'YHhH_dZddlZddlmZddlmZddlm Z ddl m cm Z ddl m cmcmZddlm cmcmZej$ZGddZGddeZy)z Impulse reponse-related code N)cache_readonlyc reZdZdZ ddZddZdZdZdddddddd d d ddd d Zdddddddd d d dd dZ y)BaseIRAnalysisz Base class for plotting and computing IRF-related statistics, want to be able to handle known and estimated processes Nc||_||_|j|j|jc|_|_|_||_|!|j}tj|}||_ ||_ |j||_|r|j|||_n|j#|||_|jj'd|_|r"|j j'd|_n!|j$j'd|_|sj|j/|_|r*t3j4|j/||_n)t3j4|j/||_|r%t;j<|j>|_ yt;j<|jB|_ y)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 V/var/www/html/planif/env/lib/python3.12/site-packages/statsmodels/tsa/vector_ar/irf.py__init__zBaseIRAnalysis.__init__sx  ',zz5::uzz$ 49df 9MME E"A LL) "..w!.> ! >> !99 r0ctr2NotImplementedErrorr+argskwargss r.covzBaseIRAnalysis.covR!!r0ctr2r6r8s r.cum_effect_covzBaseIRAnalysis.cum_effect_covUr<r0皙?) r@Tasym) impulseresponsesignif plot_paramsfigsizesubplot_params plot_stderr stderr_typereplseed componentc H|j} |j}|j}|r |r td|j ||}|rd}n|rd}nd}|durd}n| dvr td| d k(r|j | }| d k(r|j ||| || }| d k(r|j||| || | }| dk(r|j||| || | }| dk(r|j||| || | }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, 8E 4E'E % F  B B[\ \f$t,d"d.26.2)4e#**404V045>+@e#**404V045>+@e#**404V045>+@ $$T67H%)ZZ%5%5uV4B1<-41< >  r0) rCrDrErFrGrHrIrJrKrLc f|rd} |j} |j}nd} |j} |j}| dvr t d| dk(r|j |}| dk(r|j || || }|sd }tj| |||jj| |||||| }|S) a Plot cumulative impulse response functions Parameters ---------- orth : bool, default False Compute orthogonalized impulse responses impulse : {str, int} variable providing the impulse response : {str, int} variable affected by the impulse signif : float (0 < signif < 1) Significance level for error bars, defaults to 95% CI subplot_params : dict To pass to subplot plotting funcions. Example: if fonts are too big, pass {'fontsize' : 8} or some number to your taste. plot_params : dict figsize: (float, float), default (10, 10) Figure size (width, height in inches) plot_stderr : bool, default True Plot standard impulse response error bands stderr_type : str 'asym': default, computes asymptotic standard errors 'mc': monte carlo standard errors (use rpl) repl : int, default 1000 Number of replications for monte carlo standard errors seed : int np.random.seed for Monte Carlo replications z/Cumulative responses responses (orthogonalized)zCumulative responses)rArOz)`stderr_type` must be one of 'asym', 'mc'rArSrO)r3rKrErLN)rEhlinesrHrFrGrJ) rr%rr!rTr>cum_errband_mcrYrZr r[)r+r3rCrDrErFrGrHrIrJrKrLr\rr!r]r^s r.plot_cum_effectszBaseIRAnalysis.plot_cum_effectssF EE//K--J*E**KJ n ,HI If$,,$,7d",,$T4:-GF$$[&'8%)ZZ%5%5uV,64B1<-41< > r0Nr@NFF)FFF) __name__ __module__ __qualname____doc__r/r4r;r>r_rcr0r.rrsm DI14f""T$dH dTTTl>dT $$(,$%+$T>r0rceZdZdZ ddZddZ ddZ ddZ ddZ ddZ d Z e d Z d Z dd Z dd ZddZddZddZddZdZe dZdZy) IRAnalysisu Impulse response analysis class. Computes impulse responses, asymptotic standard errors, and produces relevant plots Parameters ---------- model : VAR instance Notes ----- Using Lütkepohl (2005) notation Nc tj||||||||r|j|_n|j|_|j |_i|_y)N)rr rrr,)rr/ cov_var_reprcov_a _cov_alpha _cov_sigmacov_sig_g_memo)r+r rr rrr,s r.r/zIRAnalysis.