M/PhpddlmZddlZddlmZmZddlmZmZddl Z ddl Z ddl m Z ddl mZddlmZddlmZdd lmZddlmcmcmZdd lmZmZdd lmZmZm Z dd l!m"Z"m#Z#ddl$mcm%cm&Z&ddl'mcm%cm(Z)dd l*m+Z+m,Z,ddl-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5 d(de6de7de6fdZ8d)dZ9d*dZ: d+dZ;dZ< d,dZ=dZ>dZ?GddZ@ d-d ZAd!ZBGd"d#ZCGd$d%ejDZEGd&d'ZFdS).) defaultdictN)hstackvstack)invsvd)Summary) SimpleTable)cache_readonly)HypothesisTestWarning string_like)c_sjac_sjt)duplication_matrixlagmatvec)CausalityTestResultsWhitenessTestResults) get_indexseasonal_dummies)VARLagOrderResults _compute_acovforecastforecast_intervalma_rep orth_ma_reptest_normalitynmaxlags deterministicseasonsc  tt}t|d}td|dzD]}g}d|vsd|vrH|t jt|ddd|vsd|vrK|dt j t|ddz||||d krG|t|t|d|dz ||||rt|nd }t||} | ||dz|z } | jD] \} } || | !d |D} t!|| d S)aL Compute lag order selections based on each of the available information criteria. Parameters ---------- data : array_like (nobs_tot x neqs) The observed data. maxlags : int All orders until maxlag will be compared according to the information criteria listed in the Results-section of this docstring. deterministic : str {"n", "co", "ci", "lo", "li"} * ``"n"`` - no deterministic terms * ``"co"`` - constant outside the cointegration relation * ``"ci"`` - constant within the cointegration relation * ``"lo"`` - linear trend outside the cointegration relation * ``"li"`` - linear trend within the cointegration relation Combinations of these are possible (e.g. ``"cili"`` or ``"colo"`` for linear trend with intercept). See the docstring of the :class:`VECM`-class for more information. seasons : int, default: 0 Number of periods in a seasonal cycle. exog : ndarray (nobs_tot x neqs) or `None`, default: `None` Deterministic terms outside the cointegration relation. exog_coint : ndarray (nobs_tot x neqs) or `None`, default: `None` Deterministic terms inside the cointegration relation. Returns ------- selected_orders : :class:`statsmodels.tsa.vector_ar.var_model.LagOrderResults` r!cociloliNr)lagsoffsetcni|]2\}}|tj|dz dz3S)r$)nparrayargmin).0ic_nameic_values ^/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tsa/vector_ar/vecm.py z select_order..fsN GX (##**,,q014T)rlistr rangeappendr.oneslenreshapearangerrr _estimate_var info_criteriaitemsr)datar r!r"exog exog_cointicpexogs var_model var_resultkvselected_orderss r4 select_orderrL$sP T  B ??M 1gk " " = DM$9$9 LLT++33B:: ; ; ; = DM$9$9 LLRYs4yy1199"a@@@ A A A  ! LL $ $ $ Q;; LL #d))44<z-CointRankResults.__init__..s;   g%%DD1q5   r6r$) rankrr8minr_1 test_stats crit_valsrsignif)selfrrrrrrs ` ` r4__init__zCointRankResults.__init__s{       3tax..//   %"  r6cDgd}djdkrdndzdjdzdz}tjjdz }fd t |dzD}gd d d }t |}d |dD|d<t||||||S)N)r_0rztest statisticzcritical valuez"Johansen cointegration test using rzmaximum eigenvaluez test statistic with z.0%z significance levelr$c^g|])}|j|j|j|g*Sr)rrrr1rrs r4rz,CointRankResults.summary..sF    T_Q/1B C   r6)%sr%#0.4grr) data_fmts data_alignscg|] }d|zdz S)zzr)r1rs r4rz,CointRankResults.summary..s.& & & %&FQJ & & & r6r)rAheaderstitletxt_fmthtml_fmtltx_fmt)rrrrrr8dictr )rrr num_testsrAdata_fmt html_data_fmts` r4summaryzCointRankResults.summarysDDD 0+00ww6J L7dk777 8$ $   49q=11     9q=))    :99  X & & *7 *D& & & k""     r6cN|SN)ras_textrs r4__str__zCointRankResults.__str__s||~~%%'''r6Nrr)__name__ __module__ __qualname____doc__rrrrr6r4rrsW.IM       <(((((r6rrrc 0|dvrtd|dvr:t|tur|dkrtdtdgd}||vrtdt|||}|d kr|jn|j}|d kr|jn|j}||} |j d} d } | | kr || || | fkrn | dz } | | k t| | |d | dz|d | dz| f||S) aOCalculate the cointegration rank of a VECM. Parameters ---------- endog : array_like (nobs_tot x neqs) The data with presample. det_order : int * -1 - no deterministic terms * 0 - constant term * 1 - linear trend k_ar_diff : int, nonnegative Number of lagged differences in the model. method : str, {``"trace"``, ``"maxeig"``}, default: ``"trace"`` If ``"trace"``, the trace test statistic is used. If ``"maxeig"``, the maximum eigenvalue test statistic is used. signif : float, {0.1, 0.05, 0.01}, default: 0.05 The test's significance level. Returns ------- rank : :class:`CointRankResults` A :class:`CointRankResults` object containing the cointegration rank suggested by the test and allowing a summary to be printed. )rmaxeigzDThe method argument has to be either 'trace' or'maximum eigenvalue'.r(rr$r$zHA det_order greather than 1 is not supported.Use a value of -1, 0, or 1.zdet_order must be -1, 0, or 1.)g?rg{Gz?z8Please choose a significance level from {0.1, 0.05,0.01}rrN) rmtypeintcoint_johansenlr1lr2cvtcvmindexrkr) rp det_order k_ar_diffrrpossible_signif_values coint_result test_statr signif_indexrrs r4select_coint_rankrs6((( $    ""  ??c ! !i!mm.  =>> >... +++ I   "%I>>L$*g$5$5   <;KI$*g$5$5   <;KI)//77L ;q>D C ** S>Ic<&78 8 8  1HC **   )C!G))C!G)\)*   r6c $ddl}|dvr|dtd|jddkr|d tddd lm$$fd }d }t j|}|j\}}|d krd}n|}|||}t j|dd} t| |} | |d} || |} | |d} || |} || | } |d|jd|z } | dd} || |} || | } t j | j | | jdz }t j | j | | jdz }t j | j | | jdz }t j |t j t||j }t|}t j t j ||\}}tt j t j |j t j ||}t j ||}t j|}t j|}||}|dd|f}|jdk}t j|r(|t j|j|dz}t j|}t j|}t j|df}t j|df}t j|} | j\}!