M/PhLdZddlZddlmZddlmZdZd*dZd+dZ d,d Z d-d Z d Z d Z Gd dZGddZedkrejddgddggddgddgggZejddgddggddgddgggZejddgddggddgddgggZejddgddggddgddggddgddgggZejejddddddfdejddddddfzfZejgdgdgdggdgdgd ggZejd!d"Ze eeZejeeded#$Z e d!dd"d"Z"e e"Z#eeZ$e$%de$&e$&d%d&dejddgddggddgddggddgddgggZ'ejddgddggd'dgdd(gggZ(ejddgddggd)dgd'dggd(dgddgggZ)ee'e(Z*e+e,e*e+e*-e+e*-ee+e*.e+e*/e+e*0ee)Z1e+e1/e+e10dSdS).a9 Helper and filter functions for VAR and VARMA, and basic VAR class Created on Mon Jan 11 11:04:23 2010 Author: josef-pktd License: BSD This is a new version, I did not look at the old version again, but similar ideas. not copied/cleaned yet: * fftn based filtering, creating samples with fft * Tests: I ran examples but did not convert them to tests examples look good for parameter estimate and forecast, and filter functions main TODOs: * result statistics * see whether Bayesian dummy observation can be included without changing the single call to linalg.lstsq * impulse response function does not treat correlation, see Hamilton and jplv Extensions * constraints, Bayesian priors/penalization * Error Correction Form and Cointegration * Factor Models Stock-Watson, ??? see also VAR section in Notes.txt N)signal)lagmatc6tj|}tj|}|jdkr |dddf}|jdkrtd|jd}|jd}|dz}|jdkr!t j||dddfdS|jdkrt|jdkrt j||dStj|jd|z dz|f}t|D]4}t j|dd|f|dd|fd|dd|f<5|S|jdkrBt j|dddddf|}||| |jddzddf}|SdS) aapply an autoregressive filter to a series x Warning: I just found out that convolve does not work as I thought, this likely does not work correctly for nvars>3 x can be 2d, a can be 1d, 2d, or 3d Parameters ---------- x : array_like data array, 1d or 2d, if 2d then observations in rows a : array_like autoregressive filter coefficients, ar lag polynomial see Notes Returns ------- y : ndarray, 2d filtered array, number of columns determined by x and a Notes ----- In general form this uses the linear filter :: y = a(L)x where x : nobs, nvars a : nlags, nvars, npoly Depending on the shape and dimension of a this uses different Lag polynomial arrays case 1 : a is 1d or (nlags,1) one lag polynomial is applied to all variables (columns of x) case 2 : a is 2d, (nlags, nvars) each series is independently filtered with its own lag polynomial, uses loop over nvar case 3 : a is 3d, (nlags, nvars, npoly) the ith column of the output array is given by the linear filter defined by the 2d array a[:,:,i], i.e. :: y[:,i] = a(.,.,i)(L) * x y[t,i] = sum_p sum_j a(p,j,i)*x(t-p,j) for p = 0,...nlags-1, j = 0,...nvars-1, for all t >= nlags Note: maybe convert to axis=1, Not TODO: initial conditions Nzx array has to be 1d or 2drvalid)mode) npasarrayndim ValueErrorshaperconvolveminzerosrange) xanvarnlagsntrimresultiyfyvalids ]/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tsa/varma_process.py varfilterr$sr 1 A 1 Av{{ aaafIvzz5666 71:D GAJE 1HE v{{q!AAAdF)':::: 1 qw<<1  ?1ag666 6 171:e+A-t455t H HA /!AAAaC&!AAAaC&wGGGF111Q3KK 1_Qqqq4x[! , ,E5&L"(1+q.23 rc |j\}}}||krtdtj|dz||f}|d|dddddf<|dd |d|ddddf<|dkrzt d|dzD]f}tj||f}t d|D]1} |tj||  ||| z ddddfz }2|||ddddf<g|dkr_t |dz|dzD]H}t|ddj||dz ||z dddddfjt d|S)acreates inverse ar filter (MA representation) recursively The VAR lag polynomial is defined by :: ar(L) y_t = u_t or y_t = -ar_{-1}(L) y_{t-1} + u_t the returned lagpolynomial is arinv(L)=ar^{-1}(L) in :: y_t = arinv(L) u_t Parameters ---------- ar : ndarray, (nlags,nvars,nvars) matrix lagpolynomial, currently no exog first row should be identity Returns ------- arinv : ndarray, (nobs,nvars,nvars) Notes ----- .exogenous variables not implemented not testedrrNrz+waiting for generalized ufuncs or something)rprintr rrdotNotImplementedError) arnobsversionrnvarsnvarsexarinvrtmpps rvarinversefilterr.s:HE5'  >??? Hd1fgu- . .Ea5E!AAAaaa%LQRR&E!E'!!!AAA+!