M/PhH_dZddlZddlmZddlmZddlm Z ddl m cm Z ddl m cmcmZddlm cmcmZejZGddZGddeZdS)z Impulse reponse-related code N)cache_readonlyc teZdZdZ ddZddZdZdZdddd dd dd d d ddd dZdddd dd dd d d dd dZ dS)BaseIRAnalysisz Base class for plotting and computing IRF-related statistics, want to be able to handle known and estimated processes N Fc||_||_|j|j|jc|_|_|_||_||j}tj |}||_ ||_ | ||_|r||||_n||||_|jd|_|r!|jd|_n |jd|_|st||_|r-t3j|||_n,t3j|||_|r t;j|j|_ dSt;j|j!|_ dS)N)Praxis)"modelperiodsneqsk_arnobslagsTordersigma_ulacholeskyrsvarma_repirfs svar_ma_rep svar_irfs orth_ma_rep orth_irfscumsum cum_effectssvar_cum_effectsorth_cum_effectslong_run_effects lr_effectsnpdotsvar_lr_effectsorth_lr_effectsutil comp_matrixvar_rep_Acoefs)selfr rr rrvecmsigmas ]/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tsa/vector_ar/irf.py__init__zBaseIRAnalysis.__init__s  ',z5:uz$ 49df 9ME E""A LL))  ="..w!.< !  > !9 r1ctr3NotImplementedErrorr,argskwargss r/covzBaseIRAnalysis.covR!!r1ctr3r7r9s r/cum_effect_covzBaseIRAnalysis.cum_effect_covUr=r1皙?)rrTasym) impulseresponsesignif plot_paramsfigsizesubplot_params plot_stderr stderr_typereplseed componentc ^|j} |j}|j}|r|rtd|||}|rd}n|rd}nd}|durd}n| dvrtd| d kr|| }| d kr|||| || }| d kr|||| || | }| dkr|||| || | }| dkr| ||| || | }tj |||||jj ||||||  }|S)a Plot impulse responses Parameters ---------- orth : bool, default False Compute orthogonalized impulse responses impulse : {str, int} variable providing the impulse response : {str, int} variable affected by the impulse signif : float (0 < signif < 1) Significance level for error bars, defaults to 95% CI subplot_params : dict To pass to subplot plotting funcions. Example: if fonts are too big, pass {'fontsize' : 8} or some number to your taste. plot_params : dict figsize : (float, float), default (10, 10) Figure size (width, height in inches) plot_stderr : bool, default True Plot standard impulse response error bands stderr_type : str 'asym': default, computes asymptotic standard errors 'mc': monte carlo standard errors (use rpl) repl : int, default 1000 Number of replications for Monte Carlo and Sims-Zha standard errors seed : int np.random.seed for Monte Carlo replications component: array or vector of principal component indices zFor SVAR system, set orth=Falsez"Impulse responses (orthogonalized)zImpulse responses (structural)zImpulse responsesFN)rAmcsz1sz2sz3z?? ?  t,,  (8EE  (4EE'E %  FF  B B B[\\ \f$$t,,d""d.26.2)44e##**404V045>+@@e##**404V045>+@@e##**404V045>+@@ $T67H%)Z%5uV4B1<-41< >>>  r1) rCrDrErFrGrHrIrJrKrLc D|rd} |j} |j}nd} |j} |j}| dvrt d| dkr||}| dkr||| || }|sd }tj| ||||j j | |||||| }|S) a Plot cumulative impulse response functions Parameters ---------- orth : bool, default False Compute orthogonalized impulse responses impulse : {str, int} variable providing the impulse response : {str, int} variable affected by the impulse signif : float (0 < signif < 1) Significance level for error bars, defaults to 95% CI subplot_params : dict To pass to subplot plotting funcions. Example: if fonts are too big, pass {'fontsize' : 8} or some number to your taste. plot_params : dict figsize: (float, float), default (10, 10) Figure size (width, height in