}"t/d|D]}#t j| |z |#d}|! t j|dz||#<|! t jd||#z z||#<t5||#z |||#ddf<t7||#z |||#ddf<|#||#<t9| | ||||||| S)u Johansen cointegration test of the cointegration rank of a VECM Parameters ---------- endog : array_like (nobs_tot x neqs) Data to test det_order : int * -1 - no deterministic terms * 0 - constant term * 1 - linear trend k_ar_diff : int, nonnegative Number of lagged differences in the model. Returns ------- result : JohansenTestResult An object containing the test's results. The most important attributes of the result class are: * trace_stat and trace_stat_crit_vals * max_eig_stat and max_eig_stat_crit_vals Notes ----- The implementation might change to make more use of the existing VECM framework. See Also -------- statsmodels.tsa.vector_ar.vecm.select_coint_rank References ---------- .. [1] Lütkepohl, H. 2005. New Introduction to Multiple Time Series Analysis. Springer. rNrzBCritical values are only available for a det_order of -1, 0, or 1.r%)category stacklevelr$ zMCritical values are only available for time series with 12 variables at most.)OLSc |dkr|S|tjtjddt||dzjS)Nr(r$)r.vanderlinspacer;fitresid)rrorderrs r4detrendzcoint_johansen..detrendsU B;;H C29R[QA77CC D D SUU  r6c |jdkr|S|tj|tjtj||z }|SNr)sizer.rcrpinv)rrxrs r4rzcoint_johansen..residsG 6Q;;H q"&!2!2A6677 7r6r(axis)warningswarnr rk#statsmodels.regression.linear_modelrr.asarrayrlrrcrnrrrcholeskyrflipudflatanysignror:r8logsumrrJohansenTestResult)%rprrrrrrNrfdxzr0tlxrktskksk0rsigtmpaudutempdtauindaindad non_zero_drrrriotatjunkrrs% @r4rr[sELOOO ""  *     {1~  )*    877777      Ju  EJD$2~~   GE9 % %E  " " "Br9A )** A1 A IJJB QB %A,,C -%+a.9,- .B ABBB QB %A,,C &  sy| +C &  sy| +C &  sy| +C &bfSXXsu-- . .C c((C Y]]26#s++ , ,FB ry!!"&rvc2"?"?@@ A AD D  B JrNNE 9U  D 4A 111d7 A1J vj, RWQVJ'* + ++ (4..C (4..C (D!9  C (D!9  C 74==DiGAt 1d^^fTAXqrr"bfS!nn$AbfQ1X&&&A$(I..AqqqD $(I..AqqqD Q c31c3S$ G GGr6cLeZdZdZdZedZedZedZedZ edZ edZ ed Z ed Z ed Zed Zed ZedZedZedZdS)ru Results class for Johansen's cointegration test Notes ----- See p. 292 in [1]_ for r0t and rkt References ---------- .. [1] Lütkepohl, H. 2005. New Introduction to Multiple Time Series Analysis. Springer. c d|_||_||_||_||_||_||_||_||_| |_ dS)Njohansen) _meth_rkt_r0t_eig_evec_lr1_lr2_cvt_cvm_ind) rrrrevecrrrrinds r4rzJohansenTestResult.__init__sL          r6c|jS)zResiduals for :math:`Y_{-1}`)r rs r4rzJohansenTestResult.rkt yr6c|jS)zResiduals for :math:`\Delta Y`.)rrs r4rzJohansenTestResult.r0trr6c|jS)z&Eigenvalues of VECM coefficient matrix)rrs r4rzJohansenTestResult.eigrr6c|jS)z'Eigenvectors of VECM coefficient matrix)rrs r4rzJohansenTestResult.evec  zr6c|jSzTrace statisticrrs r4 trace_statzJohansenTestResult.trace_statrr6c|jSrr rs r4rzJohansenTestResult.lr1rr6c|jSzMaximum eigenvalue statisticrrs r4 max_eig_statzJohansenTestResult.max_eig_statrr6c|jSr$r%rs r4rzJohansenTestResult.lr2!rr6c|jSz2Critical values (90%, 95%, 99%) of trace statisticrrs r4trace_stat_crit_valsz'JohansenTestResult.trace_stat_crit_vals&rr6c|jSr)r*rs r4rzJohansenTestResult.cvt+rr6c|jSz@Critical values (90%, 95%, 99%) of maximum eigenvalue statistic.rrs r4rzJohansenTestResult.cvm0rr6c|jSr.r/rs r4max_eig_stat_crit_valsz)JohansenTestResult.max_eig_stat_crit_vals5rr6c|jS)zOrder of eigenvalues)rrs r4rzJohansenTestResult.ind:rr6c|jS)z Test method)r rs r4methzJohansenTestResult.meth?rr6N)rrrrrpropertyrrrrr!rr&rr+rrr1rr4rr6r4rrs     XXXXXXXXXXXXXXr6rceZdZdZ dfd Zdd Zd Zed Zed Z ed Z xZ S)VECMuX Class representing a Vector Error Correction Model (VECM). A VECM(:math:`k_{ar}-1`) has the following form .. math:: \Delta y_t = \Pi y_{t-1} + \Gamma_1 \Delta y_{t-1} + \ldots + \Gamma_{k_{ar}-1} \Delta y_{t-k_{ar}+1} + u_t where .. math:: \Pi = \alpha \beta' as described in chapter 7 of [1]_. Parameters ---------- endog : array_like (nobs_tot x neqs) 2-d endogenous response variable. exog : ndarray (nobs_tot x neqs) or None Deterministic terms outside the cointegration relation. exog_coint : ndarray (nobs_tot x neqs) or None Deterministic terms inside the cointegration relation. dates : array_like of datetime, optional See :class:`statsmodels.tsa.base.tsa_model.TimeSeriesModel` for more information. freq : str, optional See :class:`statsmodels.tsa.base.tsa_model.TimeSeriesModel` for more information. missing : str, optional See :class:`statsmodels.base.model.Model` for more information. k_ar_diff : int Number of lagged differences in the model. Equals :math:`k_{ar} - 1` in the formula above. coint_rank : int Cointegration rank, equals the rank of the matrix :math:`\Pi` and the number of columns of :math:`\alpha` and :math:`\beta`. deterministic : str {``"n"``, ``"co"``, ``"ci"``, ``"lo"``, ``"li"``} * ``"n"`` - no deterministic terms * ``"co"`` - constant outside the cointegration relation * ``"ci"`` - constant within the cointegration relation * ``"lo"`` - linear trend outside the cointegration relation * ``"li"`` - linear trend within the cointegration relation Combinations of these are possible (e.g. ``"cili"`` or ``"colo"`` for linear trend with intercept). When using a constant term you have to choose whether you want to restrict it to the cointegration relation (i.e. ``"ci"``) or leave it unrestricted (i.e. ``"co"``). Do not use both ``"ci"`` and ``"co"``. The same applies for ``"li"`` and ``"lo"`` when using a linear term. See the Notes-section for more information. seasons : int, default: 0 Number of periods in a seasonal cycle. 