!g,>dZddlmZddlmZddlmZddlmZddl Z ddl Z ddl mZddlmcmZddlmZddlmZmZdd lmZdd lmZdd lmZdd lmZm Z ddl!m"cm#Z"dd l!m$Z$m%Z%m&Z&ddl'm(Z(m)Z)m*Z*ddl+m,Z,m-Z-m.Z.ddl/m0Z0ddl1m2Z2d,dZ3d-dZ4d.dZ5dZ6dZ7e7Z8d.dZ9dZ: d/dZ;dZd1dZ?GddZ@Gd d!eZAGd"d#ZBGd$d%eBZCGd&d'ejZEejeEeCGd(d)ZGd2d*ZHd+ZIy)3u Vector Autoregression (VAR) processes References ---------- Lütkepohl (2005) New Introduction to Multiple Time Series Analysis ) annotations)lrange) defaultdict)StringION) SimpleTable)cache_readonlydeprecated_alias) logdet_symm) OutputWarning) array_like)TimeSeriesModelTimeSeriesResultsWrapper)duplication_matrixunvecvec)outputplottingutil)CausalityTestResultsNormalityTestResultsWhitenessTestResults) IRAnalysis VARSummaryc D|j\}}}tj|dz||f}tj||d<t d|dzD]J}t d|dzD]6}||kDr||xxtj |||z ||dz z cc<8L|S)a MA(\infty) representation of VAR(p) process Parameters ---------- coefs : ndarray (p x k x k) maxn : int Number of MA matrices to compute Notes ----- VAR(p) process as .. math:: y_t = A_1 y_{t-1} + \ldots + A_p y_{t-p} + u_t can be equivalently represented as .. math:: y_t = \mu + \sum_{i=0}^\infty \Phi_i u_{t-i} e.g. can recursively compute the \Phi_i matrices with \Phi_0 = I_k Returns ------- phis : ndarray (maxn + 1 x k x k) r)shapenpzeroseyerangedot)coefsmaxnpkphisijs `/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/tsa/vector_ar/var_model.pyma_repr+,s4kkGAq! 88TAXq!$ %DffQiDG1dQh 9q!a% 9A1u Grvvd1q5k5Q<8 8G  99 Kctj|}tjj |}|r0t dtj |D] }t |tj |dkjS)z Determine stability of VAR(p) system by examining the eigenvalues of the VAR(1) representation Parameters ---------- coefs : ndarray (p x k x k) Returns ------- is_stable : bool zEigenvalues of VAR(1) repr)r comp_matrixrlinalgeigvalsprintabsall)r#verboseA_var1eigsvals r* is_stabler8Usp  e $F 99  V $D )*66$< C #J  FF4LA  " " $$r,c $|j\}}}||}tj|dz||f}t|||d|t ||dzD]?}t |D]/}||xxtj |||||z dz z cc<1A|S)u Compute autocovariance function ACF_y(h) up to nlags of stable VAR(p) process Parameters ---------- coefs : ndarray (p x k x k) Coefficient matrices A_i sig_u : ndarray (k x k) Covariance of white noise process u_t nlags : int, optional Defaults to order p of system Notes ----- Ref: Lütkepohl p.28-29 Returns ------- acf : ndarray, (p, k, k) Nr)rrr_var_acfr!r") r#sig_unlagsr%r&_resulthr)s r*var_acfr@ms,kkGAq! }XXuqy!Q' (F%'F2AJ1eai =q =A 1Ia&Q*;< z , BIC -> z , FPE -> z , HQIC -> >) __module__ __class____name__strrrrrrs r*__str__zLagOrderResults.__str__sn $.."9"9!:;""%dhh- #dhh-I$((m_KDII/?q B r,NF)rr __qualname____doc__rrrr,r*rrs, *  r,rc~eZdZdZedddZ d fd Zd dZ d ddZdd Z dd Z e dd Z xZ S)ru Fit VAR(p) process and do lag order selection .. math:: y_t = A_1 y_{t-1} + \ldots + A_p y_{t-p} + u_t Parameters ---------- endog : array_like 2-d endogenous response variable. The independent variable. exog : array_like 2-d exogenous variable. dates : array_like must match number of rows of endog References ---------- Lütkepohl (2005) New Introduction to Multiple Time Series Analysis rZrz0.11.0)remove_versionct|||||||jjdk(r t d|jj d|_t||_y)N)missingrzOnly gave one variable to VAR) superrrndimrYrrQrLn_totobs)rrr\rfreqrrs r*rz VAR.__init__#sZ eT7C ::??a <= =JJ$$Q' E  r,ctj|}||}|j||\}}}}||kr td|||zk(rtjgSt j |}|j } |} tj|dz|z |z| f} |dk7r |d|} | | z } |j} t j| ||d}tj||}|| z }tt| t||z }tt||| z dz}|||| d||s| S| | d} ||dj| | | fjdd}t| | || |d| S)z< Returns in-sample predictions or forecasts Nzend is before startrrraiser has_constantrB)rrE_get_prediction_indexrYrget_trendorderrQrr get_var_endogr"minrLreshapeswapaxesr`)rrstartendlagsr out_of_sampleprediction_indexrr&rpredictedvalues interceptrZx fittedvaluesfv_startpv_endfv_endr#s r*predictz VAR.predict,s&! =E  & &uc 2      ;23 3 %-' '88B< %%e, II((C!GeOm$CQ#GH a<x(I y (O JJ   q$e' Jvva( 4<S)3|+**7*;J:r* 6*-/:r*Dj!6$CD|%%e,//--d.>.>gNMMD(  99 !0-2$))//!2D,E"'(X\""   '* !))""78,- II  !mm88 YY  tyy// 0  !!