Dj`6dZddlZddlmZddlZddlZddlm Z ddl m Z ddl m Z ddlmZddlmcmZddlmZd d lmZmZd d lmZmZmZd d lmZd d lm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&GddeZ'GddeZ(GddeZ)ejTe)e(y)zs Vector Autoregressive Moving Average with eXogenous regressors model Author: Chad Fulton License: Simplified-BSD N)warn)Appender)Bunch)_is_using_pandas) var_model)EstimationWarning)INVERT_UNIVARIATESOLVE_LU)MLEModel MLEResultsMLEResultsWrapper)Initialization) is_invertibleconcat prepare_exog!constrain_stationary_multivariate#unconstrain_stationary_multivariateprepare_trend_specprepare_trend_dataceZdZdZ d fd ZddZedZedZedZ dZ dZ fd Z dd Z ejd Zeej&j dfd ZxZS)VARMAXuM Vector Autoregressive Moving Average with eXogenous regressors model Parameters ---------- endog : array_like The observed time-series process :math:`y`, , shaped nobs x k_endog. exog : array_like, optional Array of exogenous regressors, shaped nobs x k. order : iterable The (p,q) order of the model for the number of AR and MA parameters to use. trend : str{'n','c','t','ct'} or iterable, optional Parameter controlling the deterministic trend polynomial :math:`A(t)`. Can be specified as a string where 'c' indicates a constant (i.e. a degree zero component of the trend polynomial), 't' indicates a linear trend with time, and 'ct' is both. Can also be specified as an iterable defining the non-zero polynomial exponents to include, in increasing order. For example, `[1,1,0,1]` denotes :math:`a + bt + ct^3`. Default is a constant trend component. error_cov_type : {'diagonal', 'unstructured'}, optional The structure of the covariance matrix of the error term, where "unstructured" puts no restrictions on the matrix and "diagonal" requires it to be a diagonal matrix (uncorrelated errors). Default is "unstructured". measurement_error : bool, optional Whether or not to assume the endogenous observations `endog` were measured with error. Default is False. enforce_stationarity : bool, optional Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. Default is True. enforce_invertibility : bool, optional Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. Default is True. trend_offset : int, optional The offset at which to start time trend values. Default is 1, so that if `trend='t'` the trend is equal to 1, 2, ..., nobs. Typically is only set when the model created by extending a previous dataset. **kwargs Keyword arguments may be used to provide default values for state space matrices or for Kalman filtering options. See `Representation`, and `KalmanFilter` for more details. Attributes ---------- order : iterable The (p,q) order of the model for the number of AR and MA parameters to use. trend : str{'n','c','t','ct'} or iterable Parameter controlling the deterministic trend polynomial :math:`A(t)`. Can be specified as a string where 'c' indicates a constant (i.e. a degree zero component of the trend polynomial), 't' indicates a linear trend with time, and 'ct' is both. Can also be specified as an