0 means no seasons. first_season : int, default: 0 Season of the first observation. Notes ----- A VECM(:math:`k_{ar} - 1`) with deterministic terms has the form .. math:: \Delta y_t = \alpha \begin{pmatrix}\beta' & \eta'\end{pmatrix} \begin{pmatrix}y_{t-1}\\D^{co}_{t-1}\end{pmatrix} + \Gamma_1 \Delta y_{t-1} + \dots + \Gamma_{k_{ar}-1} \Delta y_{t-k_{ar}+1} + C D_t + u_t. In :math:`D^{co}_{t-1}` we have the deterministic terms which are inside the cointegration relation (or restricted to the cointegration relation). :math:`\eta` is the corresponding estimator. To pass a deterministic term inside the cointegration relation, we can use the `exog_coint` argument. For the two special cases of an intercept and a linear trend there exists a simpler way to declare these terms: we can pass ``"ci"`` and ``"li"`` respectively to the `deterministic` argument. So for an intercept inside the cointegration relation we can either pass ``"ci"`` as `deterministic` or `np.ones(len(data))` as `exog_coint` if `data` is passed as the `endog` argument. This ensures that :math:`D_{t-1}^{co} = 1` for all :math:`t`. We can also use deterministic terms outside the cointegration relation. These are defined in :math:`D_t` in the formula above with the corresponding estimators in the matrix :math:`C`. We specify such terms by passing them to the `exog` argument. For an intercept and/or linear trend we again have the possibility to use `deterministic` alternatively. For an intercept we pass ``"co"`` and for a linear trend we pass ``"lo"`` where the `o` stands for `outside`. The following table shows the five cases considered in [2]_. The last column indicates which string to pass to the `deterministic` argument for each of these cases. ==== =============================== =================================== ============= Case Intercept Slope of the linear trend `deterministic` ==== =============================== =================================== ============= I 0 0 ``"n"`` II :math:`- \alpha \beta^T \mu` 0 ``"ci"`` III :math:`\neq 0` 0 ``"co"`` IV :math:`\neq 0` :math:`- \alpha \beta^T \gamma` ``"coli"`` V :math:`\neq 0` :math:`\neq 0` ``"colo"`` ==== =============================== =================================== ============= References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. .. [2] Johansen, S. 1995. *Likelihood-Based Inference in Cointegrated * *Vector Autoregressive Models*. Oxford University Press. Nnoner$rrc t||||||+|jd|jdkstd|jjdkrtd|jj|_||_|jjd|_ |dz|_ ||_ ||_ | |_ | |_| |_d|_dS)N)missingrz/exog_coint must have as many rows as enodg_tot!r$zOnly gave one variable to VECMec)superrrkrmrpndimrnrrrCrrOr coint_rankr!r"r]load_coef_repr) rrprBrCdatesfreqr:rr>r!r"r] __class__s r4rz VECM.__init__s eT7CCC  "$Q'5;q>99NOO O :?a  =>> >$J$Q' M "$* ("r6mlc||dkr|Std|d)u Estimates the parameters of a VECM. The estimation procedure is described on pp. 269-304 in [1]_. Parameters ---------- method : str {"ml"}, default: "ml" Estimation method to use. "ml" stands for Maximum Likelihood. Returns ------- est : :class:`VECMResults` References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. rCz#{} not recognized, must be among {})_estimate_vecm_mlrmformat)rrs r4rzVECM.fitsD& T>>))++ +5<rnrcr. real_if_closer VECMResultsrO endog_namesrAr@)rrtrvrwryrnrrrrr_rJ beta_tilde alpha_tilde gamma_tilder sigma_u_tildes r4rEzVECM._estimate_vecm_mls8.= F I O N   L  / / +{FG KN)-g{F)K)K&S#sD!Q,T_,,-/33D99< %j11 VJJ7H7H,I(J(JKK ggj))--    %%))*55 6 6  ;??:<88<.5sEEEqJNEEEr6rc2g|]}jD] }d||fz S)z season%d.%srL)r1srrs r4rz,VECM._lagged_param_names..8sL)A&r6r$r)cg|]}d|zS)z lin_trend.%srrTs r4rz,VECM._lagged_param_names..?sIII1NQ.IIIr6Nc2g|]}jD] }d||fz S)z exog%d.%srVr1exog_norrs r4rz,VECM._lagged_param_names..BsL)wl*r6chg|].}tjD]}jD] }d|dz||fz/S)z L%d.%s.%sr$)r8rrL)r1n2rn1rs r4rz,VECM._lagged_param_names..Iss   4>**  &    1q5"b/ )     r6)r!rLr"r8rBrkr param_namess` r4_lagged_param_nameszVECM._lagged_param_namess8&  4% % % EED4DEEE EK ?? K     &    r6clg}jdkrdS|fdtjDz }|S)u Returns parameter names (for alpha) for the summary. Returns ------- param_names : list of str Returns a list of parameter names for the loading coefficients which are called :math:`\alpha` in [1]_ (see chapter 6). References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. rNcxg|]6}tjD]}jd|dzj|fzz 7S)z%d.%sr$)r8r>r?rL)r1rzrrs r4rz/VECM._load_coef_param_names..gsh   4?++    'QUD4DQ4G,H"H H    r6)r>r8rr_s` r4_load_coef_param_nameszVECM._load_coef_param_namesRs` ?a  4     49%%    r6ctg}|fdtjDz }djvr#|fdtjDz }djvr#|fdtjDz }j2|fdtdjjddzDz }|S) aZ Returns parameter names (for beta and deterministics) for the summary. Returns ------- param_names : list of str Returns a list of parameter names for the cointegration matrix as well as deterministic terms inside the cointegration relation (if present in the model). cng|]1}tjD]}djzdz|dz|dzfz2S)zbeta.%d.%dr$)r8rr?)r1rrzrs r4rz+VECM._coint_param_names..~sh   49%%  $- - 4QA F    r6r'c6g|]}djzd|dzzzS)zconst.rgr$r?rs r4rz+VECM._coint_param_names..s>4..Q?r6r*c6g|]}djzd|dzzzS)z lin_trend.rgr$rirs r4rz+VECM._coint_param_names..s>t22TQU^Cr6NcRg|]#}tjD] }d|dz|fz $S)zexog_coint%d.%sr$)r8rrZs r4rz+VECM._coint_param_names..sXty))"QUG$44r6r$)r8r>r!rCrkr_s` r4_coint_param_nameszVECM._coint_param_namesos3     4?