$e!44"s G c tj|x|_}|dkr td|j|z |z }|j |d}|j dn|j |d}tj|||d}|tj|| dddd} || d} tj| | f} ~ |} tj| jd| jd|jdzf}| ddd|jf|ddd|jf<| |dd|j|j| jdzf<| dd|jdf|dd|j| jdzdf<~ ~ t|jD]} tj|dd| fdk(jr|dd| fxx|z cc<tjtj|dd| fdk(jstj|dd| f|zdz|dd| f<||d} tj j#|| d d}| tj$||z }t'| }|||jdz }||j(|z|zz }tj$|j*|}|r||z }n$tj,|tj.}t1||||||j2||j4j6||j }t9|S) a lags : int Lags of the endogenous variable. offset : int Periods to drop from beginning-- for order selection so it's an apples-to-apples comparison trend : {str, None} As per above rzoffset must be >= 0NrrrrrBgV瞯<)rcond)rrrrr\)rrrrYrrr\rr column_stackemptyrr!diffr3rjr/lstsqr"rLrQrM full_likenanrrrrVARResultsWrapper)rroffsetrrrxrr\zrx_insttemp_zr(y_samplerrvavobsdf_residsserwvarfits r*rzVAR._estimate_vars#"&!4!4U!;; w A:23 3}}t#f, 67#yy(tdii.@   ud%g N  ""dUV asA4%&\FF ,AF!''!*aggaj1771:&=>?A#)!^t||^*;#Aa qwwqz 999 :06q$,,.7H0IAa *,, -t||$ 9A!Q$ A%**,!Q$4!Q$()Q.335771QT7+d2q8!Q$  9<HE:1=266!V,,H    tzz!} $GDII,w67ffUWWe$ (NELLbff-E    ""))//  !((r,c|jdr t|nd}|j|jz |z d|jzz}|=t t dt|j dz dzz}t||}n||kDr tdtt}|j|dk7rdnd}t||dzD]O}|j|||z | }|jjD]\} } || j!| Q|jD cic],\} } | t#j$| j'|z.} } } t)|| d Scc} } w) a  Compute lag order selections based on each of the available information criteria Parameters ---------- maxlags : int if None, defaults to 12 * (nobs/100.)**(1./4) trend : str {"n", "c", "ct", "ctt"} * "n" - no deterministic terms * "c" - constant term * "ct" - constant and linear term * "ctt" - constant, linear, and quadratic term Returns ------- selections : LagOrderResults r~rr gY@g?zwmaxlags is too large for the number of observations and the number of equations. The largest model cannot be estimated.r)r&rF)r) startswithrLrrQrroundrrrYrlistr\r!r info_criteriaitemsrrrEargminr) rrrntrend max_estimablerp_minr%r>r&rrs r*r zVAR.select_order su& %//4U!2V;TYYO ?%c$**o&=7%K KLMG'=1G& ! $YY*eslugk* !A'''A+U'KF,,224 !1A a  !  !9<  041Arxx{!!#e+ +  sO%@@  s21E4ctd)zM Not implemented. Formulas are not supported for VAR models. z*formulas are not supported for VAR models.NotImplementedError)clsformularsubset drop_colsargskwargss r* from_formulazVAR.from_formula@s""NOOr,)NNNnone)NNrr~)NolsNr~F)rz int | None)rr~)Nr~NN)rrrrr rZrrrrr  classmethodrC __classcell__rs@r*rr sr& gh?A@F#/f#  Y5Y5vP)d4Al37PPr,rceZdZdZ ddZdZdZddZddZddZ d Z d Z dd Z dd Z d ZedZedZddZddZddZddZdZeZdZd dZdZy)! VARProcessa Class represents a known VAR(p) process Parameters ---------- coefs : ndarray (p x k x k) coefficients for lags of endog, part or params reshaped coefs_exog : ndarray parameters for trend and user provided exog sigma_u : ndarray (k x k) residual covariance names : sequence (length k) _params_info : dict internal dict to provide information about the composition of `params`, specifically `k_trend` (trend order) and `k_exog_user` (the number of exog variables provided by the user). If it is None, then coefs_exog are assumed to be for the intercept and trend. Nczt||_|jd|_||_||_||_||_|i}|jdd|_ |j D|j jdk7r|j jdnd}||jz }nd}|jd||_ |j|jz|_ |jdkDr&|jdk(r|dddf|_ y||_ ytj|j|_ y)Nr k_exog_userrrrB)rLrrrQr# coefs_exogrOrgetrMrrk_exogrrr)rr#rNrOr _params_infok_exk_cs r*rzVARProcess.__init___s J KKN  $   L'++M1= ?? &/3/C/Cq/H4??((+aD)))CC#'' 37 llT%5%55 <>#333,,, r,c0t|j|S)aXDetermine stability based on model coefficients Parameters ---------- verbose : bool Print eigenvalues of the VAR(1) companion Notes ----- Checks if det(I - Az) = 0 for any mod(z) <= 1, so all the eigenvalues of the companion matrix must lie outside the unit circle )r4)r8r#)rr4s r*r8zVARProcess.is_stablesW55r,c d}||jdkDs|jdkDr\|jddd|jfj |j j }|jjd}n|j}n|jd}||d}n|}n|||k7r tdtj|j||j||||}|S)a( simulate the VAR(p) process for the desired number of steps Parameters ---------- steps : None or int number of observations to simulate, this includes the initial observations to start the autoregressive