U ├mЬdу @s╥dZddlZddlmZdddДZdddДZedkРr╬d Zd Z dZ eаeаeбge бZ eаe e e fбZddgddgddggeddЕddЕdf<ee eГZeeаee dЕdfeаe dd Еdfeаe ббd kбГd Zd Z d ZdZ dZeаeаeбge бZ eаe e e fбZddgddgddggeddЕddЕdf<eаee e fбZee eedНZee eeedН\ZZeeаeekбГeeаee dЕdfeаe dd Еdfeаe ббd ekбГded<ee eeГ\ZZejeаe e fбe fZ ee eeГ\ZZded<ddgddgddggeddЕddЕdf<ee eeГ\Z Z!eаeаeбd eаeбgбZ"eаe e fбeddЕddЕdf<eаe e fбeddЕddЕdf<ded<ee"eГZ#eаe"eddЕddЕdfбZ$eаe"eddЕddЕdfбZ%eeаeаe"eddЕddЕdfdбdd Еdfe#e dЕdfkбГeeаeаe"eddЕddЕdfdбdd Еdfe#e dЕdfkбГddl&m'Z'm(Z(e'e ddЕdfГZ)ee)deа*e ddЕdfбkГe(e ddЕdfГZ+dS)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 щN)┌signalcCst|jd}|jd}tа|jб}t||ГD]D}|||||ЕddЕtjf|jddНjddН||ddЕf<q*|S)aь 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) rNщйZaxis)┌shape┌np┌zeros┌range┌newaxis┌sum)┌x┌B┌const┌p┌T┌xhat┌tйr·V/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/statsmodels/sandbox/tsa/varma.py┌VAR s! BrcCsЇ|jd}|jd}|jd}tа|jб}tа|jб}t||Г} t| |ГD]а} ||| || ЕddЕtjf|jddНjddН|| || ЕddЕtjf|jddНjddН|| ddЕf<|| ddЕf|| ddЕf|| ddЕf<qJ||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)rrr┌maxrr r )rr┌Cr ┌P┌Qrr┌e┌startrrrr┌VARMAMs 2. .r┌__main__щщщrщ )r gр?)rrrZvalid)┌acovf┌acf)r)r),┌__doc__┌numpyrZscipyrrr┌__name__r┌KrZcolumn_stackZarangerZonesrr┌print┌allZ correlaterr rrZxhat1Zxhat2Zerr2Zxhat3Zerr3Zr_Zxhat4Zerr4Zxhat5Zerr5Zx0Zxhat0Zxcorr00Zxcorr01Zstatsmodels.tsa.stattoolsr!r"Zaav┌varZaacrrrr┌s\ - ( <(@( FF"