++     4% % % t// K 4% % % t// K ? & $Q(=a(@1(DEE K r6) NNNNr8r$r$rrr)rC) rrrrrrrEr5rardrl __classcell__)rBs@r4r7r7EseeT ######B44 4 4 l11X1fX8((X(((((r6r7ceZdZdZ d6dZedZedZedZed Z ed Z ed Z ed Z ed Z edZedZedZedZedZedZedZedZedZedZedZedZedZdZd7dZd7dZd7dZd7d Zd7d!Z ed"Z!ed#Z"d8d%Z#ed&Z$d9d'Z%d:d)Z& d;d+Z'dd4Z/d7d5Z0dS)?rKu'Class for holding estimation related results of a vector error correction model (VECM). Parameters ---------- endog : ndarray (neqs x nobs_tot) Array of observations. exog : ndarray (nobs_tot x neqs) or `None` Deterministic terms outside the cointegration relation. exog_coint : ndarray (nobs_tot x neqs) or `None` Deterministic terms inside the cointegration relation. k_ar : int, >= 1 Lags in the VAR representation. This implies that the number of lags in the VEC representation (=lagged differences) equals :math:`k_{ar} - 1`. coint_rank : int, 0 <= `coint_rank` <= neqs Cointegration rank, equals the rank of the matrix :math:`\Pi` and the number of columns of :math:`\alpha` and :math:`\beta`. alpha : ndarray (neqs x `coint_rank`) Estimate for the parameter :math:`\alpha` of a VECM. beta : ndarray (neqs x `coint_rank`) Estimate for the parameter :math:`\beta` of a VECM. gamma : ndarray (neqs x neqs*(k_ar-1)) Array containing the estimates of the :math:`k_{ar}-1` parameter matrices :math:`\Gamma_1, \dots, \Gamma_{k_{ar}-1}` of a VECM(:math:`k_{ar}-1`). The submatrices are stacked horizontally from left to right. sigma_u : ndarray (neqs x neqs) Estimate of white noise process covariance matrix :math:`\Sigma_u`. deterministic : str {``"n"``, ``"co"``, ``"ci"``, ``"lo"``, ``"li"``} * ``"n"`` - no deterministic terms * ``"co"`` - constant outside the cointegration relation * ``"ci"`` - constant within the cointegration relation * ``"lo"`` - linear trend outside the cointegration relation * ``"li"`` - linear trend within the cointegration relation Combinations of these are possible (e.g. ``"cili"`` or ``"colo"`` for linear trend with intercept). See the docstring of the :class:`VECM`-class for more information. seasons : int, default: 0 Number of periods in a seasonal cycle. 0 means no seasons. first_season : int, default: 0 Season of the first observation. delta_y_1_T : ndarray or `None`, default: `None` Auxiliary array for internal computations. It will be calculated if not given as parameter. y_lag1 : ndarray or `None`, default: `None` Auxiliary array for internal computations. It will be calculated if not given as parameter. delta_x : ndarray or `None`, default: `None` Auxiliary array for internal computations. It will be calculated if not given as parameter. model : :class:`VECM` An instance of the :class:`VECM`-class. names : list of str Each str in the list represents the name of a variable of the time series. dates : array_like For example a DatetimeIndex of length nobs_tot. Attributes ---------- nobs : int Number of observations (excluding the presample). model : see Parameters y_all : see `endog` in Parameters exog : see Parameters exog_coint : see Parameters names : see Parameters dates : see Parameters neqs : int Number of variables in the time series. k_ar : see Parameters deterministic : see Parameters seasons : see Parameters first_season : see Parameters alpha : see Parameters beta : see Parameters gamma : see Parameters sigma_u : see Parameters det_coef_coint : ndarray (#(determinist. terms inside the coint. rel.) x `coint_rank`) Estimated coefficients for the all deterministic terms inside the cointegration relation. const_coint : ndarray (1 x `coint_rank`) If there is a constant deterministic term inside the cointegration relation, then `const_coint` is the first row of `det_coef_coint`. Otherwise it's an ndarray of zeros. lin_trend_coint : ndarray (1 x `coint_rank`) If there is a linear deterministic term inside the cointegration relation, then `lin_trend_coint` contains the corresponding estimated coefficients. As such it represents the corresponding row of `det_coef_coint`. If there is no linear deterministic term inside the cointegration relation, then `lin_trend_coint` is an ndarray of zeros. exog_coint_coefs : ndarray (exog_coint.shape[1] x `coint_rank`) or `None` If deterministic terms inside the cointegration relation are passed via the `exog_coint` parameter, then `exog_coint_coefs` contains the corresponding estimated coefficients. As such `exog_coint_coefs` represents the last rows of `det_coef_coint`. If no deterministic terms were passed via the `exog_coint` parameter, this attribute is `None`. det_coef : ndarray (neqs x #(deterministic terms outside the coint. rel.)) Estimated coefficients for the all deterministic terms outside the cointegration relation. const : ndarray (neqs x 1) or (neqs x 0) If a constant deterministic term outside the cointegration is specified within the deterministic parameter, then `const` is the first column of `det_coef_coint`. Otherwise it's an ndarray of size zero. seasonal : ndarray (neqs x seasons) If the `seasons` parameter is > 0, then seasonal contains the estimated coefficients corresponding to the seasonal terms. Otherwise it's an ndarray of size zero. lin_trend : ndarray (neqs x 1) or (neqs x 0) If a linear deterministic term outside the cointegration is specified within the deterministic parameter, then `lin_trend` contains the corresponding estimated coefficients. As such it represents the corresponding column of `det_coef_coint`. If there is no linear deterministic term outside the cointegration relation, then `lin_trend` is an ndarray of size zero. exog_coefs : ndarray (neqs x exog_coefs.shape[1]) If deterministic terms outside the cointegration relation are passed via the `exog` parameter, then `exog_coefs` contains the corresponding estimated coefficients. As such `exog_coefs` represents the last columns of `det_coef`. If no deterministic terms were passed via the `exog` parameter, this attribute is an ndarray of size zero. _delta_y_1_T : see