process. If offset is not None, then exog of the model are used if they were provided in the model offset : None or ndarray (steps, neqs) If not None, then offset is added as an observation specific intercept to the autoregression. If it is None and either trend (including intercept) or exog were used in the VAR model, then the linear predictor of those components will be used as offset. This should have the same number of rows as steps, and the same number of columns as endogenous variables (neqs). seed : {None, int} If seed is not None, then it will be used with for the random variables generated by numpy.random. initial_values : array_like, optional Initial values for use in the simulation. Shape should be (nlags, neqs) or (neqs,). Values should be ordered from less to most recent. Note that this values will be returned by the simulation as the first values of `endog_simulated` and they will count for the total number of steps. nsimulations : {None, int} Number of simulations to perform. If `nsimulations` is None it will perform one simulation and return value will have shape (steps, neqs). Returns ------- endog_simulated : nd_array Endog of the simulated VAR process. Shape will be (nsimulations, steps, neqs) or (steps, neqs) if `nsimulations` is None. NrrzKif exog or offset are used, then steps mustbe equal to their length or None)rPseedinitial_values nsimulations)rMrrrPr"rNrMrrrYrvarsimr#rO)rrPr&r\r]r^steps_rZs r* simulate_varzVARProcess.simulate_varsJ >!#t||a'7**1m m+;<@@OO%%**003\\!_F =~!evo 7 KK JJ  LL)% r,cT|j|||}tj|S)zc Plot a simulation from the VAR(p) process for the desired number of steps )rPr&r\)rarplot_mts)rrPr&r\rZs r*plotsimzVARProcess.plotsims,   E&t  D  ##r,cjtjj|j|jS)u Long run intercept of stable VAR process Lütkepohl eq. 2.1.23 .. math:: \mu = (I - A_1 - \dots - A_p)^{-1} \alpha where \alpha is the intercept (parameter of the constant) )rr/rC _char_matrrs r*intercept_longrunzVARProcess.intercept_longruns!yyt~~t~~>>r,c"|jS)uS Long run intercept of stable VAR process Warning: trend and exog except for intercept are ignored for this. This might change in future versions. Lütkepohl eq. 2.1.23 .. math:: \mu = (I - A_1 - \dots - A_p)^{-1} \alpha where \alpha is the intercept (parameter of the constant) )rgrs r*rzVARProcess.means%%''r,c0t|j|S)z Compute MA(:math:`\infty`) coefficient matrices Parameters ---------- maxn : int Number of coefficient matrices to compute Returns ------- coefs : ndarray (maxn x k x k) r)r+r#)rr$s r*r+zVARProcess.ma_rep sdjjt,,r,ct|||S)a Compute orthogonalized MA coefficient matrices using P matrix such that :math:`\Sigma_u = PP^\prime`. P defaults to the Cholesky decomposition of :math:`\Sigma_u` Parameters ---------- maxn : int Number of coefficient matrices to compute P : ndarray (k x k), optional Matrix such that Sigma_u = PP', defaults to Cholesky descomp Returns ------- coefs : ndarray (maxn x k x k) )r)rr$rs r*rzVARProcess.orth_ma_reps"4q))r,cTtjj|jS)zwCompute long-run effect of unit impulse .. math:: \Psi_\infty = \sum_{i=0}^\infty \Phi_i )rr/rrfrs r*long_run_effectszVARProcess.long_run_effects,syy}}T^^,,r,cTtjj|jSN)rr/rrOrs r*rzVARProcess._chol_sigma_u5syy!!$,,//r,cxtj|j|jj dz S)z Characteristic matrix of the VARr)rr rQr#rrs r*rfzVARProcess._char_mat9s)vvdii 4::>>!#444r,cFt|j|j|S)zwCompute theoretical autocovariance function Returns ------- acf : ndarray (p x k x k) r<)r@r#rOrr<s r*rJzVARProcess.acf>stzz4<Please provide an exog_future argument to the forecast method. exog_futureTrB)optionalrrzexog_future only has z# observations. It must have steps (z) observations. r~rttt)r\rYr rrNsizerMrr1rronesrcrrr`r#)rrZrPr~err_msgr[exogsexog_lin_trends r*r`zVARProcess.forecast_s" 99 !8&  99 [%8'  ! A   "  #u,!''