iterable defining the non-zero polynomial exponents to include, in increasing order. For example, `[1,1,0,1]` denotes :math:`a + bt + ct^3`. error_cov_type : {'diagonal', 'unstructured'}, optional The structure of the covariance matrix of the error term, where "unstructured" puts no restrictions on the matrix and "diagonal" requires it to be a diagonal matrix (uncorrelated errors). Default is "unstructured". measurement_error : bool, optional Whether or not to assume the endogenous observations `endog` were measured with error. Default is False. enforce_stationarity : bool, optional Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. Default is True. enforce_invertibility : bool, optional Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. Default is True. Notes ----- Generically, the VARMAX model is specified (see for example chapter 18 of [1]_): .. math:: y_t = A(t) + A_1 y_{t-1} + \dots + A_p y_{t-p} + B x_t + \epsilon_t + M_1 \epsilon_{t-1} + \dots M_q \epsilon_{t-q} where :math:`\epsilon_t \sim N(0, \Omega)`, and where :math:`y_t` is a `k_endog x 1` vector. Additionally, this model allows considering the case where the variables are measured with error. Note that in the full VARMA(p,q) case there is a fundamental identification problem in that the coefficient matrices :math:`\{A_i, M_j\}` are not generally unique, meaning that for a given time series process there may be multiple sets of matrices that equivalently represent it. See Chapter 12 of [1]_ for more information. Although this class can be used to estimate VARMA(p,q) models, a warning is issued to remind users that no steps have been taken to ensure identification in this case. References ---------- .. [1] Lütkepohl, Helmut. 2007. New Introduction to Multiple Time Series Analysis. Berlin: Springer. c  ^|_|_|_|_|_t |d_t |d_|dvr tdj dk(rjdk(r tdj dkDrjdkDrtdt|_ | _ tj\__jj dk(xrjddk(_t%|\_}j&dkD_t+|dst-j.|}t1j d} | jz_|j4d} | } | j2z}| j7dd| j7d t8t:zt=||f||| d | j&dkDsjdkDrj"sd j@_!i_"jFjzjDd <jFd zj zjDd<jFd zjzjDd<jFj&zjDd<jdk(rjFjDd<nDjdk(r5t jFjFdzzd z jDd<jFjzjDd<tIjDjK_&tOjjjPdzj}|dd_)|dd_*jdkDr j"rj&dkDr8t-jVjXjPfj@d<t-jZjF}dj@d|z<j dkDrXt-jZj dz jFz}|djFz|df}dj@d|z<t-jZjdz jFz}|d| dzjFzz|d| jFzzf}dj@d|z<t-jZjF}dj@d|z<|d| jFzz|df}jdkDrdj@d|z<j"r/j&dk(r t,j\dd| ddf_/n=jdkDsj&dkDrt,j\dd| ddf_/j dkDr t,j\dd| ddf_0nt,j\dd| | df_0jdk(r(dt-jZjFz_1n3jdk(r$t-jdjF_3jr'dt-jZjFz_4fd}d}|d |\_5}|d|\_6}|d|\_7}|d|\_8}|d|\_9}|d|\_:}d_;xjxgdt{| j}zz c_<y) Nrr )diagonal unstructuredz3Invalid error covariance matrix type specification.zNInvalid VARMAX(p,q) specification; at least one p,q must be greater than zero.zcEstimation of VARMA(p,q) models is not generically robust, due especially to identification issues.initialization stationaryinversion_method)exogk_statesk_posdefFtrendarma regressionr state_covrobs_cov)offsetstate_intercept)design) transition) selectionr-)r')r(c`j|}tj|||z}||z }||fSN) parametersnps_)keyr)length param_sliceselfs eC:\Crop_Prediction\Backend\crop-ai-system\venv\Lib\site-packages\statsmodels\tsa\statespace\varmax.py_slicezVARMAX.