delta_y_1_T in Parameters _y_lag1 : see y_lag1 in Parameters _delta_x : see delta_x in Parameters coint_rank : int Cointegration rank, equals the rank of the matrix :math:`\Pi` and the number of columns of :math:`\alpha` and :math:`\beta`. llf : float The model's log-likelihood. cov_params : ndarray (d x d) Covariance matrix of the parameters. The number of rows and columns, d (used in the dimension specification of this argument), is equal to neqs * (neqs+num_det_coef_coint + neqs*(k_ar-1)+number of deterministic dummy variables outside the cointegration relation). For the case with no deterministic terms this matrix is defined on p. 287 in [1]_ as :math:`\Sigma_{co}` and its relationship to the ML-estimators can be seen in eq. (7.2.21) on p. 296 in [1]_. cov_params_wo_det : ndarray Covariance matrix of the parameters :math:`\tilde{\Pi}, \tilde{\Gamma}` where :math:`\tilde{\Pi} = \tilde{\alpha} \tilde{\beta'}`. Equals `cov_params` without the rows and columns related to deterministic terms. This matrix is defined as :math:`\Sigma_{co}` on p. 287 in [1]_. stderr_params : ndarray (d) Array containing the standard errors of :math:`\Pi`, :math:`\Gamma`, and estimated parameters related to deterministic terms. stderr_coint : ndarray (neqs+num_det_coef_coint x `coint_rank`) Array containing the standard errors of :math:`\beta` and estimated parameters related to deterministic terms inside the cointegration relation. stderr_alpha : ndarray (neqs x `coint_rank`) The standard errors of :math:`\alpha`. stderr_beta : ndarray (neqs x `coint_rank`) The standard errors of :math:`\beta`. stderr_det_coef_coint : ndarray (num_det_coef_coint x `coint_rank`) The standard errors of estimated the parameters related to deterministic terms inside the cointegration relation. stderr_gamma : ndarray (neqs x neqs*(k_ar-1)) The standard errors of :math:`\Gamma_1, \ldots, \Gamma_{k_{ar}-1}`. stderr_det_coef : ndarray (neqs x det. terms outside the coint. relation) The standard errors of estimated the parameters related to deterministic terms outside the cointegration relation. tvalues_alpha : ndarray (neqs x `coint_rank`) tvalues_beta : ndarray (neqs x `coint_rank`) tvalues_det_coef_coint : ndarray (num_det_coef_coint x `coint_rank`) tvalues_gamma : ndarray (neqs x neqs*(k_ar-1)) tvalues_det_coef : ndarray (neqs x det. terms outside the coint. relation) pvalues_alpha : ndarray (neqs x `coint_rank`) pvalues_beta : ndarray (neqs x `coint_rank`) pvalues_det_coef_coint : ndarray (num_det_coef_coint x `coint_rank`) pvalues_gamma : ndarray (neqs x neqs*(k_ar-1)) pvalues_det_coef : ndarray (neqs x det. terms outside the coint. relation) var_rep : (k_ar x neqs x neqs) KxK parameter matrices :math:`A_i` of the corresponding VAR representation. If the return value is assigned to a variable ``A``, these matrices can be accessed via ``A[i]`` for :math:`i=0, \ldots, k_{ar}-1`. cov_var_repr : ndarray (neqs**2 * k_ar x neqs**2 * k_ar) This matrix is called :math:`\Sigma^{co}_{\alpha}` on p. 289 in [1]_. It is needed e.g. for impulse-response-analysis. fittedvalues : ndarray (nobs x neqs) The predicted in-sample values of the models' endogenous variables. resid : ndarray (nobs x neqs) The residuals. References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. 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Notes ----- See p. 297 in [1]_. Using the rule .. math:: vec(B R) = (B' \otimes I) vec(R) for two matrices B and R which are compatible for multiplication. This is rule (3) on p. 662 in [1]_. References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. NrFr)r>rrrrrr.rorrcrnrr~rxrkrrurrbrr<r) rrrMrr12rrmat2 first_rows last_rows_1d last_rowss r4 stderr_cointzVECMResults.stderr_coint sX* OD-t|T]KK2f 8q==8QF## #37735>>""wtvr{1~~..!'*w K A + , ,  s4<0004:= > >  Xq!f%% wrwtxx~~6677  (($)a-#*=q)A(MM z9-...r6cv|jd|jj}||jjdS)Nrr)rrurr<rkrret_1dims r4 stderr_alphazVECMResults.stderr_alpha2s7%&7 &78 0<<r.rorwrr)rrrrs r4 tvalues_betazVECMResults.tvalues_betaWsO OXq!f%% IabbMD$4QRR$88 z9-...r6cN|jjdkr|jS|j|jz Sr)rxrrrs r4tvalues_det_coef_cointz"VECMResults.tvalues_det_coef_coint^s-   #q ( (& &"T%???r6c |j|jz Sr)rzrrs r4 tvalues_gammazVECMResults.tvalues_gammadrr6cN|jjdkr|jS|j|jz Sr)r{rrrs r4tvalues_det_coefzVECMResults.tvalues_det_coefhs* =  " "= }t333r6czdtjjt |jz dzSNr$r%)rstatsnormcdfabsrrs r4 pvalues_alphazVECMResults.pvalues_alphao0EK$((T-?)@)@AAAQFFr6ctj|j|jf}|j|jd}dtjjt|z dz}t||fSr) r.ror>rrrrrrr)rr tval_lastrs r4 pvalues_betazVECMResults.pvalues_betassjXt@AA %do&7&78 )--c)nn===B z9-...r6c|jjdkr|jSdtjjt |jz dzSNrr$r%)rxrrrrrrrrs r4pvalues_det_coef_cointz"VECMResults.pvalues_det_coef_cointzsJ   #q ( (& &EK$((T-H)I)IJJJaOOr6czdtjjt |jz dzSr)rrrrrrrs r4 pvalues_gammazVECMResults.pvalues_gammarr6c|jjdkr|jSdtjjt |jz dzSr)r{rrrrrrrrs r4pvalues_det_coefzVECMResults.pvalues_det_coefsH =  " "= EK$((T-B)C)CDDDIIr6c(tj|jdtfdtfg}|tjjd|dz z |zz |d<|tjjd|dz z |zz|d<|S)Nlowerupperrr$r%)r.rorkfloatrrrppf)reststderrru struct_arrs r4_make_conf_intzVECMResults._make_conf_intsX Iw.%0@A    %+"&&q519}55> > 7 %+"&&q519}55> > 7r6rcD||j|j|Sr)rrurrrus r4conf_int_alphazVECMResults.conf_int_alpha""4:t/@%HHHr6cD||j|j|Sr)rrwrrs r4 conf_int_betazVECMResults.conf_int_betas""49d.>FFFr6cD||j|j|Sr)rrxrrs r4conf_int_det_coef_cointz#VECMResults.conf_int_det_coef_coints'""  !;U   r6cD||j|j|Sr)rrzrrs r4conf_int_gammazVECMResults.conf_int_gammarr6cD||j|j|Sr)rr{rrs r4conf_int_det_coefzVECMResults.conf_int_det_coefs""4=$2FNNNr6c|j|jj}|j}|j}t j|j||f}|t j |z|d<|jj dkr|dxx|ddd|fz cc<|dd||jdz zdf ||jdz <td|jdz D]4}|dd||z||dzzf|dd||dz z||zfz ||<5|S)Nrr%r$) rurcrwrnrzrr.rorOr~rr8)rrrzrsrrs r4var_repzVECMResults.var_reps6 Z^^DIK ( (  I HdiA& ' 'BKNN"! :?Q   aDDDE!!!RaR%L DDD %aaadi!m)<)>)>&> ??Adi!m 1di!m,,  !!!QUQ!a%[001AAAqAE{QU2234!r6c |jdz dkr|jStj|jdz|jz|jdz|jzf}tj|jdz}t ||f|d|jdzdd|jdzzf<td|jD]l}|jdz|dz |jdzzz}|jdz|dz |jdzzz}t | |f||||jdzz||d|jdzzzf<m| ||jdz d|jdz df<|}||jz|jzS)a\ Gives the covariance matrix of the corresponding VAR-representation. More precisely, the covariance matrix of the vector consisting of the columns of the corresponding VAR coefficient matrices (i.e. vec(self.var_rep)). Returns ------- cov : array (neqs**2 * k_ar x neqs**2 * k_ar) r$rr%N) rOrr.rorr~rr8rn)rvecm_var_transformationeyer start_row start_colvvts r4 cov_var_reprzVECMResults.cov_var_reprs> 9q=A  ) )"$( Y!^di 'a$))C D# # k$)q.)) C:   di1n 2DIN 22 2 q$)$$ $ $A Q!a%49>)AAI Q!a%49>)AAIc{## $I Q66IDIN(:::<   JMa 1 1DIN?3D3D DE%T++ce33r6 c,t|j|Sr)rr)rmaxns r4rzVECMResults.ma_repsdlD)))r6cJtj|jSr)r.rrrrs r4 _chol_sigma_uzVECMResults._chol_sigma_usy!!$,///r6c$t|||S)a/Compute orthogonalized MA coefficient matrices. For this purpose a matrix P is used which fulfills :math:`\Sigma_u = PP^\prime`. P defaults to the Cholesky decomposition of :math:`\Sigma_u` Parameters ---------- maxn : int Number of coefficient matrices to compute P : ndarray (neqs x neqs), optional Matrix such that :math:`\Sigma_u = PP'`. Defaults to Cholesky decomposition. Returns ------- coefs : ndarray (maxn x neqs x neqs) )r)rrPs r4rzVECMResults.orth_ma_reps&4q)))r6c |j|td|j|td| |jd|krtd|j|td|j|td|#|jd|dz krtd |jj|j d}g}g}tj|}|j |jz} |j j dkr4| || |j j|j dkr]|j| z|j z} t|j || d } | | | |jjt#|j |j} | d dztj|z} |jj dkr4| | | |jj|<| |d|| |jjd |jvrQ| || |j|jjjt#|j |jd } | d dztj|z} d|jvrQ| | | |j|jjj||jdkr |dddf}tj|jd d|d|dz f}| || |j|jjj|gkrtj|nd}|gkrtj|}nd}| t=||j||j |||StC||j|||S)a[ Calculate future values of the time series. Parameters ---------- steps : int Prediction horizon. alpha : float, 0 < `alpha` < 1 or None If None, compute point forecast only. If float, compute confidence intervals too. In this case the argument stands for the confidence level. exog : ndarray (steps x self.exog.shape[1]) If self.exog is not None, then information about the future values of exog have to be passed via this parameter. The ndarray may be larger in it's first dimension. In this case only the first steps rows will be considered. Returns ------- forecast - ndarray (steps x neqs) or three ndarrays In case of a point forecast: each row of the returned ndarray represents the forecast of the neqs variables for a specific period. The first row (index [0]) is the forecast for the next period, the last row (index [steps-1]) is the steps-periods-ahead- forecast. Nzaexog_fc is None: Please pass the future values of the VECM's exog terms via the exog_fc argument!zxThis VECMResult-instance's exog attribute is None. Please do not pass a non-None value as the method's exog_fc-argument.rzMThe argument exog_fc must have at least steps elements in its first dimensionzsexog_coint_fc is None: Please pass the future values of the VECM's exog_coint terms via the exog_coint_fc argument!zThis VECMResult-instance's exog_coint attribute is None. Please do not pass a non-None value as the method's exog_coint_fc-argument.r$zSThe argument exog_coint_fc must have at least steps elements in its first dimensionTr(r'rjr*)rurB)"rBrmrkrCrprnrOr.r:rNrrr9r"r]rrrRr=rrr!rurcr|r}r=rr~r[rrrr)rstepsruexog_fc exog_coint_fclast_observationsrB trend_coefs exog_constr\first_future_season exog_seasonalexog_lin_trendexog_lin_trend_coints r4predictzVECMResults.predict s6 9 W_  9 !4-   7=#3e#;#;2  ? &=+@*  ? "}'@7   $)  " " KK ' ' '   t~/ 0 0 0   KK ( ( (   t0 1 1 1 4% % % KK # # #   tz~~d.>.@AAC D D D,TY NNN3B7!;bi>N>NN 4% % % KK, - - -   tz~~d.B.DEEG H H H  $!Q&& -aaag 6 I%}[uqy['ABM KK & & &   tz~~d.C.EFFH I I I)- rt$$$ "  )K00KKK  $!   !4<eT r6Tc |||\}}}|jj}|||jdn || d}t j|||||j|ddidS)a Plot the forecast. Parameters ---------- steps : int Prediction horizon. alpha : float, 0 < `alpha` < 1 The confidence level. plot_conf_int : bool, default: True If True, plot bounds of confidence intervals. n_last_obs : int or None, default: None If int, restrict plotted history to n_last_obs observations. If None, include the whole history in the plot. ruNlocz lower left)rI plot_stderrlegend_options)rrprnrOplot plot_var_forcrI) rrru plot_conf_int n_last_obsmidrrrrs r4 plot_forecastzVECMResults.plot_forecasts$!LLeL<<UE JL(0AdikkNNa o    *%!<0      r6c & "#d|cxkrdksntdttf"t|"r|g}t "fd|Dst dfd|D}fd|D#|Yt|"r|g}t "fd |Dst d fd |D}fd |D}|.#fd t jD}fd|D}jjj dz j dzf\}}}}tj j j j zjdjj} t#|j| |d} t)|t)|z|dz z} t+j j } j| jjdz } j| jjdz } t/j| || z|dz|dz zzft2} || z}d}t |dz D]*}|D]%}#D] }d| |||z||zz|dz|zzf<|dz }!&+t/j| t7| jd| j}g}| #|| | djt/j||z|f}t |dz D];}|dd|dz |z d|z f|ddd| fz |||z|dz|zddf<<|ddd| f|| dddf<||t/j|}t/j||j}t?|d||dz z| zd||dz z| zf}| j |||zz | z z|z }|t/j!||z}t?| |z| jz}||j|z|zz}|| z }| || j"zf}tGj$j%|}|&|} |'d|z }!tQ||||!