a \:btd|t|f||} |rhtd| |fn | durhd} t|j| |_|||}|j || || | | | dS)uz Fit the SVAR model and solve for structural parameters Parameters ---------- A_guess : array_like, optional A vector of starting values for all parameters to be estimated in A. B_guess : array_like, optional A vector of starting values for all parameters to be estimated in B. maxlags : int Maximum number of lags to check for order selection, defaults to 12 * (nobs/100.)**(1./4), see select_order function method : {'ols'} Estimation method to use ic : {'aic', 'fpe', 'hqic', 'bic', None} Information criterion to use for VAR order selection. aic : Akaike fpe : Final prediction error hqic : Hannan-Quinn bic : Bayesian a.k.a. Schwarz verbose : bool, default False Print order selection output to the screen trend, str {"c", "ct", "ctt", "n"} "c" - add constant "ct" - constant and trend "ctt" - constant, linear and quadratic trend "n" - co constant, no trend Note that these are prepended to the columns of the dataset. s_method : {'mle'} Estimation method for structural parameters solver : {'nm', 'newton', 'bfgs', 'cg', 'ncg', 'powell'} Solution method See statsmodels.base for details override : bool, default False If True, returns estimates of A and B without checking order or rank condition maxiter : int, default 500 Number of iterations to perform in solution method maxfun : int Number of function evaluations to perform Notes ----- Lütkepohl pp. 146-153 Hamilton pp. 324-336 Returns ------- est : SVARResults N)maxlagsverbosez#%s not recognized, must be among %szUsing %d based on %s criterionr)trendsolveroverridemaxitermaxfun) rZ select_orderr sortedprintlenrnobs_get_init_params_estimate_svar)r)A_guessB_guessr3methodZicr5r4Zs_methodr6r7r8r9lagsZ selections start_paramsrrrfitms&7   zSVAR.fitcCs|j}|j}|dvr\|dur6tdg|}q`t||kr`d}t|t||fng}|j}|dvr|durtdg|}qt||krd}t|t||fng}tj ||fS)zL Returns either the given starting or .1 if none are given. )abaNg?z/len(A_guess) = %s, there are %s parameters in A)rFbz/len(B_guess) = %s, there are %s parameters in B) rlowerr%sumr"arrayr<r r&Zr_)r)r@rAZvar_typeZ n_masked_amsgZ n_masked_brrrr>s$     zSVAR._get_init_paramsnmcCst|}|j} tj| ||dd} | |d} tjj| | ddd} | t| | } t| }||j ||}t| j | }||}||_ |j ||||d\}}|j }|j}t| | | |||j||jj|||||d S) zQ lags : int trend : {str, None} As per above raise)r5Z has_constantN)Zrcondr)r7r6r8)namesr5r*modelr r r%r&)utilget_trendorderrZ get_var_endogr"linalgZlstsqdotr<rTsigma_u _solve_ABr%r& SVARResultsZ endog_namesdatar*)r)rDrCr8r9r5r6r7k_trendrzZy_sampleZ var_paramsZresidZavobsZdf_residZsseZomegar r r%r&rrrr?s,     zSVAR._estimate_svarcCs|j}|j}|j}|j}t||}t||}|durH|d|||<|durd||||||<|j}|j} |j} t t ||} t t | j | | } t |d\} }| |}| d| tdtjtt |d|t| }|S)z Loglikelihood for SVAR model Notes ----- This method assumes that the autoregressive parameters are first estimated, then likelihood with structural parameters is estimated Ng@)r r r%r&r<r=rrWr"rUnplinvrVrlogZpiZdetZtrace)r)paramsr r r%r&A_lenZB_lenr=rrWWZtrc_inZsignZb_logdetZ b_slogdetZliklrrrloglikes2   z SVAR.loglikecCs|j}t||ddS)z Return the gradient of the loglike at AB_mask. Parameters ---------- AB_mask : unknown values of A and B matrix concatenated Notes ----- Return numerical gradient g:0yE>)epsilon)rdrr)ZAB_maskrdrrrscore-s z SVAR.scorecCs|j}t||S)z, Returns numerical hessian. )rdrrfrrrhessian<sz SVAR.hessianc s|j}|j}|j}|j}t||} |d| ||<|| d||<|sj|||} || || ntdt j |||dddj } | d| ||<| | d||<||fS)a Solves for MLE estimate of structural parameters Parameters ---------- override : bool, default False If True, returns estimates of A and B without checking order or rank condition solver : str or None, optional Solver to be used. The default is 'nm' (Nelder-Mead). Other choices are 'bfgs', 'newton' (Newton-Raphson), 'cg' conjugate, 'ncg' (non-conjugate gradient), and 'powell'. maxiter : int, optional The maximum number of iterations. Default is 500. Returns ------- A_solve, B_solve: ML solutions for A, B matrices Nz+Order/rank conditions have not been checkedg#B ;F)rDrBr8ZgtolZdisp) r%r&r r r< _compute_J check_order check_rankr;rrEra) r)rDr8r7r6r%r&r r rbJZretvalsr,rrrXCs&    zSVAR._solve_ABc