__init__sZeq'&+$T  C ++DJ))DJ''  r0cl|r|jS|j|jdz}tj|j dz|j dzf|d<t d|jdzD]3}|j|dz }||jz|jz||<5|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+r3covsiGis r.r;zIRAnalysis.cov s >># # q 01((DIINDIIN;<Qq$,,*+ -AAB4::o,DG - r0c |j}|j}|r|j||||||dS|j||||||dS)z8 IRF Monte Carlo integrated error bands Fr3rKstepsrErLburncum)r r sirf_errband_mcirf_errband_mc) r+r3rrKrErLrr r s r.rUzIRAnalysis.errband_mc sk  ,, ((dW06T.2)? ?''TG/5D-1u(> >r0c z|j}|j} |j||} |j} |j ||| ||} t j |} |j| \}}}|htj|| | fk7r&tdt| zdzt| ztj|| | zk\r td|}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. r3rKrrLrNComponent array must be  x ,Atleast one of the components does not existru)r r r4r irf_resimr&norm_signif_level_eigval_decomp_SZr"shaperTstrargmaxcopyrzsqrt)r+r3rrKrErLrrMr r rr rqWeigvaklowerupperr}js r.rVzIRAnalysis.err_band_sz10s: ,,  t,yyOOD)-D$:  " "6 *++I6 5!  xx "tDk1 !;c$i!G%!ORUVZR[![\\yy#tG|3 !OPP  t \A4[ \ $QR!V q1Qq1vq/@qQRSTUVWXUXSYzIZA[/[ [ab1f $QR!V q1Qq1vq/@qQRSTUVWXUXSYzIZA[/[ [ab1f  \ \ e|r0c |j}|j} |j||} |j} |j ||| |d} |j | \} }}|ht j|| | fk7r&tdt| zdzt| zt j|| | zk\r td|}t j|| dz| | f}t|D]G}t| D]7}t| D]'}| |||||fddf| |dd||fz||dd||f<)9It j|d }t|d z |zdz td|d z z |zdz f}t j| }t j| }t| D]T}t| D]D}| dd||f||ddd||fz|dd||f<| dd||f||ddd||fz|dd||f<FV||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. drNrrrrurrrv)r r r4r rrr"rrTrrryrzsortroundr)r+r3rrKrErLrrMr r rr rrrrgammapr}r gamma_sortindxrrs r.rWzIRAnalysis.err_band_sz2isV: ,,  t,yyOODd),$. ,,Y7 5!  xx "tDk1 !;c$i!G%!ORUVZR[![\\yy#tG|3 !OPP$ 467t LA4[ LtLA&'!AacF1 o !ABq(8K&KE!ABq(OL L L WWU+ VAXd]#A%eQvaxZ,=&>q&@@  t GA4[ G#AaE{ZQ!A -FFa!e #AaE{ZQ!A -FFa!e  G G e|r0c |j}|j} |j||} |j} |j ||| |d} t j | || | zf} t|D]D}t| D]4}t j| |dddd|fj| ||ddf<6Ft j | | | z| | zf}t j | | | z| | zf}t j | | | zf}t j | t}|Wt j|| k7rtdt| zt j|| | zk\r td|}t| D]D}t j| |d ||<t!j"||\||<||<||<Ft j || dz| | f}t|D]}}d}t| D]k}t| D][}|||||| z|dz| zf| |dd||fz||dd||f<|| dz k(s7|||||| zdf| |dd||fz||dd||f<]mt j$|d }t'|d z |zdz t'd|d z z |zdz f}t j(| }t j(| }t| D]T}t| D]D}| dd||f||ddd||fz|dd||f<| dd||f||ddd||fz|dd||f<FV||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 rrrowvarrrv)r r r4r rr"ryrzravelrintsizerTrrr;r& eigval_decomprrr)r+r3rrKrErLrrMr r rr rstackrr} stack_covrrrrcrrrrrs r.rXzIRAnalysis.err_band_sz3s8 ,,  t,yyOOD)-C$9 $gdl34t @A4[ @ "1QR!8)<)>)> ?a1f  @ @((D'$, => HHdGDL'$,7 8$ -. HHT %  wwy!d+ !ED !QRRyy#tG|3 !OPPt DA66%(!4IaL#'#5#5il#C AaD%(AaD D$ 467t UAA4[ UtUA&'!A$qy!A#w/F(F&G)TUVWVXYZ[\T\J]&]E!ABq(ODF{*+Aad1W9:,=*>1QRPQRS8AT*Ta1QhU U UWWU+ VAXd]#A%eQvaxZ,=&>q&@@  t GA4[ G#AaE{ZQ!A -FFa!e #AaE{ZQ!A -FFa!e  G G e|r0c `|j}|j}tj||||f}t |D]?