inches) plot_stderr : bool, default True Plot standard impulse response error bands stderr_type : str 'asym': default, computes asymptotic standard errors 'mc': monte carlo standard errors (use rpl) repl : int, default 1000 Number of replications for monte carlo standard errors seed : int np.random.seed for Monte Carlo replications z/Cumulative responses responses (orthogonalized)zCumulative responses)rArOz)`stderr_type` must be one of 'asym', 'mc'rArSrO)r4rKrErLN)rEhlinesrHrFrGrJ) r r&rr"rTr?cum_errband_mcrYrZr r[)r,r4rCrDrErFrGrHrIrJrKrLr\rr"r]r^s r/plot_cum_effectszBaseIRAnalysis.plot_cum_effectssF  )EE/K-JJ*E*KJ n , ,HII If$$,,$,77d"",,$T4:-GG F$[&'8%)Z%5uV,64B1<-41< >>> r1NrNFF)FFF) __name__ __module__ __qualname____doc__r0r5r<r?r_rcr1r/rrs DI14141414f""""""T$dH dTTTTTTTl>dT $$(,$%+$T>>>>>>>r1rceZdZdZ ddZddZ dd Z dd Z dd Z dd Z dZ e dZ dZ ddZ ddZddZddZddZddZdZe dZdZdS) IRAnalysisu Impulse response analysis class. Computes impulse responses, asymptotic standard errors, and produces relevant plots Parameters ---------- model : VAR instance Notes ----- Using Lütkepohl (2005) notation NrFc t||||||||r |j|_n |j|_|j|_i|_dS)N)rr rrr-)rr0 cov_var_reprcov_a _cov_alpha _cov_sigmacov_sig_g_memo)r,r rr rrr-s r/r0zIRAnalysis.__init__sheq'&+$T  C C C  *+DJJ)DJ'  r1c>|r|S||jdz}tj|jdz|jdzf|d<t d|jdzD]'}|j|dz }||jz|j z||<(|S)u Compute asymptotic standard errors for impulse response coefficients Notes ----- Lütkepohl eq 3.7.5 Returns ------- r) _orth_cov _empty_covmr r#zerosr rangeGror)r,r4covsiGis r/r<zIRAnalysis.cov s  $>>## # q 011(DINDIN;<<Qq$,*++ - -AAB4:o,DGG r1rBr@dc |j}|j}|r|||||||dS|||||||dS)z8 IRF Monte Carlo integrated error bands Fr4rKstepsrErLburncum)r r sirf_errband_mcirf_errband_mc) r,r4rrKrErLrr r s r/rUzIRAnalysis.errband_mc sv  ,  >((dW06T.2)?? ?''TG/5D-1u(>> >r1c |j}|j} |||} |j} |||| ||} t j|} || \}}}|xtj || | fkr2tdt| zdzt| ztj || | zkrtd|}tj | }tj | }t| D]}t| D]}| dd||f|||dd|||ff| ztj||||||ffzz|dd||f<| dd||f|||dd|||ff| ztj||||||ffzz |dd||f<||fS)a IRF Sims-Zha error band method 1. Assumes symmetric error bands around mean. Parameters ---------- orth : bool, default False Compute orthogonalized impulse responses repl : int, default 1000 Number of MC replications signif : float (0 < signif < 1) Significance level for error bars, defaults to 95% CI seed : int, default None np.random seed burn : int, default 100 Number of initial simulated obs to discard component : neqs x neqs array, default to largest for each Index of column of eigenvector/value to use for each error band Note: period of impulse (t=0) is not included when computing principle component References ---------- Sims, Christopher A., and Tao Zha. 1999. "Error Bands for Impulse Response". Econometrica 67: 1113-1155. r4rKrrLrNComponent array must be  x ,Atleast one of the components does not existru)r r r5r irf_resimr'norm_signif_level_eigval_decomp_SZr#shaperTstrargmaxcopyrzsqrt)r,r4rrKrErLrrMr r rr rqWeigvaklowerupperr}js r/rVzIRAnalysis.err_band_sz10s(: ,  t,,yOOD)-D$::  "6 * *++I66 5!  