__init__.._slice s:__S)F%%v7K f F& &)orderr"error_cov_typemeasurement_errorenforce_stationarityenforce_invertibility)?r<r=r>r?r;intk_ark_ma ValueErrorrrr" trend_offsetrpolynomial_trendk_trendsize_trend_is_constrk_exogmle_regressionrr2 asanyarraymax_k_ordershape setdefaultr r super__init__ssm_time_invariantr1k_endogsumvaluesk_paramsrnobs _trend_data _final_trendzerosr diag_indicesr3_idx_state_intercept_idx_transition_idx_state_cov tril_indices_idx_lower_state_cov _idx_obs_cov _params_trend _params_ar _params_ma_params_regression_params_state_cov_params_obs_cov _final_exog _init_keyslistkeys)r7endogrr;r"r<r=r>r?rDkwargs _min_k_arrTr!r trend_dataidxr9r) __class__s` r8rQzVARMAX.__init__s -!2$8!%:" aM aM  != =/0 0 99>dii1n?@ @ 99q=TYY] =" $  (.@.L+t| $ 5 5 : :a ?!> $ 5 5a 8A = +40d#kkAo t,MM%(E 1% !DII- ++a.T]]* *L9 ,.?(.JK   x( FL ;;?t||a/8L8L',DHH $#'<<$,,#> $ a$)) ; $ a$)) ;(, t{{(B %   * ,+/<>    N 2(* (ED %  ! ! ,rt||/L LD  ' %+GV%<"F"(v"6"(v"6*0v*F')/ V)D&'-i'@$f  57;FKKM7JK Kr:c ,|j|fd|i|S)Nr)_clone_from_init_kwds)r7rmrrns r8clonez VARMAX.clone7s)t))%EdEfEEr:cdttfiS)Nfit) VARMAXResultsVARMAXResultsWrapper)r7s r8 _res_classeszVARMAX._res_classes:s ';<==r:ctj|jtj}t j |j j}|j}tj|jd}d}|jdkDr9|jdkDr*tj|j|jf}n7|jdkDr |j}n|jdkDr |j}tj tj"|r7tj tj"|d}||}|||}tjd}tjd}|jdkDs|jdkDrtj$j'|j)|}|tj(||z}|jdkDr|d|jj*}|j,dkDr||jdj*}g}|j.dkDr |j.nd} t1j2|} | j5| dd} |j.dkDr7tj6| j8j*j;}| j<}|j.dkDr|j>r|jA|j,|j.z|j,j*jA|j,|j,|j.j*} tCdgtE| z} | stGd |dz}g}|jHdkDrt1j2|}|j5|jHdd}tj6|j8j*j;}|jJr|jA|j,|jHz|j,j*jA|j,|j,|jHj*} tCdgtE| z}|stGd |dz}|j.dkDr|jdkDs |jLr|jA|j,|j.z|j,j*jA|j,|j,|j.j*} tjN|j,tjP| dz }|jdkDrtj(||}|jLdkDrtj(||}|jdkDr|j;||jR<|j.dkDr|||jT<|jHdkDr|||jV<|jLr|j;||jX<|jZd k(r(| j\j_||j`<nb|jZd k(rStj$jc| j\}||jdj;||j`<|jfr_|jHdkDr)j\j_||jh<|S| j\j_||jh<|S) NdtypeW) requirementsrr )axisn)maxlagsicr"z\Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.z\Non-stationary starting moving-average parameters found. Using zeros as starting parameters.rr)5r2r[rWfloat64pd DataFramermcopy interpolaterequirebfillrFrIc_rYranyisnanlinalgpinvdotTrTrArVARrwarrayparamsravelresidr>reshaperrkrrBr?rJeyerUrcrdrerfr<sigma_urrgcholeskyrar=rh)r7rrmrmask trend_params exog_paramstrendexog_params ar_paramsrAmod_arres_arcoefficient_matricesr ma_paramsmod_mares_ma invertibletmp cov_factors r8 start_paramszVARMAX.start_params>s$--rzz: TZZ__./!!# 5;;=s; <  RVVD"23 3E||a/ >@@ ||a.t||}=??   IIMtyyqu%DT= 99q=/11779I  99q=T66!!LL499,dll!gdllDLL$));q>B B B B   4<<( 4;;' DOOA&'qQ(8 9 9     * , t||,k!n, K N 2 t||,qs 456Q/[^,Ak!n-=>?? 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Notes ----- Constrains the factor transition to be stationary and variances to be positive. r ndminr|rrr#rr')r2rr[rNr}rcrAr>r<diagrgrRrarrrdrrTrrrBr?rrerfr=rh)r7 unconstrained constrainedr'state_cov_lower coefficientsrvariances r8transform_paramszVARMAX.transform_paramss,a8 hh}22-:M:MN +88J8J*K D&&' 99q=T66""j0GGM$2H2H$I1$LM $$6"$((488K+@+F+F1>1D1D#F"$"8"89  9 9:FF?O4E4EF )9AA dllTYY68L2, J + (+?