CsP|j}|j}|j}|j}ttd||d|dg}t|D]}|} || kr^|krBnqBttd||ddg} d| t||| dd|d|d<t||g} d| | |f<d| || f<|t| | ddddfj }| d} qJqB|j } t | } t|dt ||f}t|dt ||f}d}d}t ||dkrtj |dd}t|dD]$}||rzd|||f<|d7}qzt ||dkrtj |dd}t|dD]$}||rd|||f<|d7}qt |}tt| t|||}d|}tt| t|||}tj||dd }|S) Ng?rr]Fr)orderrOgZaxis)rrWr%r&r"r#intrangerUZravelrVr^Zpinvr<r_Zkronappend)r)A_solveB_solverrWr%r&ZD_nTjiuZTijZD_nZD_plZS_BZS_DZj_dZA_veckZB_vecZinvAZJ_p1iZJ_p1ZJ_p2rlrrrrirsN" ,  $         zSVAR._compute_JcCs(tj|ddtj|ddkr$tddS)Nrrorz3Order condition not met: solution may not be unique)r"sizer )r)rlrrrrjszSVAR.check_ordercCs*tj|}|tj|ddkr&tddS)Nrroz3Rank condition not met: solution may not be unique.)r"rTZ matrix_rankryr )r)rlZrankrrrrks zSVAR.check_rank)NNNNr) NNNr.Nr/Fr0r1Fr2r2)r/rMF)Fr1)__name__ __module__ __qualname____doc__rrrrEr>r?rdrgrhrXrirjrk __classcell__rrr,rrs&3 N ,'/<rc@s.eZdZdZd ddZd ddZd dd ZdS) SVARProcessa Class represents a known SVAR(p) process Parameters ---------- coefs : ndarray (p x k x k) intercept : ndarray (length k) sigma_u : ndarray (k x k) names : sequence (length k) A : neqs x neqs np.ndarray with unknown parameters marked with 'E' A_mask : neqs x neqs mask array with known parameters masked B : neqs x neqs np.ndarry with unknown parameters marked with 'E' B_mask : neqs x neqs mask array with known parameters masked NcCs>t||_|jd|_||_||_||_||_||_||_ dS)Nr) r<k_arrrcoefs interceptrWrsrtrP)r)rrrWrsrtrPrrrrs  zSVARProcess.__init__ cCstdS)z' Unavailable for SVAR N)NotImplementedError)r)maxnPrrr orth_ma_repszSVARProcess.orth_ma_repcsJdur&|j}|j}tt|||j|d}tfdd|DS)zW Compute Structural MA coefficient matrices using MLE of A, B Nrcsg|]}t|qSr)r"rU).0rrrr z+SVARProcess.svar_ma_rep..)rsrtr"rUr^r_Zma_reprK)r)rrrsrtZma_matsrrr svar_ma_reps  zSVARProcess.svar_ma_rep)N)rN)rN)rzr{r|r}rrrrrrrrs  rcs:eZdZdZdZdfdd Zddd ZdddZZS)rYa Estimate 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 Attributes ---------- aic bic bse coefs : ndarray (p x K x K) Estimated A_i matrices, A_i = coefs[i-1] cov_params dates detomega df_model : int df_resid : int endog endog_lagged fittedvalues fpe intercept info_criteria k_ar : int k_trend : int llf model names neqs : int Number of variables (equations) nobs : int n_totobs : int params k_ar : int Order of VAR process params : ndarray (Kp + 1) x K A_i matrices and intercept in stacked form [int A_1 ... A_p] pvalue names : list variables names resid sigma_u : ndarray (K x K) Estimate of white noise process variance Var[u_t] sigma_u_mle stderr trenorder tvalues rNr/cs| |_||_||_| |_|jj\|_|_|j||_t | }|dkrP|d}nd}||_ ||_ ||_ t | |||_||_||_|j|j d}|||j|jf}|jd}|dd}||_||_||_| |_tj|||||| ddS)Nrrr])rP)rQr endog_laggedr*rZn_totobsrr=rRrSr[Zk_exog trendorderZmake_lag_namesZ exog_namesrarWZreshapeZswapaxescopyr r r%r&rr)r)rrrarWZ lag_orderr r r%r&rQr5rPr*r[rZreshapedrrr,rrr)s6    zSVARResults.__init__rcCs.|j}|j}tt||}t|||ddS)z Analyze structural impulse responses to shocks in system Parameters ---------- periods : int Returns ------- irf : IRAnalysis T)rperiodsZsvar)r r r"rUr^r_r)r)rZ var_orderr r rrrrirfTs zSVARResults.irfF皙?dc&s|j}|} |j} |j} |j} |j} |j}|j}t ||d||f}|j }|j }|j }|j }|jj}|jj}|jj}g}fdd}||}||}t|D]}tj| | | |||d}||d}t||||d}|dkrtj|dd }t||} |d| }|| d}|j| ||d }!|dkrT|t|!j ||!j |||!j|d ||<qtj|dd }"tt|d |dttd|d |df}#|"|#dddddddf}$|"|#dddddddf}%|$|%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 rcsr|jddS|S)Nrro)Zcumsum)Zimpulsescumrraggs z(SVARResults.sirf_errband_mc..agg)seedstepsNrrrro)r3r@rArr])rmeanrrrWrdf_modelr=r"r#r r r%r&rQr r!rrqrRZvarsimrr<rErrtolistrsortrpround)&r)ZorthreplrZsignifrZburnrrrrrrWrrr=Zma_collr r r%r&ZA_passZB_passZs_typeZg_listrZopt_AZopt_BrvZsimsmodZmean_ABsplitZsresZma_sortindexrIupperrrrsirf_errband_mcfsX            zSVARResults.sirf_errband_mc)NNNNNr/NN)rN)FrrrNrF) rzr{r|r}Z _model_typerrrr~rrr,rrYs<+ rY) r}Znumpyr"Z numpy.linalgrTr^rZstatsmodels.tsa.tsatoolsrZstatsmodels.tools.decoratorsrZstatsmodels.tools.numdiffrrZstatsmodels.tsa.base.tsa_modelZtsabaseZ tsa_modelZtsbaseZstatsmodels.tsa.vector_ar.irfrZstatsmodels.tsa.vector_ar.utilZ vector_arrRZ#statsmodels.tsa.vector_ar.var_modelrr rZTimeSeriesModelrrrYrrrrs"     0