*+, w!))"oo22a7dT__=N=N  ::  % LL ( MMA t}}q058  $**  LL ( 4::  LL1, -  " LL %K//%0K4::{E;GGr,c&|j|}t|j}tj|||f}tj||f}t |D]-}||}||jz|j z}||zx||<}/|S)a] Compute theoretical forecast error variance matrices Parameters ---------- steps : int Number of steps ahead Notes ----- .. math:: \mathrm{MSE}(h) = \sum_{i=0}^{h-1} \Phi \Sigma_u \Phi^T Returns ------- forc_covs : ndarray (steps x neqs x neqs) )r+rLrOrrr!rM) rrPrNr&rRrSr?rTrUs r*rbzVARProcess.mses";;u%  HHeQ]+ !Q u /A1+C $suu,C#(3; .IaL5  / r,cv|j|}tj|j}|dd||fSrn)rVrrcrQ)rrPrdres r*rfzVARProcess._forecast_varss7  'yy#AtTM""r,c d|cxkrdkstdtdtj|}|j|||}t j |j |}|||zz }|||zz} ||| fS)u Construct forecast interval estimates assuming the y are Gaussian Parameters ---------- y : {ndarray, None} The initial values to use for the forecasts. If None, the last k_ar values of the original endogenous variables are used. steps : int Number of steps ahead to forecast alpha : float, optional The significance level for the confidence intervals. exog_future : ndarray, optional Forecast values of the exogenous variables. Should include constant, trend, etc. as needed, including extrapolating out of sample. Returns ------- point : ndarray Mean value of forecast lower : ndarray Lower bound of confidence interval upper : ndarray Upper bound of confidence interval Notes ----- Lütkepohl pp. 39-40 rrzalpha must be between 0 and 1)r~)rYrrir`rrjrf) rrZrPrkr~rlrmrnrorps r*rqzVARProcess.forecast_intervals>5}1}<= =<= =  " "5 )q%[I++E23#a%i/ #a%i/ z:55r,c|jjd}|jjd}|j}tj|tj|dz }tj |dz ||f}t |dz D]"}tj||dzdd ||<$tj|d}||dS)to_vecmrrN)GammaPi)r#rridentityrrr! concatenate)rr&r%rGrugammar(s r*rzVARProcess.to_vecms JJ  Q  JJ  Q  JJ{{1~q! , -!a%A'q1u 0A!a%' A./E!H 0ua(b))r,rFr)NNNNN)NNN rNrnr)皙?N)rrrrrrWrr8rardrgrr+rrlrrrfrJrur|r`rbrVrfrqrrr,r*rKrKJs*DH1>0 6JX$ ? ( -*&-0055>8"9Hx>L#)6V *r,rKceZdZdZdZ d5fd ZdZedZedZ e dZ e dZ d6d Z d6d Zd7d Zd6d Zd6d Ze dZe dZdZdZe dZedZe dZe dZe dZeZe dZe dZe dZe dZe dZ e dZ!e dZ"e dZ#d8dZ$d9d Z% d:d!Z& d;d"Z'd#Z(d$Z)d%Z*dd)Z.d?d*Z/d@d+Z0dAd,Z1d?d-Z2e d.Z3e d/Z4ed0Z5ed1Z6ed2Z7ed3Z8e d4Z9xZ:S)BraEstimate VAR(p) process with fixed number of lags Parameters ---------- endog : ndarray endog_lagged : ndarray params : ndarray sigma_u : ndarray lag_order : int model : VAR model instance trend : str {'n', 'c', 'ct'} names : array_like List of names of the endogenous variables in order of appearance in `endog`. dates exog : ndarray Attributes ---------- params : ndarray (p x K x K) Estimated A_i matrices, A_i = coefs[i-1] dates endog endog_lagged k_ar : int Order of VAR process k_trend : int model names neqs : int Number of variables (equations) nobs : int n_totobs : int params : ndarray (Kp + 1) x K A_i matrices and intercept in stacked form [int A_1 ... A_p] names : list variables names sigma_u : ndarray (K x K) Estimate of white noise process variance Var[u_t] rc ||_||_||_| |_|jj\|_} |j |z |_||_tj|} tj||| |jj|_ ||_| |_| } | | jd}| |z } nd}|j| d}|j!|| | f}|j#ddj%}|d| j&|_|j(jd|_||_| ||d}t.|a||j(|||y)NrrrB)rrMr)rrQ)rrrrrrrxrrrr r orig_exogr rr\rrcopyrMrNrPrMrr)rrrrrOrrrrrr\rQr endog_startrMreshapedr#rQrs r*rzVARResults.__init__+sj  ( "jj.. tMMI-  %%e,-- 9guzz';';     **Q-K ; &KK;;{|,##Yd$;<!!!Q',,. +.00oo++A. & &   OO %  r,cntj|j|j|jS)zPlot input time series)rindex)rrcrrrrs r*plotzVARResults.plotis(  JJdjj   r,cN|j|jz|jzS)z_ Number of estimated parameters per variable, including the intercept / trends )rQrrPrs r*df_modelzVARResults.df_modelos yy499$t{{22r,c4|j|jz S)z;Number of observations minus number of estimated parameters)rxrrs r*r,zVARResults.df_residvsyy4==((r,cVtj|j|jS)zW The predicted insample values of the response variables of the model. )rr"rrrs r*rzVARResults.fittedvalues{s vvd''55r,cN|j|jd|jz S)zV Residuals of response variable resulting from estimated coefficients N)rrrrs r*rvzVARResults.resids$ zz$))+&):):::r,cJt|j|jd|S)z Sample acovNrq) _compute_acovrrrrs r* sample_acovzVARResults.sample_acovsTZZ 4EBBr,c<|j|}t|S)z Sample acorrrq)r_acovs_to_acorrsrr<acovss r* sample_acorrzVARResults.sample_acorrs   u -&&r,cTtj|j||}|S)a Plot sample autocorrelation function Parameters ---------- nlags : int The number of lags to use in compute the autocorrelation. Does not count the zero lag, which will be returned. linewidth : int The linewidth for the plots. Returns ------- Figure The figure that contains the plot axes. rqrw)rryrrzs r*plot_sample_acorrzVARResults.plot_sample_acorrs."