+E+E+GK (+8+IK ( 99q=T77t||=3F3FGI(9AA dllTYY68L2, J + (+?+E+E+GK (+8+IK ( $11 2 D++,   * ,d445q8 .. / N 2d445 .. /  ! !d223Q6 ,, -r:cXtj|d}tj|j|j}||j ||j <|j dkDr/|jr"|jdk(r#tj||j}n|jdk(rttj|jdj|j}||j||j<tj||j}||jj!|j"|j"|j z}t%|\}}|j'||j<n||j||j<|j(dkDr|j*rtj,|j"|j}||j.j!|j"|j"|j(z}t%||\}}|j'||j.<n||j.||j.<||j0||j0<|jdk(r ||jdz||j<n+|jdk(r||j||j<|j2r||j4dz||j4<|S) a Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer. Parameters ---------- constrained : array_like Array of constrained parameters used in likelihood evaluation, to be transformed. Returns ------- unconstrained : array_like Array of unconstrained parameters used by the optimizer. r rr|rrrr'g?)r2rr[rNr}rcrAr>r<rrgrRrarrrdrrTrrrBr?rrerfr=rh)r7rrr'rrunconstrained_matricesrs r8untransform_paramszVARMAX.untransform_paramsRs hh{!4 !2!2+:K:KL -88J8J,K d(() 99q=T66""j0GGK0F0F$GH $$6"$((488K+@+F+F1<1B1B#D  6 67  9 9:FF?O4E4EF 't7?? dllTYY68L4L)L - "H-C-I-I-KM$// *-8-IM$// * 99q=T77t||;3D3DEI&t7?? dllTYY68L4L)L - "H-C-I-I-KM$// *-8-IM$// * // 0 d--.   * ,D223S8 $00 1 N 2D223 $00 1  ! !D00136 $.. /r:ct||tjt |j j dd}dtj|j|D\}}}}}}|jrj|jdkDr[|jdkDs|jdkDr=|j|}t|j|dkD}|r |s td|j rk|j"dkDr[|js|j"dkDr?|j|}t|j|dkD}|r|s tdyyyyy)Nr*c3<K|]}|jywr0)tolist).0arrs r8 z2VARMAX._validate_can_fix_params..s,J CJJL,Jsrr zCannot fix individual autoregressive parameters when `enforce_stationarity=True`. In this case, must either fix all autoregressive parameters or none.zCannot fix individual moving average parameters when `enforce_invertibility=True`. In this case, must either fix all moving average parameters or none.)rP_validate_can_fix_paramsr2cumsumrkr1rV array_splitrr>rArT issupersetlen intersectionrCr?rB) r7rix_ar_namesma_namesfix_allfix_anyrrs r8rzVARMAX._validate_can_fix_paramssS (5 YYtDOO2245 6s ;,J$&NN43C3CR$H,J(Hh1a  $ $Q||a499q=%00: 00:;a?7$!""  % %$))a-||tyy1}%00: 00:;a?7$!""$+7 -+8 %r:c|j|||}|jr||jj|j|j j }tj|jdd|}|j |j|j<|j|jd j@|j} ||j:| |jB<tj| | j |jd <|jDr'||jF|j|jH<yy) N) transformedincludes_fixedr r+r*rr|rrr')% handle_paramsrJrfrrTrIrr2rrrRr]rirFrr}rcrHrYrZstopnanrdrArerBrr^r<rgr_r[rNrar=rhrb) r7rrr complex_stepr interceptzerorrr$r%rs r8updatez VARMAX.updates##F 3A$C    !8!89AA dkk++,1 tyy}k:I2;++DHHT.. /+AC$$kB3*MT\\M2=> < /!!-11"5::b@*MT\\M23>?266%%|D556Q7?   4#3#3#;((2666C=@DHH&  r9 :DOO $ , , LL$,,24 DOO $ , , LL$,,24)+r2v%%&   * ,t--. HHT(( ) N 2 hhtxx '<'B'B-3\\;Ot--. D55 6$&FF?O8D:::d2Ah?D $D  + *D ":$(+T[[N(;(+DJJ&9::: +D s7AC $B.C6C:CACC CCc  |j|5t|||f||||||| | | | d | }ddd|S#1swYSxYw)N) measurement_shocks state_shocks initial_stateanchor repetitionsr extend_model extend_kwargsrr)rrPsimulate)r7r nsimulationsrrrrrrrrrrrnoutrrs r8rzVARMAX.simulate)sm  ! !