}t |D]/}tj |dddd||fd|||ddddf<1Atj||||f}tj|||df}tj||ft } t |D]O}t |D]?}tj|||ddddf\|||ddddf<|||dddf<| ||f<AQ||| 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_SZsHyy,,88T4':;t IA4[ I$&FF9Qqr!AX+>a$H1Qq! I I HHdD'73 4$gq12 HHdD\ -t [A4[ [595G5GQRSTUVWXQXHY5Z2!Aa' E!Aa'NAacF [ [%{r0cjfd}tdjdzDcgc] }|| c}Scc}w)NcDd}t|D]}|dz |z }|jvrj|}n>tjjj |}|d}|j|<t j|j|}||z}|S)Nru) rzrsr matrix_powerr)rr"kronr)r}r{midxapowpieceKr+s r._make_gzIRAnalysis.G.._make_gsA1X !eai$,,&<<,D??47799c:D8D(,DLL%diil3I Hr0ru)r rzr )r+rr}rs` @r.r{z IRAnalysis.Gs= II  (%*!T\\A-=$>?q ???sActj|j}tj|jj |}|j }|j|jdz}t|jdzD]}|dk(rd}nBtj||j|dz }||jz|j z}tjtj||j||}||jz|j z|j z } || z||<|S)Nrur)r"eyer rrrHrxr rzr#r{rorrr) r+IkPIkrr|r}apieceCiCibarbpieces r.rwzIRAnalysis._orth_cov2sVVDII ggdffhh# FF q 01t||a'( &AAvVVC!-djj244/FF2772tyy|4a8Edll*UWW4>FvoDG & r0c\tj|j}tj|jj |}d}|j |jdz}t|jdzD]&}|dkDr||j|dz z}|r|dk(rd}n2tj||}||jz|j z}tjtj||j||j} | |jz| j z|j z } || z||<|dk(r6tj|jdz|jdzf||<||jz|j z||<)|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+r3rrFr|r}rBnBnbarrs r.r>zIRAnalysis.cum_effect_covIsc VVDII ggdffhh#  q 01t||a'( /A1uq1u %6FQB$**_rtt3Frwwr4+;+;A+>?H$,,.8DFFB 6/Q6 hh 1 diil'CDDGdjj.133.Q) /, r0c b|j}|j}|j||||||dS)zM IRF Monte Carlo integrated error bands of cumulative effect Tr)r r r)r+r3rKrErLrr r s r.rbzIRAnalysis.cum_errband_mcvs@  ,,##D*1&)-Dd$D Dr0c|j}tjtj|j|j |}tj |j}|rtjtj|jjtj |j|}tjtj|||j}||jz|jz||jz|jzzS||jz|jzS)z) Returns ------- ) r!r"rtilerrrr r#rrrorr)r+r3lreFinftyrBinfBinfbars r. lr_effect_covzIRAnalysis.lr_effect_covs oo 2C8 VVDII  66"''$&&((BFF499,=>GDffRWWR-tvv6G4::%.dll*WYY67 8DJJ&1 1r0c tj|j|Dcgc]=}tjtj tj |?c}Scc}wNrS)r"arrayr;tsaunvecrdiagr+r3rs r.r]zIRAnalysis.stderrsSxx"&((("572772771:#6778 87AA-c tj|j|Dcgc]=}tjtj tj |?c}Scc}wr)r"rr>rrrrrs r.cum_effect_stderrzIRAnalysis.cum_effect_stderrs[xx"&"5"54"5"@B2772771:#67BC CBrc|j|}tjtjtj |Sr)rrrr"rr)r+r3r;s r.lr_effect_stderrzIRAnalysis.lr_effect_stderrs5  d +yy.//r0crtj||jdz|jdzftS)Nrvr)r"ryr float)r+r s r.rxzIRAnalysis._empty_covms/xx$))q.$))q.A#% %r0c|j}tj|}tj||}t j |}|t j ||j|zt j |j|zz|jz}t j|jtj|Sr2) r relimination_matrixcommutation_matrixr"rrrrr#Linv)r+rLkKkkrBs r.rz IRAnalysis.Hs II  # #A &$$Q* VVAY "''"dff%+bggdffb.AA BRTT IvvbddAEE!H%%r0ctr2r6)r+s r. fevd_tablezIRAnalysis.fevd_tabler<r0rdre)FFrBr?Nr)FFrBr?NrN)FrBr?Nr)rfrgrhrir/r;rUrVrWrXrrr{rwr>rbrr]rrrxrrrjr0r.rlrls DI ,7;03> 9=AE7rFJ48>@FJ48Ob2@@<.+Z/347 D2$8C0% & &"r0rl)rinumpyr" numpy.linalglinalgr scipy.linalgrstatsmodels.tools.decoratorsrstatsmodels.tsa.tsatoolsrtsatools"statsmodels.tsa.vector_ar.plotting vector_arrYstatsmodels.tsa.vector_ar.utilr&rmatrrlrjr0r.rsN7&&55--hh[[|D"D"r0