&&   E  *i  r,c0t|j|S)z Compute centered sample autocovariance (including lag 0) Parameters ---------- nlags : int Returns ------- rq)rrvrrs r* resid_acovzVARResults.resid_acovsTZZu55r,c<|j|}t|S)z Compute sample autocorrelation (including lag 0) Parameters ---------- nlags : int Returns ------- rq)rrrs r* resid_acorrzVARResults.resid_acorrse,&&r,c*|jddS)z6 Centered residual correlation matrix r)rrs r* resid_corrzVARResults.resid_corrs "1%%r,c|jstj|jS|j|jz|jz S)z@(Biased) maximum likelihood estimate of noise process covariance)r,rrrOrxrs r* sigma_u_mlezVARResults.sigma_u_mles:}}==. .||dmm+dii77r,c|j}tjtjj |j |z|j S)uTEstimated variance-covariance of model coefficients Notes ----- Covariance of vec(B), where B is the matrix [params_for_deterministic_terms, A_1, ..., A_p] with the shape (K x (Kp + number_of_deterministic_terms)) Adjusted to be an unbiased estimator Ref: Lütkepohl p.74-75 )rrrDr/rrMrO)rr's r* cov_paramszVARResults.cov_paramss9   wwryy}}QSS1W-t||< Estimated covariance matrix of vech(sigma_u) rB) tsarrQrr/pinvrDrOrM)rD_KD_Kinvsigxsigs r* _cov_sigmazVARResults._cov_sigmasZ $$TYY/$''$,, 56zG#fhh..r,cXt|j|j|jS)zCompute VAR(p) loglikelihood)r|rvrrxrs r*llfzVARResults.llfs!4::t'7'7CCr,ctjtj|j}|j |j |j fdS)z:Standard errors of coefficients, reshaped to match in sizeC)r)rrjdiagrrrrQ)rstderrs r*rzVARResults.stderrsB!234~~t}}dii8~DDr,c8|j}|j|dS)Stderr_endog_laggedNrPrrrs r*stderr_endog_laggedzVARResults.stderr_endog_laggeds {{56""r,c8|j}|jd|S) Stderr_dtNrrrs r* stderr_dtzVARResults.stderr_dt!skk{{4C  r,c4|j|jz S)zm Compute t-statistics. Use Student-t(T - Kp - 1) = t(df_resid) to test significance. )rrrs r*tvalueszVARResults.tvalues's {{T[[((r,c8|j}|j|dS)tvalues_endog_laggedNrPrrs r*rzVARResults.tvalues_endog_lagged/ ||EF##r,c8|j}|jd|S) tvalues_dtNrrs r*rzVARResults.tvalues_dt5kk||DS!!r,cdtjjtj|j zS)zW Two-sided p-values for model coefficients from Student t-distribution rB)rnormrrr2rrs r*pvalueszVARResults.pvalues;s) 5::== !5666r,c8|j}|j|dS)pvalues_endog_laggdNrPrrs r*pvalues_endog_laggedzVARResults.pvalues_endog_laggedCrr,c8|j}|jd|S) pvalues_dtNrrs r*rzVARResults.pvalues_dtIrr,c|j|j|j d||\}}}tj|j||||j |}|S)z Plot forecast N)rk)r plot_stderr)rqrrr plot_var_forcr)rrPrkrmidlowerrr{s r* plot_forecastzVARResults.plot_forecastQsk!22 JJ z| $e53 UE$$ JJ   **#   r,c|j|}|dk(r |S|dk(r]|jdk(rL|jdkr=||j||jz z }ddl}|j dtd|Std ) uOCompute forecast covariance matrices for desired number of steps Parameters ---------- steps : int Notes ----- .. math:: \Sigma_{\hat y}(h) = \Sigma_y(h) + \Omega(h) / T Ref: Lütkepohl pp. 96-97 Returns ------- covs : ndarray (steps x k x k) rbautorrBrNz4forecast cov takes parameter uncertainty intoaccount) stacklevelz'method has to be either 'mse' or 'auto') rbrPr_omega_forc_covrxwarningswarnr rY)rrPrfc_covrs r*rVzVARResults.forecast_covds"% U?  v {{aDLL1$4$..u5 AA M!!" FG Gr,c|j||||||}tj|d} tt |dz |zdz } tt d|dz z |zdz } | | ddddddf} | | ddddddf} | | fS)u Compute Monte Carlo integrated error bands assuming normally distributed for impulse response functions Parameters ---------- orth : bool, default False Compute orthogonalized impulse response error bands repl : int number of Monte Carlo replications to perform steps : int, default 10 number of impulse response periods signif : float (0 < signif <1) Significance level for error bars, defaults to 95% CI seed : int np.random.seed for replications burn : int number of initial observations to discard for simulation cum : bool, default False produce cumulative irf error bands Notes ----- Lütkepohl (2005) Appendix D Returns ------- Tuple of lower and upper arrays of ma_rep monte carlo standard errors )orthreplrPr\burncumraxisrBrN) irf_resimrsortrr2)rrrrPrr\rrma_collma_sortlow_idxupp_idxrrs r*irf_errband_mczVARResults.irf_errband_mcsN..DDt! '''*eFQJ-.23eQ!^t34q89Aq()Aq()e|r,c j}jj}j} j} j } | z} t j|dz||f} fd}t|D]9}tj|| | || |z}||d}||| |ddddddf<;| S)a Simulates impulse response function, returning an array of simulations. Used for Sims-Zha error band calculation. Parameters ---------- orth : bool, default False Compute orthogonalized impulse response error bands repl : int number of Monte Carlo replications to perform steps : int, default 10 number of impulse response periods signif : float (0 < signif <1) Significance level for error bars, defaults to 95% CI seed : int np.random.seed for replications burn : int number of initial observations to discard for simulation cum : bool, default False produce cumulative irf error bands Notes ----- .. [*] Sims, Christoper A., and Tao Zha. 1999. "Error Bands for Impulse Response." Econometrica 67: 1113-1155. Returns ------- Array of simulated impulse response functions rct|jjj}r|j n|j }r|j dS|S)N)r\)rrrrr)rr\rrrr+cumsum)simretrrrrrPs r* fill_collz'VARResults.irf_resim..fill_collscc *..t4::.NC/3U+9O *-3::1:% 5# 5r,)r\rPN) rQrr#rOrrxrrr!rr_)rrrrPr\rrrQr#rOrrx nobs_originalrr r(rrs`` ` ` @r*rzVARResults.irf_resimsByyyy ,,NN yyt ((D%!)T489 6 6t 1A++#d* Cde*C"+C.GAq!QJ  1r,c|j}tjj|}|j ifd}|j |}|j }tj||j|jf}td|dzD]}|dk(r |j|j z||dz <(||dz } t|D]t} t|D]d} ||dz | z } ||dz | z } tj| j|z| z|z}| ||| z|z|| jzz } fv| ||dz <|S)Nc\|vr#tjj||<|Srn)rr/ matrix_power)r(B_Bs r*bpowz(VARResults._omega_forc_cov..bpows-{ ..q!41a5Lr,r) rrr/r_bmat_forc_covr+rOrrQr!rtracerM)rrPGGinvrr'r;omegasr?omr(r)BiBjmultrrs @@r*rzVARResults._omega_forc_covs[ HHyy}}Q    !   {{5! 5$))TYY78q%!)$ AAv $  <q1u AB1X =q=Aa!eaiBa!eaiB88BDD4K"$4q$89D$a.504799<>r,ct|||S)z Compute forecast error variance decomposition ("fevd") Returns ------- fevd : FEVD instance r)FEVD)rr r!s r*fevdzVARResults.fevdRsDJ88r,c.t|t|jdddfk7r tdt|dtrDg}t |D]2\}}|j |jj||4|}t||S)z.Reorder variables for structural specificationrNzHReorder specification length should match number of endogenous variables) rLrrY isinstancerrrrrr)rr order_newr(nams r*reorderzVARResults.reorder\s u:T[[A./ /1  eAh $I#E* =3  !1!1%(!;< =E$&&r,c d|cxkrdkstdtdttft|r|g}t fd|Ds t d|Dcgc]$}t |tur|j|n|&}}|Dcgc]"}tj|j|$}}|t|r|g}t fd|Ds t d|Dcgc]$}t |tur|j|n|&}}|Dcgc]"}tj|j|$}}nCt|jDcgc] }||vs| }}|Dcgc]}|j|}}|j|j} } | dk(r d} t| t|t|z| z} |j} t!j"| | | z| d z| zzft$ }| | z}d}t| D].}|D]'}|D] }d||||z| |zz| d z|zzf<|dz }")0t!j&|t)|j*j,}t j.j1||j3z|j,z}||z|zx}}|j5d k(r| }t7j8|}nJ|j5d k(r)|| z }| | |j:zf}t7j<|}ntd |z|j?|}|jAd|z }tC|||||||d| Scc}wcc}wcc}wcc}wcc}wcc}w)u Test Granger causality 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`. kind : {'f', 'wald'} Perform F-test or Wald (chi-sq) test signif : float, default 5% Significance level for computing critical values for test, defaulting to standard 0.05 level Notes ----- Null hypothesis is that there is no Granger-causality for the indicated variables. The degrees of freedom in the F-test are based on the number of variables in the VAR system, that is, degrees of freedom are equal to the number of equations in the VAR times degree of freedom of a single equation. Test for Granger-causality as described in chapter 7.6.3 of [1]_. Test H0: "`causing` does not Granger-cause the remaining variables of the system" against H1: "`causing` is Granger-causal for the remaining variables". Returns ------- results : CausalityTestResults References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series* *Analysis*. Springer. rr