$ ' '" 9K);T)'   C    s :A)N)r rcrFTTr r0)TFF) NNNNNNNNTF)__name__ __module__ __qualname____doc__rQrupropertyrzrrrrrr contextlibcontextmanagerrrr r __classcell__rrs@r8rrsbH>ABGBFqKfF>>~~@==~QfKZ"<?D!AGF&+&+Ph''(@D?C;?FK ) r:rcneZdZdZ d fd Zd dZejdZejdZ e e jj d fd Z e e jj d fd Z ddZe e jjdfd ZxZS)rxa Class to hold results from fitting an VARMAX model. Parameters ---------- model : VARMAX instance The fitted model instance Attributes ---------- specification : dictionary Dictionary including all attributes from the VARMAX model instance. coefficient_matrices_var : ndarray Array containing autoregressive lag polynomial coefficient matrices, ordered from lowest degree to highest. coefficient_matrices_vma : ndarray Array containing moving average lag polynomial coefficients, ordered from lowest degree to highest. See Also -------- statsmodels.tsa.statespace.kalman_filter.FilterResults statsmodels.tsa.statespace.mlemodel.MLEResults c $t ||||||fi|tdi|jj|jj |jj |jj|jj|jj|jj|jj|jj|jj|jjd |_d|_d|_|jjdkDrt%j&|j(|jj*}|jj,}|jj} |j/|| z|j0j/||| j0|_|jjdkDrt%j&|j(|jj2} |jj,}|jj} | j/|| z|j0j/||| j0|_yy)N) r<r=r>r?rDr;rArBr"rFrIr)rPrQrmodelr<r=r>r?rDr;rArBr"rFrI specificationcoefficient_matrices_varcoefficient_matrices_vmar2rrrdrTrrre) r7rrfilter_resultscov_typecov_kwdsrnrrTrArrBrrs r8rQzVARMAXResults.__init__Ss  6>8X AG # "jj77!%!=!=$(JJ$C$C%)ZZ%E%E JJ33ZZ%%JJOOJJOOZZ%%zz))jj''#&  *)-%(,% ::??Q TZZ-B-B!CDIjj((G::??D!!'D.':<<ggw-aa  ) ::??Q TZZ-B-B!CDIjj((G::??D!!'D.':<<ggw-aa  ) r:c n|V|j|j|j|dd}|j}|jd}|jd}n|jd}|jd}|j d|j|j jz|j j|fd|i|}t|jd|||j_ |j|j|j} | S|j!|j} | S) Nr )r).r).r*rDrknownconstantstationary_cov)get_predictionrXprediction_resultspredicted_statepredicted_state_covrOrrDrurr rRrsmoother_resultssmoothrfilter) r7rmrrnfcast fcast_resultsrinitial_state_covmodress r8extendzVARMAXResults.extends  '' 49948'LE!44M)99&AM - A A& I  009M $ 8 8 A .$))djj6M6M*MNdjju:4:6:!/ LL'M,".  ,**T[[)C **T[[)C r:c#K|j}|j|5|jjdddf}|j |j |dd|j df|jjd|j df< d||jjdddf< dddy#||jjdddf<wxYw#1swYyxYww)az Set the final state intercept value using out-of-sample `exog` / trend Parameters ---------- exog : ndarray Out-of-sample `exog` values, usually produced by `_validate_out_of_sample_exog` to ensure the correct shape (this method does not do any additional validation of its own). out_of_sample : int Number of out-of-sample periods. Notes ----- This context manager calls the model-level context manager and additionally updates the last element of filter_results.state_intercept appropriately. Nr*r+)rrrr+rrrT)r7rrrs r8rzVARMAXResults._set_final_exogs(jj   & I--==aeDK JJt{{ #%| |R78    / /  b0@ A I=H##33ArE: I I>I##33ArE: I Is5C,A2C B>C 5 C,>CC  C)%C,c#K|xr|jjdkD}|r{t|jjddt j d|jj fg}|jjdkDr(t|jjdd|ddg}nd}|jj|jzdz }|jj|||}|jjdddf}|jjdddddf} |jj|| |j!