x ""tDk11 !;c$ii!G%!ORUVZR[R[![\\\y##tG|33 !OPPP  t \ \A4[[ \ \ $QRR!V q1QQQq1vq/@qQRSTUVWXUXSYzIZA[A[/[ [abb1f $QRR!V q1QQQq1vq/@qQRSTUVWXUXSYzIZA[A[/[ [abb1f  \e|r1c |j}|j} |||} |j} |||| |d} || \} }}|xt j|| | fkr2tdt| zdzt| zt j || | zkrtd|}t j || dz| | f}t|D]T}t| D]B}t| D]0}| |||||fddf| |dd||fz||dd||f<1CUt j |d }t|d z |zdz td|d z z |zdz f}t j| }t j| }t| D]h}t| D]V}| dd||f||ddd||fz|dd||f<| dd||f||ddd||fz|dd||f<Wi||fS) a IRF Sims-Zha error band method 2. This method Does not assume symmetric error bands around mean. Parameters ---------- orth : bool, default False Compute orthogonalized impulse responses repl : int, default 1000 Number of MC replications signif : float (0 < signif < 1) Significance level for error bars, defaults to 95% CI seed : int, default None np.random seed burn : int, default 100 Number of initial simulated obs to discard component : neqs x neqs array, default to largest for each Index of column of eigenvector/value to use for each error band Note: period of impulse (t=0) is not included when computing principle component References ---------- Sims, Christopher A., and Tao Zha. 1999. "Error Bands for Impulse Response". Econometrica 67: 1113-1155. rrNrrrrurr rv)r r r5r rrr#rrTrrryrzsortroundr)r,r4rrKrErLrrMr r rr rrrrgammapr}r gamma_sortindxrrs r/rWzIRAnalysis.err_band_sz2is: ,  t,,yOODd),$.. ,,Y77 5!  x ""tDk11 !;c$ii!G%!ORUVZR[R[![\\\y##tG|33 !OPPP$ 4677t L LA4[[ L LtLLA&'!AacF111 o !ABBq(8K&KE!ABBq(OOL LWU+++ VAXd]##A%eQvaxZ,=&>&>q&@@  t G GA4[[ G G#AAAaE{ZQ!A -FFaaa!e #AAAaE{ZQ!A -FFaaa!e  Ge|r1c |j}|j} |||} |j} |||| |d} t j| || | zf} t|D]C}t| D]1}t j| |dddd|fj | ||ddf<2Dt j| | | z| | zf}t j| | | z| | zf}t j| | | zf}t j| t}|ct j || krtdt| zt j|| | zkrtd|}t| D]H}t j| |d ||<t!j||\||<||<||<It j|| dz| | f}t|D]}d}t| D]}t| D]m}|||||| z|dz| zf| |dd||fz||dd||f<|| dz kr.|||||| zdf| |dd||fz||dd||f<nt j|d }t'|d z |zdz t'd|d z z |zdz f}t j| }t j| }t| D]h}t| D]V}| dd||f||ddd||fz|dd||f<| dd||f||ddd||fz|dd||f<Wi||fS) a IRF Sims-Zha error band method 3. Does not assume symmetric error bands around mean. Parameters ---------- orth : bool, default False Compute orthogonalized impulse responses repl : int, default 1000 Number of MC replications signif : float (0 < signif < 1) Significance level for error bars, defaults to 95% CI seed : int, default None np.random seed burn : int, default 100 Number of initial simulated obs to discard component : vector length neqs, default to largest for each Index of column of eigenvector/value to use for each error band Note: period of impulse (t=0) is not included when computing principle component References ---------- Sims, Christopher A., and Tao Zha. 1999. "Error Bands for Impulse Response". Econometrica 67: 1113-1155. rrruNdtypez"Component array must be of length rrrowvarr rv)r r r5r rr#ryrzravelrintsizerTrrr<r' eigval_decomprrr)r,r4rrKrErLrrMr r rr rstackrr} stack_covrrrrcrrrrrs r/rXzIRAnalysis.err_band_sz3s;8 ,  t,,yOOD)-C$99 $gdl344t @ @A4[[ @ @ "1QRR!8)<)> ? ?a111f  @(D'$, =>> HdGDL'$,7 8 8$ -.. HT % % %  wy!!d++ !ED !QRRRy##tG|33 !OPPPt D DA6%(!444IaL#'#5il#C#C AaD%(AaDD$ 4677t U UAA4[[ U UtUUA&'!A$qy!A#w/F(F&G)TUVWVXVXYZ[\T\J]&]E!ABBq(ODF{{*+Aad1W9::,=*>1QRRPQRS8AT*Ta1QhU U WU+++ VAXd]##A%eQvaxZ,=&>&>q&@@  t G GA4[[ G G#AAAaE{ZQ!A -FFaaa!e #AAAaE{ZQ!A -FFaaa!e  Ge|r1c ^|j}|j}tj||||f}t |D]C}t |D]1}tj|dddd||fd|||ddddf<2Dtj||||f}tj|||df}tj||ft } t |D]S}t |D]A}tj|||ddddf\|||ddddf<|||dddf<| ||f<BT||| fS)z Returns ------- W: array of eigenvectors eigva: list of eigenvalues k: matrix indicating column # of largest eigenvalue for each c_i,j Nrurrr) r r r#ryrzr<rr'r) r,rr r cov_holdr}rrrrs r/rzIRAnalysis._eigval_decomp_SZsy,8T4':;;t I IA4[[ I I$&F9QQQqrr!AX+>a$H$H$H1QQQqqq!! I HdD'73 4 4$gq122 HdD\ - - -t [ [A4[[ [ [595GQRSTUVUVUVWXWXWXQXHY5Z5Z2!Aaaa' E!Aaaa'NAacFF [%{r1cjjfdfdtdjdzDS)Ncd}t|D]y}|dz |z }|jvrj|}n3tjjj|}|d}|j|<t j|j|}||z}z|S)Nru) rzrsr matrix_powerr*rr#kronr)r}r{midxapowpieceKr,s r/_make_gzIRAnalysis.G.._make_gsA1XX  !eai$,&&<,DD?479c::D8D(,DL%dil33IHr1c&g|] }|Srjrj).0r}rs r/ z IRAnalysis.G..0s!???q ???r1ru)r rzr )r,rrs`@@r/r{z IRAnalysis.GsZ I       (@???E!T\A-=$>$>????r1ctj|j}tj|jj|}|j}||jdz}t|jdzD]}|dkrd}n5tj ||j |dz }||j z|jz}tj tj||j ||}||jz|jz|jz } || z||<|S)Nrur)r#eyer rrrHrxr rzr$r{rorrr) r,IkPIkrr|r}apieceCiCibarbpieces r/rwzIRAnalysis._orth_cov2sVDI  gdfh## F q 011t|a'(( & &AAvvVC!--dj24/F272ty|44a88Edl*UW4>FvoDGG r1ctj|j}tj|jj|}d}||jdz}t|jdzD]}|dkr||j |dz z}|r|dkrd}n'tj ||}||j z|jz}tj tj||j ||j } | |jz| jz|jz } || z||<|dkr*tj|jdz|jdzf||<||j z|jz||<|S)a Compute asymptotic standard errors for cumulative impulse response coefficients Parameters ---------- orth : bool Notes ----- eq. 3.7.7 (non-orth), 3.7.10 (orth) Returns ------- rrurrv)r#rr rrrrxr rzr{r$rorrrrry) r,r4rrFr|r}rBnBnbarrs r/r?zIRAnalysis.cum_effect_covIsZ VDI  gdfh##  q 011t|a'(( / /A1uuq1u % /66FFQB$*_rt3Frwr4+;A+>??HH$,.8DFB 6/Q66 h 1 dil'CDDDGdj.13.Q r1c V|j}|j}|||||||dS)zM IRF Monte Carlo integrated error bands of cumulative effect Tr)r r r)r,r4rKrErLrr r s r/rbzIRAnalysis.cum_errband_mcvsB  ,##D*1&)-Dd$DD Dr1c|j}tjtj|j|j|}tj|j}|rtjtj|j jtj|j|}tjtj|||j }||j z|jz||j z|jzzS||j z|jzS)z) Returns ------- ) r"r#rtilerrrr r$rrrorr)r,r4lreFinftyrBinfBinfbars r/ lr_effect_covzIRAnalysis.lr_effect_covs o 22C88 VDI    26"'$&(BF49,=,=>>GGDfRWR--tv66G4:%.dl*WY67 8DJ&1 1r1cftjd||DS)Nc ~g|]:}tjtjtj|;Srjtsaunvecr#rdiagrrs r/rz%IRAnalysis.stderr..sD77727271::#6#677777r1rS)r#arrayr<r,r4s r/r]zIRAnalysis.stderrs@x77"&((("5"577788 8r1cftjd||DS)Nc ~g|]:}tjtjtj|;Srjrrs r/rz0IRAnalysis.cum_effect_stderr..sJBBB27271::#6#677BBBr1rS)r#rr?rs r/cum_effect_stderrzIRAnalysis.cum_effect_stderrsKxBB"&"5"54"5"@"@BBBCC Cr1c||}tjtjtj|S)NrS)rrrr#rr)r,r4r<s r/lr_effect_stderrzIRAnalysis.lr_effect_stderrs:  d ++y..///r1c^tj||jdz|jdzftS)Nrvr)r#ryr float)r,r s r/rxzIRAnalysis._empty_covms3x$)q.$)q.A#%%% %r1ch|j}tj|}tj||}t j|}|t j||j|zt j|j|zz|jz}t j |jtj |Sr3) r relimination_matrixcommutation_matrixr#rrrrr$Linv)r,rLkKkkrBs r/rz IRAnalysis.Hs I  #A & &$Q** VAYY "'"df%%+bgdfb.A.AA BRT IvbdAE!HH%%%r1ctr3r7)r,s r/ fevd_tablezIRAnalysis.fevd_tabler=r1rdre)FFrBr@Nr)FFrBr@NrN)FrBr@Nr)rfrgrhrir0r<rUrVrWrXrrr{rwr?rbrr]rrrxrrrjr1r/rlrls  DI    ,7;03>>>> 9=AE7777rFJ48>>>>@FJ48OOOOb2@@^@<.++++Z/347 D D D D2222$8888CCCC0000%%% & &^ &"""""r1rl)rinumpyr# numpy.linalglinalgr scipy.linalgrstatsmodels.tools.decoratorsrstatsmodels.tsa.tsatoolsrtsatools"statsmodels.tsa.vector_ar.plotting vector_arrYstatsmodels.tsa.vector_ar.utilr'rmatrrlrjr1r/rs,777777&&&&&&&&&555555555555------------h[[[[[[[[|D"D"D"D"D"D"D"D"D"D"r1