signif has to be between 0 and 1c36K|]}t|ywrnr(.0r~ allowed_typess r* z,VARResults.test_causality..s@A:a/@zFcaused has to be of type string or int (or a sequence of these types).c36K|]}t|ywrnr/r0s r*r3z,VARResults.test_causality..sEz!]3Er4zOcausing has to be of type string or int (or a sequence of these types) or None.z5Cannot test Granger Causality in a model with 0 lags.rBrwaldr^zkind %s not recognizedgrangertestr)"rYrrr(r3 TypeErrortyperrrUr!rQr RuntimeErrorrLrPrrrr"rrrMr/rrrrrr,r^rrr)rcausedcausingkindrr~ caused_ind causing_indr(r&r%err num_restr num_det_termsrcols_detrowr)ing_inded_indCbmiddlelam_wald statisticdfdistpvalue crit_valuer2s @r*test_causalityzVARResults.test_causalityosbFQ?@ @?@ @c fm ,XF@@@, CIIQ47c>$**Q-q8II=CDdnnTZZ3D D  '=1")EWEE:HOO!Q3tzz!}A=OGOBIJQ4>>$**a8JKJ&+DII&6N!::M1NKN.89tzz!}9G9yy$))1 6ICs# #L3v;.2   HHi]!2Q!VaZ!?@ N}$q A& (FKLAc8f,q7{:Q!VaZGGH1HC  VVAs4;;==) *q4??#44qss:; "F{R//9 ::<6 !B::b>D ZZ\S  9,IQ./B77B.6sAA:a/Ar4zIcausing has to be of type string or int (or a a sequence of these types).rrBinstr6r8)"rYrrr(r3r:r;rrrUr!rQrxrrLrOvechrrrnonzerorr"r/rrrrDrMrrrrr)rr>rr~rAr(r@r=r&rr%rCrO vech_sigma_usig_mask vech_sig_maskrerrFCsdCdrJwald_statisticrMrNrOrPr2s @r*test_inst_causalityzVARResults.test_inst_causalitys~FQ?@ @?@ @c g} -iGAAA0 DKKaDGsN4::a=9KK>EFt~~djj!4F F!&tyy!1JAQk5IaJ J)34A$**Q-44))TYY a1L3v;. ,,yy) 88GMM*-.j(),-[() (+ zz-(+ HHi\!235 A# "C !Ac49n  " VVA| $ IINN-a0 1 VVAq\rBGGGW$==DEIbddVmb01 zz"~(XXa&j) #         KLFJ4s")K2'K7 K<K<%Lc ||jz dkrtd|jdd}tj|j}t ||}tj j|d}td|dzD]H}||} tj| j|z| z|z} |r| |j|z z} || z }J||r|jdzn |jz}|jdz||jz z} tj| } | j|} | j!d|z }t#||| | |||S)u6 Residual whiteness tests using Portmanteau test Parameters ---------- nlags : int > 0 The number of lags tested must be larger than the number of lags included in the VAR model. signif : float, between 0 and 1 The significance level of the test. adjusted : bool, default False Flag indicating to apply small-sample adjustments. Returns ------- WhitenessTestResults The test results. Notes ----- Test the whiteness of the residuals using the Portmanteau test as described in [1]_, chapter 4.4.3. References ---------- .. [1] Lütkepohl, H. 2005. *New Introduction to Multiple Time Series* *Analysis*. Springer. rzhThe whiteness test can only be used when nlags is larger than the number of lags included in the model (z).rrB)rrYrrsrvrr/rr!rrMrxrQrrrrr)rr<radjustedrLu acov_listcov0_invrrto_addrMrNrOrPs r*test_whitenesszVARResults.test_whitenesslsT: 499  !"ii[,   JJtzz "!!U+ 99==1.q%!)$ A1BXXbddXo2X=>F$))a-'  I  xTYY!^TYY> YY!^utyy0 1zz"~#XXa&j) # z62vuh  r,c|r|j|}n|j|}dtj|jz }t j |ddtjd|dz||}|jd|S)ap Plot autocorrelation of sample (endog) or residuals Sample (Y) or Residual autocorrelations are plotted together with the standard :math:`2 / \sqrt{T}` bounds. Parameters ---------- nlags : int number of lags to display (excluding 0) resid : bool If True, then the autocorrelation of the residuals is plotted If False, then the autocorrelation of endog is plotted. linewidth : int width of vertical bars Returns ------- Figure Figure instance containing the plot. rBrN)xlabel err_boundrxz3ACF plots for residuals with $2 / \sqrt{T}$ bounds ) rrrrjrxrryrcsuptitle)rr<rvrxacorrsboundr{s r*r|zVARResults.plot_acorrs, %%e,F&&u-FBGGDII&&&& 12J99Q *   KL r,ct||S)a Test assumption of normal-distributed errors using Jarque-Bera-style omnibus Chi^2 test. Parameters ---------- signif : float Test significance level. Returns ------- result : NormalityTestResults Notes ----- H0 (null) : data are generated by a Gaussian-distributed process )r)r)rrs r*rzVARResults.test_normalitys$d622r,cTtjj|jS)z Return determinant of white noise covariance with degrees of freedom correction: .. math:: \hat \Omega = \frac{T}{T - Kp - 1} \hat \Omega_{\mathrm{MLE}} )rr/detrOrs r*detomegazVARResults.detomegasyy}}T\\**r,cL|j}|j}|j}||dzz||jzz}|jrt |j }ntj }|d|z |zz}|tj||z |zz}|dtjtj|z|z |zz}|jr6||jz|jz |ztj|z} ntj} |||| dS)z+information criteria for lagorder selectionrBg@)rrrr) rxrQrrPr,r rrinfrtrexp) rrxrQr free_paramsldrrrrs r*r4zVARResults.info_criteriasyyyyII $!)+dT[[.@@ ==T--.B&&BC$J+--BFF4L4';66S266"&&,//$6+EE ==4==(DMM9dBRVVBZOC&&C3SAAr,c |jdS)zAkaike information criterionrr4rs r*rzVARResults.aic !!%((r,c |jdS)uSFinal Prediction Error (FPE) Lütkepohl p. 147, see info_criteria rrvrs r*rzVARResults.fpe s !!%((r,c |jdS)zHannan-Quinn criterionrrvrs r*rzVARResults.hqic s!!&))r,c |jdS)z&Bayesian a.k.a. Schwarz info criterionrrvrs r*rzVARResults.bic rwr,c|j}|j}||z}tj||f}tj|j |d|ddf<tj ||z ||dd| f<tjj|ddz}tjtj|ddd}||S)a The roots of the VAR process are the solution to (I - coefs[0]*z - coefs[1]*z**2 ... - coefs[p-1]*z**k_ar) = 0. Note that the inverse roots are returned, and stability requires that the roots lie outside the unit circle. Nr) rQrrrrr#r r/eigargsortr2)rrQrr%arrrootsrs r*rzVARResults.roots syyyy 4Khh1v 3ETE1H VVAH-DE6TE6M c"1%+jj'"-Szr,)Nr~NNNrr)rT)rrb)Fr[rrNdF)Fr[rNrF)rNNr)Nr^rr)rrF)rTr);rrrr _model_typerrpropertyrr,rrrvrrrrrrrrrrrrrrbserrrrrrrrrrVrrrrrr#r&r+rQr^rer|rror4rrrrrrHrIs@r*rrs'RK < | 33 ))66 ;; C' , 6 '&& 88 =,,>>++//DDEE C## !! ))$$ "" 77$$ ""&"N    1hIN>@#J8" ?.9 '&@ Dy v5 n$L3( + +BB.))))**))r,rc eZdZdddddddddZej ejeZddiZej ejeZ y)r% columns_eqcovcov_eq)rrrrrrOrrconf_intmultivariate_confintN) rrr_attrswrap union_dictsr _wrap_attrs_methods _wrap_methodsrr,r*r%r%+ sj F#$"" ,,fK23H$D$$ ..Mr,r%c,eZdZdZddZdZdZddZy) r%zc Compute and plot Forecast error variance decomposition and asymptotic standard errors NcN||_||_|j|_|jj|_|j |||_|j j|_|jd|dzjd}t|j}|jj|dd||f}tj|}t|D]$}||j||z j||<&|jdd|_y)N)r!r rBrrr)r rrQrrr#irfobj orth_irfsrrrbr empty_liker!rMrdecomp) rrrr irfsrngrbr&r(s r*rz FEVD.__init__H s  JJ [[,, ii1gi> ..x(A-5515=TYYjjnnW%ack2}}T"w -AAwyy3q6),,DG -mmAq) r,cnt}t|j}t|jD]e}t j |j|||j}|jd|j|z|j|dzgt|jy)Nz FEVD for %s  ) rrr r!rQr pprint_matrixrrwriter1getvalue)rbufrr(ppms r*rz FEVD.summarya sjT\\"tyy! "A&&t{{1~sDJJGC IIo 1 5 6 IIcDj !  " cllnr,ct)zLCompute asymptotic standard errors Returns ------- r;rs r*rzFEVD.covm s "!r,c 6ddlm}|j}|xs |j}|j ||\}}|j dt j|t|z Dcgc] }t|} }t j|} |jjd} |d} t|D]} || } | | j}g}t|D]R}|dkDr||dz nd}||}| j| ||z f|| ||j|d|}|j!|T| j#|j| | j%\}}|j'||d t)j*d |Scc}w) zPlot graphical display of FEVD Parameters ---------- periods : int, default None Defaults to number originally specified. Can be at most that number rN)nrowsfigsizez,Forecast error variance decomposition (FEVD)rrBr)bottomcolorlabelz upper right)locg333333?)right)matplotlib.pyplotpyplotrQr subplotsrirrcrrrrr!rMbarrr set_titleget_legend_handles_labelslegendradjust_subplots)rr r plot_kwdspltr&r{axesr~colorstickslimitsaxr( this_limitshandlesr)rrhandlelabelss r*rz FEVD.plotu s ( II)T\\LLq'L: T CD"$))AU";a"?@Q#a&@@ '"##A& !Wq (AaB )++KG1X './!e AE*#AEM! )**Q-   v& ' LLA '+ (0668 7F 6  t, AAs*FrF)N)rr)rrrrrrrrrr,r*r%r%B s *2 "1r,r%cR||jdz }g}t|dzD]`}|dkDr(tj||dj|d| }n tj|j|}|j |btj |t|z Srh)rr!rr"rMrrErL)rr<r>lagrs r*rr s AFF1I A FUQY 7qwyy!EcT(+AqssAA a  88F c!f $$r,ctjtj|d}|tj||z S)Nr)rrjrouter)rsds r*rr s3 q" #B 288B# ##r,rrrn)rrrrr)Jr __future__rstatsmodels.compat.pythonr collectionsriornumpyrpandasr scipy.statsrstatsmodels.base.wrapperbasewrapperrstatsmodels.iolib.tablerstatsmodels.tools.decoratorsrr statsmodels.tools.linalgr statsmodels.tools.sm_exceptionsr statsmodels.tools.validationr statsmodels.tsa.base.tsa_modelr rstatsmodels.tsa.tsatoolsrtsatoolsrrrstatsmodels.tsa.vector_arrrr1statsmodels.tsa.vector_ar.hypothesis_test_resultsrrrstatsmodels.tsa.vector_ar.irfr statsmodels.tsa.vector_ar.outputrr+r8r@r:rVrbr`rfrqr|rrrrrrKrResultsWrapperr%populate_wrapperr%rrrr,r*rs%#,#''/I093'&CC<< 57 &R%0&R4<8v,=> 2 F/d=0.b7 7 |zP/zPz n*n*j iiX!++('4ddT %$r,