M/Ph dZddlZddlmZddZddZedkrdZdZ d Z ej ej ege zZ eje e e fZddgddgdd ggeddddd f<ee eZeejee ddfeje dd dfeje dzkdZdZ dZd Z d Zej ej ege zZ eje e e fZddgddgdd ggeddddd f<ejee e fZee ee Zee eee \ZZeejeekeejee ddfeje dd dfeje dzezkd ed<ee ee\ZZejeje e fe fZ ee ee\ZZd ed<ddgddgdd ggeddddd f<ee ee\Z Z!ej ej edej ezgZ"eje e fedddddf<eje e feddddd f<ded<ee"eZ#eje"edddddfZ$eje"eddddd fZ%eejeje"edddddfddd dfe#e ddfkeejeje"eddddd fddd dfe#e dd fkddl&m'Z'm(Z(e'e dddfZ)ee)dej*e dddfke(e dddfZ+dSdS)aJVAR and VARMA process this does not actually do much, trying out a version for a time loop alternative representation: * textbook, different blocks in matrices * Kalman filter * VAR, VARX and ARX could be calculated with signal.lfilter only tried some examples, not implemented TODO: try minimizing sum of squares of (Y-Yhat) Note: filter has smallest lag at end of array and largest lag at beginning, be careful for asymmetric lags coefficients check this again if it is consistently used changes 2009-09-08 : separated from movstat.py Author : josefpkt License : BSD N)signalc4|jd}|jd}tj|j}t||D]S}||||z |ddtjf|zddz||ddf<T|S)a multivariate linear filter Parameters ---------- x: (TxK) array columns are variables, rows are observations for time period B: (PxKxK) array b_t-1 is bottom "row", b_t-P is top "row" when printing B(:,:,0) is lag polynomial matrix for variable 1 B(:,:,k) is lag polynomial matrix for variable k B(p,:,k) is pth lag for variable k B[p,:,:].T corresponds to A_p in Wikipedia const : float or array (not tested) constant added to autoregression Returns ------- xhat: (TxK) array filtered, predicted values of x array Notes ----- xhat(t,i) = sum{_p}sum{_k} { x(t-P:t,:) .* B(:,:,i) } for all i = 0,K-1, for all t=p..T xhat does not include the forecasting observation, xhat(T+1), xhat is 1 row shorter than signal.correlate References ---------- https://en.wikipedia.org/wiki/Vector_Autoregression https://en.wikipedia.org/wiki/General_matrix_notation_of_a_VAR(p) rNaxis)shapenpzerosrangenewaxissum)xBconstpTxhatts ]/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/sandbox/tsa/varma.pyVARr sB  A  A 8AG  D 1QZZNN Qqs1uQQQrz121499q9AAEE1EMMMQqqqS Kct|jd}|jd}|jd}tj|j}tj|j}t||} t | |D]} ||| |z | ddtjf|zddz|| |z | ddtjf|zddz|| ddf<|| ddf|| ddfz || ddf<||fS)z multivariate linear filter x (TxK) B (PxKxK) xhat(t,i) = sum{_p}sum{_k} { x(t-P:t,:) .* B(:,:,i) } + sum{_q}sum{_k} { e(t-Q:t,:) .* C(:,:,i) }for all i = 0,K-1 rNrr)rr r maxr r r ) rrCrPQrrestartrs rVARMArMsG  A  A  A 8AG  D A !HHE 5^^$$ a!Aaaa 23A5:::BBFFAFNNN!Aaaa *+A-222::>>A>FFGQqqqS 1QQQ3$qs)#!AAA# 7Nr__main__r)rg?)rrrvalid)acovfacf)r),__doc__numpyr scipyrrr__name__rKr column_stackarangeronesrrprintall correlaterrr rxhat1xhat2err2xhat3err3r_xhat4err4xhat5err5x0xhat0xcorr00xcorr01statsmodels.tsa.stattoolsr&r'aavvaraacrrrFs<0 ****Z6 z A A A1q())A1QA1qeQqE"Aaaa!eH 3q88D E&"&abbd\R\!CRCE(7271::>>q@@ A ABBB A A A A E1q())A1QA1qeQqE"Aaaa!eH!AaA C!5 ! ! !E%!AU+++KE4 E&"&% !!! E&"&qrr!t  Qss1uXgbgajj A A! CE II J JKKKAeH%!A,,KE4 hbh!uooa A%!A,,KE4AeH1qeQqE"Aaaa!eH%!A,,KE4 )")A,,)")A,,7 8 8Brw!u~~Aaaa!eHrw!u~~Aaaa!eHAeH C1IIEfr!AAAaaaE(++Gfr!AAAaaaE(++G E&"&!!"Qqqq1uXg66ss1u=uQRRT{J K KLLL E&"&!!"Qqqq1uXg66ss1u=uQRRT{J K KLLL54444444 %!!!A#--C E#a&FBF1QQQqS6NN "### #a!f++CCCIr