| ||dd S)u Test for Granger-causality. The concept of Granger-causality is described in chapter 7.6.3 of [1]_. Test |H0|: "The variables in `causing` do not Granger-cause those in `caused`" against |H1|: "`causing` is Granger-causal for `caused`". Parameters ---------- caused : int or str or sequence of int or str If int or str, test whether the variable specified via this index (int) or name (str) is Granger-caused by the variable(s) specified by `causing`. If a sequence of int or str, test whether the corresponding variables are Granger-caused by the variable(s) specified by `causing`. causing : int or str or sequence of int or str or `None`, default: `None` If int or str, test whether the variable specified via this index (int) or name (str) is Granger-causing the variable(s) specified by `caused`. If a sequence of int or str, test whether the corresponding variables are Granger-causing the variable(s) specified by `caused`. If `None`, `causing` is assumed to be the complement of `caused` (the remaining variables of the system). signif : float, 0 < `signif` < 1, default 5 % Significance level for computing critical values for test, defaulting to standard 0.05 level. Returns ------- results : :class:`statsmodels.tsa.vector_ar.hypothesis_test_results.CausalityTestResults` References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. .. |H0| replace:: H\ :sub:`0` .. |H1| replace:: H\ :sub:`1` rr$z signif has to be between 0 and 1c38K|]}t|VdSr isinstancer1c allowed_typess r4 z5VECMResults.test_granger_causality..s-@@A:a//@@@@@@r6zFcaused has to be of type string or int (or a sequence of these types).cZg|]'}t|tur j|n|(SrrrrIr1r*rs r4rz6VECMResults.test_granger_causality..s1IIIQ477c>>$*Q--qIIIr6c:g|]}tj|SrrrIr/s r4rz6VECMResults.test_granger_causality..s%???1i A..???r6Nc38K|]}t|VdSrr'r)s r4r,z5VECMResults.test_granger_causality..s-EEz!]33EEEEEEr6zOcausing has to be of type string or int (or a sequence of these types) or None.cZg|]'}t|tur j|n|(Srr.r/s r4rz6VECMResults.test_granger_causality..s1OOO!Q3tz!}}AOOOr6c:g|]}tj|Srr1r/s r4rz6VECMResults.test_granger_causality..s%EEE9TZ33EEEr6cg|]}|v| Srr)r1r caused_inds r4rz6VECMResults.test_granger_causality..s#NNN!::M:M1:M:M:Mr6c*g|]}j|Sr)rIr/s r4rz6VECMResults.test_granger_causality..s:::tz!}:::r6Tr\r]r^rBrCrr trendr%rr(grangerr)testr))rmstrrr(rs TypeErrorr8rrprNrOr_r!r"r]rBrCrrnrr;rVrkr.rorrcrparamsr9rrrrdf_residrrrsfrr)$rcausedcausingr causing_indrrrIrrErB var_results num_restr num_det_termsCcols_detrowrzing_inded_indCax_min_p_componentsx_min_prx_xx_x_11rsig_alpha_min_pmiddlewald_statistic f_statisticdff_distributionpvalue crit_valuer+r6s$` @@r4test_granger_causalityz"VECMResults.test_granger_causalitysVFQ?@@ @c fm , , XF@@@@@@@@@ , JIII&III???????  '=11 $")EEEEWEEEEE :POOOwOOOGEEEEWEEEK ?NNNNeDI&6&6NNNK::::k:::GZDIM49q=H 1a%   LY**!   !#tnn((#(>> LL3v;;.!a%8 %d&8$,GG 9 TY_Q/ /M ? & T_215 5M H M)AFa!e,<< =U   }$q1u  A&  (FKLAc8f,q7{:Q!VaZGGH1HCC VAs;-crc2455 6 6    % %dA233ik 2 2 2(AE1:&&q1u  A!!!QUQYa''(1QQQ!V94 AEQUaK'* + +AAAssF)QQQ!!'***).//fWgi((S )a1q5kM) )+HQ!a%[=-H+H H %QU])BCaGbgfg666Q(13.//bdVmb01$y0 [11 2+"";//#''F 33 #           r6c Rt|j|j|j|jz|jd|j|j}|j|j|j}}}t|j j | |d}|j |j_ |||S)u Test for instantaneous causality. The concept of instantaneous causality is described in chapters 3.6.3 and 7.6.4 of [1]_. Test |H0|: "No instantaneous causality between the variables in `caused` and those in `causing`" against |H1|: "Instantaneous causality between `caused` and `causing` exists". Note that instantaneous causality is a symmetric relation (i.e. if `causing` is "instantaneously causing" `caused`, then also `caused` is "instantaneously causing" `causing`), thus the naming of the parameters (which is chosen to be in accordance with :meth:`test_granger_causality()`) may be misleading. Parameters ---------- causing : int or str or sequence of int or str If int or str, test whether the corresponding variable is causing the variable(s) specified in caused. If sequence of int or str, test whether the corresponding variables are causing the variable(s) specified in caused. signif : float, 0 < `signif` < 1, default 5 % Significance level for computing critical values for test, defaulting to standard 0.05 level. Returns ------- results : :class:`statsmodels.tsa.vector_ar.hypothesis_test_results.CausalityTestResults` Notes ----- This method is not returning the same result as `JMulTi`. This is because the test is based on a VAR(k_ar) model in `statsmodels` (in accordance to pp. 104, 320-321 in [1]_) whereas `JMulTi` seems to be using a VAR(k_ar+1) model. Reducing the lag order by one in `JMulTi` leads to equal results in `statsmodels` and `JMulTi`. References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. .. |H0| replace:: H\ :sub:`0` .. |H1| replace:: H\ :sub:`1` Tr8rr9)rCr)r_r!r"rNrOr]rBrCrrrprnrrI_resultstest_inst_causality)rrCrrBrIrrErEs r4r]zVECMResults.test_inst_causalityMsZ&   LY**!   )TY a1$*,--11!31GG %)Z "..wv.NNNr6c0tj||dS)NT)periodsvecm)irf IRAnalysis)rr_s r4razVECMResults.irfs~dG$????r6c|j}|jjdkrt||jf}t j|j|j}|j}|j jdkrt||j f}t j||j t j||j z}||j d|j zjS)z Return the in-sample values of endog calculated by the model. Returns ------- fitted : array (nobs x neqs) The predicted in-sample values of the models' endogenous variables. rN)rwrxrrr.rcrurnrzr{rrrr)rrwrrzrus r4 fittedvalueszVECMResults.fittedvaluessy   #a ' '4!4566D VDJ ' '  =  ! !E4=122E&T\**RVE4=-I-II$,{{3366r6cD|jj|jd|jz S)z Return the difference between observed and fitted values. Returns ------- resid : array (nobs x neqs) The residuals. N)rprnrOrdrs r4rzVECMResults.resids!z|DIKK(4+<<tjtj |dkrtj |}td|dzD]@}||} tj | j |z| z|z} |r | |j|z z} || z }A||r |jdzn|jz}|jdz||jz dzz|j|jzz } t$j| } | |} | d|z }t/||| | |||S)u$ Test the whiteness of the residuals using the Portmanteau test. This test is described in [1]_, chapter 8.4.1. Parameters ---------- nlags : int > 0 signif : float, 0 < `signif` < 1 adjusted : bool, default False Returns ------- result : :class:`statsmodels.tsa.vector_ar.hypothesis_test_results.WhitenessTestResults` References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series Analysis*. Springer. rr$r%)r.rrrrrrqrrrsrtrealr8rrnrNrrOr>rrchi2rArr)rnlagsradjusted statisticu acov_listc0_invrctto_addrVdistrXrYs r4test_whitenesszVECMResults.test_whitenesss* Jtz " "!!U++ T\"" <2= ( (RVBGFOOq4H-I-I (WV__Fq%!)