|j"ddd } | jdddf|jjdddf< d|r,tj$|jjdddf<yy#|r,tj$|jjdddf<wwxYww) a Set the final predicted state value using out-of-sample `exog` / trend Parameters ---------- exog : ndarray Out-of-sample `exog` values, usually produced by `_validate_out_of_sample_exog` to ensure the correct shape (this method does not do any additional validation of its own). out_of_sample : int Number of out-of-sample periods. Notes ----- We need special handling for forecasting with `exog`, because if we had these then the last predicted_state has been set to NaN since we did not have the appropriate `exog` to create it. rr*Nr )rrDrT)rr return_ssm)rrIrrmr2r[rTrrDrXrurr r rRinitialize_knownrrr) r7r out_of_sampleflag tmp_endogtmp_exogtmp_trend_offsettmp_modrrtmp_ress r8_set_final_predicted_statez(VARMAXResults._set_final_predicted_states(6!2!2Q!6    %rxxDJJ4F4F0G'H JKIzz  1$!4::??23#7bq"BC#zz66BQF jj&&yx4D'FG**::1b5AH!00DDQ2XNN KK ( ((8F ) HnnT[[d48T%KG ''2.    / /2 6 D =?VV##33ArE:t=?VV##33ArE:sFHG#/H0HHc |d}|jj|||d\}} } } |jj|| }i} |jjdkDr&|jj|j z| d<|j |5|j|| 5t|$d||||||| d|} dddddd S#1swYxYw#1swY SxYw)NrT)silentrD)startenddynamicinformation_setindexrrr) r_get_prediction_index_validate_out_of_sample_exogrFrDrXrr!rPr)r7r$r%r&r'r(rrn_start_endrrrrrrs r8rzVARMAXResults.get_predictions  =E JJ , ,UCt , L 'mQzz66t]K ::   ! ''$))3 . ) ! !$ ' ;00}E ;g,;S'$35t"/;4:; ; ;   ; ; ;  s$C!+CC!C C!!C+c ||dk(rd} n1|dk(r |j} n|jj|\} } } | dkr|j| z} | |jkDr tdt | |z|jz d} |jj || }|j || 5t| |f|||||||| d| }ddd|S#1swYSxYw)Nr$rr%z4Cannot anchor simulation after the estimated sample.)rrrrrrrr) rXr_get_index_locrCrLr*r!rPr)r7rrrrrrrrrrnilocrrrrrs r8rzVARMAXResults.simulates  >Vw.D u_99D226:JD!Q !899t#D $)) () )D</$));Q? zz66t]K  , ,T= A '"1C);T)   C    s 5CC#cd}|j|jz }|jjdkDr|dkDr|jj| d}t j 5} | j |jj|| j |j|||jj|j||||} ddd| S#1swY SxYw)Nr)r$r%revisions_details_start state_index) rXrrIrr ExitStack enter_contextrr!r news) r7previousr$r%periodsr1r2rrstackrs r8_news_previous_resultsz$VARMAXResults._news_previous_results(s HMM1 ::  q ]Q%6::??M>?3D ! ! # )u    > >t D E    C Cm!% &'',,))C(?'-)C  )  ) s (A6C((C2c  ddlm|j}|jdkDr/|jdkDr d}d|jd|jd}n2|jdkDrd}d|jz}nd }d|jz}|j dkDr|d z }||zg}|j dkDr|jd |jr|jd t|)||| }|rtjt|j}dfd } |jj } |jj} |jj} |jj } |jj }g}t#| D]}g}d}| dkDr4|jtj||| | zz| || | zz }| dkDrF|| z| z}|dz| z| z}|j|tj||z|| | dzzz }| dkDrF|| z| z}|dz| z| z}|j|tj||z|| | dzzz }|dkDr9|j|tj||z|dz|zz|| |zz }|jjr@|jtj$|jj&|z dz dtj(|}|j||jj*}t-|t.s|g}d||z}| |||}|j0j|tjt|j|jj2}| ||dd}|j0j|g}||gfD]E}tj$|j5}t|dkDs5|j|Gtj(|}tj$t/t7|j9t7|}t|dkDr'| ||dd}|j0j||S)Nr)summary_paramsVARMA(,)rz(%s)VMAXrzmeasurement error)alphar$ model_namedisplay_paramsc||j||j||j||j||j |f}g}t j |jj|jD]N}|r$dj|jddd}n|}||jvrd|z}|j|P |d|d|S)Nrr*z %s (fixed)F)ynamexnamerBuse_ttitle)rbsezvaluespvaluesconf_intr2rdatarrjoinsplit fixed_paramsappend) r7rrI strip_endrrname param_namerBr;s r8 make_tablez)VARMAXResults.summary..make_tablefsT[[.||D)4<<+=}}U+D13! HHTYY%:%:;DAHHJ3D %(XXdjjocr.B%C %) t000%1J%> &&z23&c[,1eMMr:r r#rzResults for equation %szError covariance matrixF)rSzOther parameters)T)statsmodels.iolib.summaryr;rrArBrIrFrRr=rPsummaryr2arangerrrrTrrrW concatenaterrrktablesrgflattenset difference)r7rBr$separate_paramsspecrCr;rXindicesrVrTrArBrFrI endog_masksrmasksr)r%rrrItablestate_cov_maskm inverse_maskr;rrs ` @r8rXzVARMAXResults.summaryEsh<!! 99q=TYY] J {!DII;a0E YY]Jdii(EJdii(E ;;? # J 5() <rs.)3/''=6==*X XX vHJHV /,/*M:r: