic is exactly (<1e-13) the same result as bptest in R-stats with defaults (studentize=True). **Implementation** This is calculated using the generic formula for LM test using $R^2$ (Greene, section 17.6) and not with the explicit formula (Greene, section 11.4.3), unless `robust` is set to False. The degrees of freedom for the p-value assume x is full rank. References ---------- .. [1] Greene, W. H. Econometric Analysis. New Jersey. Prentice Hall; 5th edition. (2002). .. [2] Breusch, T. S.; Pagan, A. R. (1979). "A Simple Test for Heteroskedasticity and Random Coefficient Variation". Econometrica. 47 (5): 1287–1294. .. [3] Koenker, R. (1981). "A note on studentizing a test for heteroskedasticity". Journal of Econometrics 17 (1): 107–112. exog_hetrUrzThe Breusch-Paganr[r#)rrr'meanr&rrZrrressrrra) r[rrobustr=r|rknvarsrrrrs r0rrsH 8Za0AA*+5'*a/A   N''KD Y]]_F ==D OOE#) vzzA~B uzz}}R+T 88r2c^[USSS9n[USSURSS4S9n[US5 URupE[R"U5upgUS S 2U4US S 2U4-nURupHXUS- -S - U-:Xde[ US-U5R 5n U Rn U Rn XIR-n U R[RRU5S- :Xde[RRXR5n XX4$) a White's Lagrange Multiplier Test for Heteroscedasticity. Parameters ---------- resid : array_like The residuals. The squared residuals are used as the endogenous variable. exog : array_like The explanatory variables for the variance. Squares and interaction terms are automatically included in the auxiliary regression. Returns ------- lm : float The lagrange multiplier statistic. lm_pvalue :float The p-value of lagrange multiplier test. fvalue : float The f-statistic of the hypothesis that the error variance does not depend on x. This is an alternative test variant not the original LM test. f_pvalue : float The p-value for the f-statistic. Notes ----- Assumes x contains constant (for counting dof). question: does f-statistic make sense? constant ? References ---------- Greene section 11.4.1 5th edition p. 222. Test statistic reproduces Greene 5th, example 11.3. r:rUrr[rr#)rr&zWhite's heteroskedasticityNrT)rr&rr' triu_indicesrrZrrrdf_modelr(r*rrra)r[r:r=r|rknvars0i0i1rrrrrrs r0rr.sJ 4a(A5'!''!*aAAA3477LD __V $FB QU8a2h D**KD fqj)B.7 77 7 a  " " $F ==D OOE  B ??bii33D9A= == = ZZ]]2 /F t ""r2cr[R"U5n[R"U5nURupxUcUS-nOSU:aUS:a [Xs-5nUcUn O!SU:aUS:aU[Xt-5-n OX4-n Ub)[R"USS2U45n X nXSS24n[ USUUSU5R 5n [ X SXS5R 5n U RU R- n UR5S;a7[RRXRU R5nSnOUR5S;a;[RRSU - U RU R5nS nOUR5S ;az[RRXRU R5n[RRXRU R5nS[UU5-nS nO [S 5eU(at[!5nS UlU UlUUlU RU R4UlU UlU UlUUlUUlSR3XU5UlXUU4$XU4$)a Goldfeld-Quandt homoskedasticity test. This test examines whether the residual variance is the same in 2 subsamples. Parameters ---------- y : array_like endogenous variable x : array_like exogenous variable, regressors idx : int, default None column index of variable according to which observations are sorted for the split split : {int, float}, default None If an integer, this is the index at which sample is split. If a float in 055 USS2U 4nU "US[UR 5[UR 5SS9n U R@SS2SS24n[RB"U/UV s/sHoU -PM sn -5n URRDnU"URR<RFU 5nUc0OUnURIXES9nU RSURS- nU RSn[RJ"UUUU- S9nURMUUSS9$![ a [S5ef=fs sn f)a1 Ramsey's RESET test for neglected nonlinearity Parameters ---------- res : RegressionResults A results instance from a linear regression. power : {int, List[int]}, default 3 The maximum power to include in the model, if an integer. Includes powers 2, 3, ..., power. If an list of integers, includes all powers in the list. test_type : str, default "fitted" The type of augmentation to use: * "fitted" : (default) Augment regressors with powers of fitted values. * "exog" : Augment exog with powers of exog. Excludes binary regressors. * "princomp": Augment exog with powers of first principal component of exog. use_f : bool, default False Flag indicating whether an F-test should be used (True) or a chi-square test (False). cov_type : str, default "nonrobust Covariance type. The default is "nonrobust` which uses the classic OLS covariance estimator. Specify one of "HC0", "HC1", "HC2", "HC3" to use White's covariance estimator. All covariance types supported by ``OLS.fit`` are accepted. cov_kwargs : dict, default None Dictionary of covariance options passed to ``OLS.fit``. See OLS.fit for more details. Returns ------- ContrastResults Test results for Ramsey's Reset test. See notes for implementation details. Notes ----- The RESET test uses an augmented regression of the form .. math:: Y = X\beta + Z\gamma + \epsilon where :math:`Z` are a set of regressors that are one of: * Powers of :math:`X\hat{\beta}` from the original regression. * Powers of :math:`X`, excluding the constant and binary regressors. * Powers of the first principal component of :math:`X`. If the model includes a constant, this column is dropped before computing the principal component. In either case, the principal component is extracted from the correlation matrix of remaining columns. The test is a Wald test of the null :math:`H_0:\gamma=0`. If use_f is True, then the quadratic-form test statistic is divided by the number of restrictions and the F distribution is used to compute the critical value. z/result must come from a linear regression modelr#zjexog contains only a constant column. The RESET test requires exog to have at least 1 non-constant column. test_type)fittedr:princomp)optionsrTrrrUzpower must be >= 2rz,power must be an integer or list of integersrz.power must contains distinct integers all >= 2r(Nr:rz+Model contains only constant or binary data)PCAnipals)ncomp standardizedemeanmethodr)rr)'r4rr5boolr7 k_constantr:r&r9rrrrr'rarray ExceptionrlensetrrrYrrallstatsmodels.multivariate.pcar+tolistpopdata const_idxfactorsrrGr8rZrr)rspowerr'rrrr:rbinaryr+retainpcapaug_exog mod_classmodnrestrnparamsr_mats r0 linear_resetrIs9| c3 4 4IJJ CII !!ciinn&:&:1&=&B01 1I{$BDI:|dCJ eW %E% 1912 2 !UQYc2 MHHU#.E ::?c#e*oQ?!!MN N 99>>DHjj))*1d73 f iinn888++a8H0HI# ::<<JK K!fW*o4 >>YYsyy|,335F JJs399>>334 5ai.C#QD,@cnn-h@kk!RaR% yy$U";U!8U";;aF XwRAS 5- n [R8R;U R<U -U- 5n GNf=f)a@ Rainbow test for linearity The null hypothesis is the fit of the model using full sample is the same as using a central subset. The alternative is that the fits are difference. The rainbow test has power against many different forms of nonlinearity. Parameters ---------- res : RegressionResults A results instance from a linear regression. frac : float, default 0.5 The fraction of the data to include in the center model. order_by : {ndarray, str, List[str]}, default None If an ndarray, the values in the array are used to sort the observations. If a string or a list of strings, these are interpreted as column name(s) which are then used to lexicographically sort the data. use_distance : bool, default False Flag indicating whether data should be ordered by the Mahalanobis distance to the center. center : {float, int}, default None If a float, the value must be in [0, 1] and the center is center * nobs of the ordered data. If an integer, must be in [0, nobs) and is interpreted as the observation of the ordered data to use. Returns ------- fstat : float The test statistic based on the F test. pvalue : float The pvalue of the test. Notes ----- This test assumes residuals are homoskedastic and may reject a correct linear specification if the residuals are heteroskedastic. z3res must be a results instance from a linear model.frac use_distancez7order_by and use_distance cannot be simultaneouslyused.rNr#r)rrzvorder_by must contain valid column names from the exog data used to construct res,and exog must be a pandas DataFrame. __index___rrUrz¢er must be in (0, 1) when a float.centerz(center must be in [0, nobs) when an int.)cdist mahalanobis)metricVI?zqfrac is too small to perform test. frac * nobsmust be greater than the number of exogenousvariables in the model.).r4rr5rrrkr7r8r:r9r'ndarrayrstrr; orig_exogcopy IndexErrorKeyErrorrr& sort_valuesrrrrscipy.spatial.distancerZr(invr] LinAlgErrorrrravelceilastypefloorslicerrZrXrzrrra)rsrTrNrUrYrkr8r:colsname center_obsrZr/virirlowidxuppidxmi_slres_minobs_miss_missfstatrrs r0r r {sP c3 4 4MNN dF #D\>:L 88D IIOOE 99>>D !" " h + +!(JQeLH(C(($: Hyy~~//9>>@ D, ,4::a=1DJ##H-Dzz$*-H~#)>Tav fe $ $&'C' !IJJ6*+Ffh/Fv(q( !KLL* 0 3#Csuus{T12BTmCjj& y WWSAH%, - 4 4S 9F XXft{* + 2 23 7F A&34 4 && !E utE{ + / / 1Fll  &&q)G JJE B %ZD7N +e 3foo EE 77::eTG^V__ =D $;a) H!GHH H6yy$$ 31%Csuus{T12B 3s1N93N4N14A PPc UcSn[R"U5n[R"X"USS2SS24545nURupE[ X5R 5nUR [R"US- US-S- U55nXFR-n[RRXS- 5n XU4$)a Lagrange multiplier test for linearity against functional alternative # TODO: Remove the restriction limitations: Assumes currently that the first column is integer. Currently it does not check whether the transformed variables contain NaNs, for example log of negative number. Parameters ---------- resid : ndarray residuals of a regression exog : ndarray exogenous variables for which linearity is tested func : callable, default None If func is None, then squares are used. func needs to take an array of exog and return an array of transformed variables. Returns ------- lm : float Lagrange multiplier test statistic lm_pval : float p-value of Lagrange multiplier tes ftest : ContrastResult instance the results from the F test variant of this test Notes ----- Written to match Gretl's linearity test. The test runs an auxiliary regression of the residuals on the combined original and transformed regressors. The Null hypothesis is that the linear specification is correct. Nc0[R"US5$)NrU)r'r>)r=s r0funclinear_lm..func s88Aq> !r2r#rU) r'rrur&rrZrrrrrra) r[r:r|exog_auxrkrlsftestrlm_pvals r0rrsF | " ::d Dd412;&789H::LD U  ! ! #B IIbffVaZ!a@ AE BjjmmB +G  r2cP[USSS9n[USSS9nURSS:d3[R"[R"US5S:H5(d [ S5e[R "URS5upE[R"US S 2U4US S 2U4-SS5nS nS nXgURS5--n[RRUS S 9n [R"U R55[R"U5:n US S 2[R"U )5S4nX3-n U [R"U 5- n [R "UR"U 5n U[R"USS9- nXS S 2S 4-nUR"R!U5nU R![RR%X55nURSn[&R(R+UU5nUUU4$)a White's Two-Moment Specification Test Parameters ---------- resid : array_like OLS residuals. exog : array_like OLS design matrix. Returns ------- stat : float The test statistic. pval : float A chi-square p-value for test statistic. dof : int The degrees of freedom. See Also -------- het_white White's test for heteroskedasticity. Notes ----- Implements the two-moment specification test described by White's Theorem 2 (1980, p. 823) which compares the standard OLS covariance estimator with White's heteroscedasticity-consistent estimator. The test statistic is shown to be chi-square distributed. Null hypothesis is homoscedastic and correctly specified. Assumes the OLS design matrix contains an intercept term and at least one variable. The intercept is removed to calculate the test statistic. Interaction terms (squares and crosses of OLS regressors) are added to the design matrix to calculate the test statistic. Degrees-of-freedom (full rank) = nvar + nvar * (nvar + 1) / 2 Linearly dependent columns are removed to avoid singular matrix error. References ---------- .. [*] White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroscedasticity. Econometrica, 48: 817-838. r:rUrr[r#rrXzPWhite's specification test requires at least twocolumns where one is a constant.Ng+=gvIh%<=r)moder)rr&r'rptpr9rdeletevarr(qrrbdiagonalr_whererr\r]solverrra)r[r:r=erratolrtolrrmasksqesqmndevsr devxrrdofrrs r0rrsd 4a(A5'*AwwqzA~RVVBFF1aLC$788<= =__QWWQZ (FB 99Qq"uX!R%(!Q /D D D  # #C T $A 66!**, "''#, .D 288TE?1%% &D %CRWWS\!H tvvx A "''$Q' 'DQW D  4A 55& 'D **Q-C ::==s #D s?r2 olsresultsc [U[5(d [S5eURRnURR n[ USSSSURS4S9nUbXdnXTnURupxUcUn[R[R"Xx45-n [R[R"U5-n [R[R"U5-n [R[R"U5-n USUn [RRU 5U RS:a S n[U5eUSUn[RR[R"U R U 5U[R""U5--5n[R"U R U5n[R"UU5nUXS- '[R"XaS- U5nUXS- 'XQS- U- XS- 'S[R"XaS- [R"UXaS- 55-XS- '[%X5HnUUUS-2SS24nUUn[R"UU5n[R&"U5U U'UU- n[R&"U5U U'[R"UUR 5nS[R"UU5-nU[R"UUR 5U- - nUUU-U- R)5-nUU U'[R&"U5U U'GM U [R*"U 5- nXq- nUUSR-SS 9nU[R*"U5- nUUS- SR/5nUS :XaS nOUS :XaSnOUS:XaSnO [S5eU[R*"U5-SU-[R0"SXq- 5-[R*"U5- -[R2"S/S//5-n XU UUUU 4$)u Calculate recursive ols with residuals and Cusum test statistic Parameters ---------- res : RegressionResults Results from estimation of a regression model. skip : int, default None The number of observations to use for initial OLS, if None then skip is set equal to the number of regressors (columns in exog). lamda : float, default 0.0 The weight for Ridge correction to initial (X'X)^{-1}. alpha : {0.90, 0.95, 0.99}, default 0.95 Confidence level of test, currently only two values supported, used for confidence interval in cusum graph. order_by : array_like, default None Integer array specifying the order of the residuals. If not provided, the order of the residuals is not changed. If provided, must have the same number of observations as the endogenous variable. Returns ------- rresid : ndarray The recursive ols residuals. rparams : ndarray The recursive ols parameter estimates. rypred : ndarray The recursive prediction of endogenous variable. rresid_standardized : ndarray The recursive residuals standardized so that N(0,sigma2) distributed, where sigma2 is the error variance. rresid_scaled : ndarray The recursive residuals normalize so that N(0,1) distributed. rcusum : ndarray The cumulative residuals for cusum test. rcusumci : ndarray The confidence interval for cusum test using a size of alpha. Notes ----- It produces same recursive residuals as other version. This version updates the inverse of the X'X matrix and does not require matrix inversion during updating. looks efficient but no timing Confidence interval in Greene and Brown, Durbin and Evans is the same as in Ploberger after a little bit of algebra. References ---------- jplv to check formulas, follows Harvey BigJudge 5.5.2b for formula for inverse(X'X) updating Greene section 7.5.2 Brown, R. L., J. Durbin, and J. M. Evans. “Techniques for Testing the Constancy of Regression Relationships over Time.” Journal of the Royal Statistical Society. Series B (Methodological) 37, no. 2 (1975): 149-192. z!res a regression results instancerNrTr#r)rrrr&Nz"The initial regressor matrix, x[:skip], issingular. You must use a value of skip large enough to ensure that the first OLS estimator is well-defined. )rg?g333333?rKgtV?gGz?g}?5^I?z#alpha can only be 0.9, 0.95 or 0.99rUgr)r4rr5r7r8r:rr&r'rrr(r*r9rgr\r]rrangerrir_rrrr3)!rsrLlamdarMrNr|r=rkrrparamsrresidrypredrvarrawx0err_msgy0xtxixtybetayipredr xiyiresiditmpr rresid_scalednrrsigma2rresid_standardizedrcusumrrcusumcis! r0rPrPmsz c3 4 4;<< A A(Jed  7H K K''KD |ffrxx ..G VVbhhtn $F VVbhhtn $Fffrxx~%G 5DB yyR 288A;.!! 5DB 99==b)EBFF5M,AA BD &&r C 66$ DG1H VVAQhK &FF!8{V+F!8BFF1AX;tQax[0IJJG1H 4  qQwz] qTD!JJv&q fJJv&q ffT244  C bffS#%%(2--sV|b(//11 ZZ^ %(RWWW--M +C45 ! % %1 % -F'"''&/9  + 2 2 4F }  $  $ >??BGGCL 1q5299Q +D#Drww H $  3%#()H V%8- H r2cURRn[URSURSS4S9nURup4US-n[ R XSS2S4-XUR5- 4nURS5nX6SS2SS2S4USS2SSS24-RS5-nUSS2SS2S4USS2SSS24-RS5n [ R"[ R"[ RRU5U 55n [ R"/SQS[4S [ 4/S 9n X4$) aa Test for model stability, breaks in parameters for ols, Hansen 1992 Parameters ---------- olsresults : RegressionResults Results from estimation of a regression model. Returns ------- teststat : float Hansen's test statistic. crit : ndarray The critical values at alpha=0.95 for different nvars. Notes ----- looks good in example, maybe not very powerful for small changes in parameters According to Greene, distribution of test statistics depends on nvar but not on nobs. Test statistic is verified against R:strucchange References ---------- Greene section 7.5.1, notation follows Greene r[rr#)r&rUN))rUg)\(?)gffffff?)g@)gGz@rkcritr)r7r:rr[r&r'r+rrsumtracer\r(rgr3rr) rr=r[rkrresid2rscorerrhcrit95s r0 breaks_hansenrs%< A z''Q HE''KD aZF qD>!F[[]$:; F 9r2c[R"U5R5n[U5nUS-R 5nUS:a X2U- - U-nUR 5[R "U5- n[R"U5R5n/SQn[RRU5nXWU4$)u Cusum test for parameter stability based on ols residuals. Parameters ---------- resid : ndarray An array of residuals from an OLS estimation. ddof : int The number of parameters in the OLS estimation, used as degrees of freedom correction for error variance. Returns ------- sup_b : float The test statistic, maximum of absolute value of scaled cumulative OLS residuals. pval : float Probability of observing the data under the null hypothesis of no structural change, based on asymptotic distribution which is a Brownian Bridge crit: list The tabulated critical values, for alpha = 1%, 5% and 10%. Notes ----- Tested against R:structchange. Not clear: Assumption 2 in Ploberger, Kramer assumes that exog x have asymptotically zero mean, x.mean(0) = [1, 0, 0, ..., 0] Is this really necessary? I do not see how it can affect the test statistic under the null. It does make a difference under the alternative. Also, the asymptotic distribution of test statistic depends on this. From examples it looks like there is little power for standard cusum if exog (other than constant) have mean zero. References ---------- Ploberger, Werner, and Walter Kramer. “The Cusum Test with OLS Residuals.” Econometrica 60, no. 2 (March 1992): 271-285. rUr))r#gGz?)rg(\?)rgQ?) r'rrir5rrr_rbrr kstwobignra)r[rrk nobssigma2rsup_brrrs r0breaks_cusumolsresidr+sT JJu  # # %E u:D1*!!#J ax$;/$6  ,,A FF1IMMOE -D ??  e $D  r2)F)r~N)NFrNTF)NF)NFr)T)NNNr F)rOr(Fr~N)NN)r^NFN)N)NrXrKN)r)9rstatsmodels.compat.pandasrcollections.abcrnumpyr'pandasrscipyr#statsmodels.regression.linear_modelrrstatsmodels.stats._adnormrr statsmodels.stats._lillieforsr r r r statsmodels.tools.validationrrrrrrstatsmodels.tsa.tsatoolsr__all__rVr1r@rBrrrrrrrr_r`rrrrrIr!r rrrPrrrLr2r0rs06$MC , L F0&>> DN6r9D$(TJnFJ,1X$v7#e'tkde'$e'P7#$E$$ENE"O'#O'd rzz c d ,O9d7#t9=7<q!h5!9>26p:"p:f(+V?Dk\.bPfu%<@$(M&M`*Z9r2