$$  A1BXbdVmb069::F ($)a-'  IIx>TY!^^TY>  INedi/!3 4i$/) * {####XXa&j)) # z62vuh   r6c|r|jn|jdd|jdf}|j}|r|jn|j|jd}t j|j||dS)z Plot the input time series. Parameters ---------- with_presample : bool, default: `False` If `False`, the pre-sample data (the first `k_ar` values) will not be plotted. N)rIr)rprOrIr@rplot_mtsrn)rwith_presamplerrrIr@s r4 plot_datazVECMResults.plot_datasl) HDJJdjDIKK.H ,I $*TY[[2I ace444444r6c ,-ddlm-t} d-fd }g}g}g}g}g}|jjdkr/||jd||jd||jd||j d| } | dd} | d d} |tj | | f|j d z dkr#||j||j||j||j|} | d} | d } |tj | | ft'|dkrkt)|} t)|} t)|}t)|}t+|}t-|jD] }g}d}d |jvr6||tj|d z||jz }|jdkrPt-|jd z D]8}||tj|d z||jz }9d |jvr6||tj|d z||jz }|jXt-|jjd D]8}||tj|d z||jz }9|j d z dkrX||jz|j d z z}|d z|jz|j d z z}||tj||ztj|}|jj |}dd|zz}||| | |||||jj!| }|j"| |j#}|j$}|j%}|j&}|'}|d} |d } tj | | f}|jj(} g}!t-|jD]}|j)dkr)||j)z}||j)z}tj||}|!||jj |}d|z}||||||||| | }|j"|g}"g}#g}$g}%g}&|j)dkrA|"|j*j+|#|j,j+|$|j-j+|%|j.j+|/} | dj+} | d j+} |&tj | | f|j0jdkr#|"|j0|#|j1|$|j2|%|j3|4} | d} | d } |&tj | | ft)|"}'t)|#}(t)|$})t)|%}*t+|&}+|jj5},t-|j)D]}g}d}|j)dkrQ||jz}||jz}||tj||z||j|j)zz }d|jvr6||tj|d z||j)z }d|jvr6||tj|d z||j)z }|j6Xt-|j6jd D]8}||tj|d z||j)z }9tj|}dd|d zzz}|||'|(|)|*|+||,| }|j"||S)a Return a summary of the estimation results. Parameters ---------- alpha : float 0 < `alpha` < 1, default 0.05 Significance level of the shown confidence intervals. Returns ------- summary : :class:`statsmodels.iolib.summary.Summary` A summary containing information about estimated parameters. r)summary_paramsTc  |||||||||||f} fdtj||D}  | d| d|S)Ncxg|]6}r0d|dddn|7S).Nr()joinsplit)r1name strip_ends r4rz;VECMResults.summary..make_table..0 sR3<EC"-...r6F)ynamexnameruuse_tr)r.r/tolist)rr?std_errt_valuesp_valuesconf_intrrIrrresr`rurys ` r4 make_tablez'VECMResults.summary..make_table st   CHUOOD188::K">!  r6rrrrrr$r&)ndminr)Nz'Det. terms outside the coint. relation z*& lagged endog. parameters for equation %sz,Loading coefficients (alpha) for equation %sr'r*zCointegration relations for zloading-coefficients-column %d)T)7statsmodels.iolib.summaryryrr{rr9flattenrrrrr.r[rOrzrrrrr;rrr8rr!r/r"rBrkr= concatenaterHrLratablesrurrrrrdr>rwrnrrrrrxrrrrrlrC).rrurrlagged_params_componentsstderr_lagged_params_components tvalues_lagged_params_components pvalues_lagged_params_components!conf_int_lagged_params_componentsrrr lagged_paramsstderr_lagged_paramstvalues_lagged_paramspvalues_lagged_paramsconf_int_lagged_paramsrmasksr,rMrendreq_namertablerse_at_ap_aci_aa_names alpha_maskscoint_componentsstderr_coint_componentstvalues_coint_componentspvalues_coint_componentsconf_int_coint_componentsrPr tvalues_coint pvalues_cointconf_int_coint coint_namesrys. ` @r4rzVECMResults.summary sJ  =<<<<<))       F$& *,'+-(+-(,.) =  ! ! $ + +DM,A,A,A,L,L M M M + 2 2$,,3,77    - 3 3%--C-88    - 3 3%--C-88   --E-::HW%--C-88EW%--C-88E - 4 4//    9q=1   $ + +DJ,>,>,@,@ A A A + 2 243D3L3L3N3N O O O , 3 3"**,,    - 3 3"**,,   ***77HW%--//EW%--//E - 4 4//    ' ( (A - -"#;<*>*>!>???di'F*>*>!>???di'F9("49?1#566,, Vbhq.B.B.B%BCCC$)+9q=1$$ MTY];Eq5DI-Q?CLL")E3*?*?!?@@@~e,,*03=BWLM# !())*J2  %%e,,,, J    ((** ((** ((**"""//W %%''W %%''u~..*3 ty!! ) )A""DO+do-y,,   t $ $ $j,Q/GBWLEJasCtWeE N ! !% ( ( ( ("$#% #% $&! ?Q    # #DIK$7$7$9$9 : : : # * *4+;+=+E+E+G+G H H H $ + +D,=,?,G,G,I,I J J J $ + +D,=,?,G,G,I,I J J J)))66HW%'//11EW%'//11E % , ,R_eU^-L-L M M M   #a ' '  # #D$7$?$?$A$A B B B # * **2244    % + ++3355    % + ++3355   33%3@@HW%--//EW%--//E % , ,R_eU^-L-L M M M'((566 788 788  9::j3 t''( )( )AEF""DI di' Vbis&;&;;<<<$)do55t))) Vbhq&:&:&::;;;$/)t))) Vbhq&:&:&::;;;$/)*t4Q788..ALL"(1A*>*>*>!>???do-FF>%((D.2a!e<= J  E N ! !% ( ( ( (r6) rrrNNNNNN)r)r)rN)r NNN)rTN)Nr)rrFF)1rrrrrr rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr rrr$rZr]rardrrrsrwrrr6r4rKrKsAA\']*]*]*]*~  ^ GG^G++^+2??^?,99^9#/#/^#/J==^=<<^<FF^F ==^=AA^A..^.//^/ @@^@ ..^.44^4 GG^G//^/ PP^P GG^GJJ^J   IIIIGGGG    IIIIOOOO^ 4444^44l****00^0*****DDDDNAE    @Y Y Y Y v<O<O<O<O|@@@@77^7( = =^ =3333,4 4 4 4 l 5 5 5 5||||||r6rK)rrNNr)r)rFNN)rrr)G collectionsrnumpyr.rr numpy.linalgrrr scipy.statsrrstatsmodels.iolib.tabler statsmodels.tools.decoratorsr statsmodels.tools.sm_exceptionsr statsmodels.tools.validationr statsmodels.tsa.base.tsa_modeltsabase tsa_modeltsbasestatsmodels.tsa.coint_tablesrrstatsmodels.tsa.tsatoolsrrr1statsmodels.tsa.vector_ar.hypothesis_test_resultsrrstatsmodels.tsa.vector_ar.irf vector_arra"statsmodels.tsa.vector_ar.plottingplottingrstatsmodels.tsa.vector_ar.utilrr#statsmodels.tsa.vector_ar.var_modelrrrrrrrrrr=rLrRrVr_rhr|rrrrrrTimeSeriesModelr7rKrr6r4rs###### !!!!!!!! ------//////777777AAAAAA444444////////////55555555DDDDDDDDDD,+++++++++++111111111111FFFFFFFF                      G6G6 G6G6 G6G6G6G6T5>5>5>5B$$$0 r/r/r/r/j$$$N+.+.+.\D(D(D(D(D(D(D(D(P9=DDDDNFHFHFHR^^^^^^^^BSSSSS6 !SSSl kkkkkkkkkkr6