||qa  A(E%=))C1U^^ 5 5rvr!ufU1Q3qqq7^444E!AAAaaa%LL!||uQwtAv&& U UA "QRR&,ac!E'"nQQQqqq&8 9 ? @ @ @&&STT T Lrc F|j\}}}|dz }|jd}||krtd|jd|krtd|tj||z|f}|} nIt ||jd} tj|| z|f}||| |jdz | <||| d<t | | |zD]L} t d|D]9} || xxtj|| | z ddf||  z cc<:M|S)aEgenerate an VAR process with errors u similar to gauss uses loop Parameters ---------- ar : array (nlags,nvars,nvars) matrix lagpolynomial u : array (nobs,nvars) exogenous variable, error term for VAR Returns ------- sar : array (1+nobs,nvars) sample of var process, inverse filtered u does not trim initial condition y_0 = 0 Examples -------- # generate random sample of VAR nobs, nvars = 10, 2 u = numpy.random.randn(nobs,nvars) a21 = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[-0.8, 0. ], [ 0., -0.6]]]) vargenerate(a21,u) # Impulse Response to an initial shock to the first variable imp = np.zeros((nobs, nvars)) imp[0,0] = 1 vargenerate(a21,imp) rrr!zu needs to have nvars columnsN)rr#rr rmaxrr$) r&u initvaluesrr)r*nlagsm1r'sarstartrr-s r vargenerater6sXJHE5'aiG 71:D  >???wqzU8999hW e,--GZ-a011hU E*++/9E*"1% %e +,CK 5t $ $00q 0 0A FFFbfS1QQQZA// /FFFF 0 Jrc tj|j}||xx||zz cc<tj|j}tj|}||tj|j | |< |z fdtt D}||t|<|S)apad with zeros along one axis, currently only axis=0 can be used sequentially to pad several axis Examples -------- >>> padone(np.ones((2,3)),1,3,axis=1) array([[ 0., 1., 1., 1., 0., 0., 0.], [ 0., 1., 1., 1., 0., 0., 0.]]) >>> padone(np.ones((2,3)),1,1, fillvalue=np.nan) array([[ NaN, NaN, NaN], [ 1., 1., 1.], [ 1., 1., 1.], [ NaN, NaN, NaN]]) cHg|]}t||Sslice.0kendindstartinds r zpadone..+IIIuXa[&),,IIIr) r arrayremptyfillrr rlentuple) rfrontbackaxis fillvaluershapearroutmyslicer?r@s @@rpadonerOs& HQW  E $KKKEDL!KKKx  H (5//CHHYxHHTN  FIIIIIeCKK6H6HIIIGCg JrcRtj|j}||xx||zzcc<tj|j}tj|j||<|zfdt t D}|t|S)a;trim number of array elements along one axis Examples -------- >>> xp = padone(np.ones((2,3)),1,3,axis=1) >>> xp array([[ 0., 1., 1., 1., 0., 0., 0.], [ 0., 1., 1., 1., 0., 0., 0.]]) >>> trimone(xp,1,3,1) array([[ 1., 1., 1.], [ 1., 1., 1.]]) cHg|]}t||Sr9r:r<s rrAztrimone..,rBr)r rCrrr rrFrG) rrHrIrJrrLrNr?r@s @@rtrimonerRs HQW  E $KKKEDL!KKKx  HxHHTN  FIIIIIeCKK6H6HIIIG U7^^ rc|j\}}}tjtj||dddddf| fS)z?make reduced lagpolynomial into a right side lagpoly array N)rr r_eye)r&rrnvarexs rar2fullrW3sEE4 5V$$T!!!AAAX.s2 33rc|dd S)zconvert full (rhs) lagpolynomial into a reduced, left side lagpoly array this is mainly a reminder about the definition rNr9)r&s rar2lhsrY:s qrrF7Nrc2eZdZdZdZdZdZdZd dZdS) _Vara<obsolete VAR class, use tsa.VAR instead, for internal use only Examples -------- >>> v = Var(ar2s) >>> v.fit(1) >>> v.arhat array([[[ 1. , 0. ], [ 0. , 1. ]], [[-0.77784898, 0.01726193], [ 0.10733009, -0.78665335]]]) c<||_|j\|_|_dSN)yrr'r))selfr^s r__init__z _Var.__init__Ts ! 4:::rc||_|j}t|j|dd}|ddd|f|_|dd|df|_t j|j|jd}||_ |d ||||_ t|j |_ |d|_|d |_dS) aestimate parameters using ols Parameters ---------- nlags : int number of lags to include in regression, same for all variables Returns ------- None, but attaches arhat : array (nlags, nvar, nvar) full lag polynomial array arlhs : array (nlags-1, nvar, nvar) reduced lag polynomial for left hand side other statistics as returned by linalg.lstsq : need to be completed This currently assumes all parameters are estimated without restrictions. In this case SUR is identical to OLS estimation results are attached to the class instance bothin)trimoriginalNr"rcondrrr)rr)rr^yredxredr linalglstsq estresultsreshapearlhsrWarhatrssxredrank)r_rr)lmatress rfitz_Var.fitXs6  dfe&4@@@6E6N 566N ioodi"o==V^^E5%88 TZ(( q6A rcnt|dst|j|j|_|jS)z:calculate estimated timeseries (yhat) for sample yhat)hasattrrr^rorvr_s rpredictz _Var.predicts3 tV$$ 6!$&$*55DIyrc|jddddftjtj|jj|jdddddfz|_dS)a covariance matrix of estimate # not sure it's correct, need to check orientation everywhere # looks ok, display needs getting used to >>> v.rss[None,None,:]*np.linalg.inv(np.dot(v.xred.T,v.xred))[:,:,None] array([[[ 0.37247445, 0.32210609], [ 0.1002642 , 0.08670584]], [[ 0.1002642 , 0.08670584], [ 0.45903637, 0.39696255]]]) >>> >>> v.rss[0]*np.linalg.inv(np.dot(v.xred.T,v.xred)) array([[ 0.37247445, 0.1002642 ], [ 0.1002642 , 0.45903637]]) >>> v.rss[1]*np.linalg.inv(np.dot(v.xred.T,v.xred)) array([[ 0.32210609, 0.08670584], [ 0.08670584, 0.39696255]]) N)rpr rjinvr$riTparamcovrxs rcovmatz _Var.covmats\($tAAA+. IMM"&di88 9 9!!!AAAd( CD rrNct|tj||jf}t|j||jS)acalculates forcast for horiz number of periods at end of sample Parameters ---------- horiz : int (optional, default=1) forecast horizon u : array (horiz, nvars) error term for forecast periods. If None, then u is zero. Returns ------- yforecast : array (nobs+horiz, nvars) this includes the sample and the forecasts N)r2)r rr)r6ror^)r_horizr1s rforecastz _Var.forecasts8 9%,--A4:qTV<<< C C E EE 7?fUmmH-DG!%D  &(erve}}&<%A%A%C%C!CD hqk  VG rr&c||}n+|dkr|j}n|dkr|j}ntd|d|jS)z4stack lagpolynomial vertically in 2d array Nr&rno array or name givenr")r&rrrmrr_rnames rvstackzVarmaPoly.vstacksY =AA T\\AA T\\AA566 6yyT\***rc||}n+|dkr|j}n|dkr|j}ntd|ddd|jjS)z6stack lagpolynomial horizontally in 2d array Nr&rrrrr")r&rrswapaxesrmrr|rs rhstackzVarmaPoly.hstacksj =AA T\\AA T\\AA566 6zz!A&&r4<88::rverticalc||}n+|dkr|j}n|dkr|j}ntd|d|j}|j\}}t j||}||ddd|f<|S)zDstack lagpolynomial vertically in 2d square array with eye Nr&rrr")r>)r&rrrmrrr rU)r_rr orientationastackedlenpkr)amats r stacksquarezVarmaPoly.stacksquares =AA T\\AA T\\AA566 699R..~ uveu%%%!QQQvvX rctj|jdd|jddfd}|d|jS)z;stack ar and lagpolynomial vertically in 2d array rNrr")r concatenater&rrmrr_rs rvstackarma_minus1zVarmaPoly.vstackarma_minus1sD NDGABBK5a 8 8yyT\***rctj|jdd|jddfd}|ddd|jS)zustack ar and lagpolynomial vertically in 2d array this is the Kalman Filter representation, I think rNrrr")r rr&rrrmrrs rhstackarma_minus1zVarmaPoly.hstackarma_minus1sR NDGABBK5a 8 8zz!A&&r4<888rc||}n;|jr$||jdd }n|jdd }||}t jtj|ddd}||_t j |dk S)a>check whether the auto-regressive lag-polynomial is stationary Returns ------- isstationary : bool *attaches* areigenvalues : complex array eigenvalues sorted by absolute value References ---------- formula taken from NAG manual Nrr") r reduceformr&rr sortrjeigvals areigenvaluesabsrr_rrevs rgetisstationaryzVarmaPoly.getisstationarys" =AA  !__TW--abb11WQRR[L"" WRY&&t,, - -ddd 3r Q##%%%rc||}n9|jr#||jdd}n|jdd}|jddkr&t jgtj|_dS||}t j tj |ddd}||_t j |dk S)a>check whether the auto-regressive lag-polynomial is stationary Returns ------- isinvertible : bool *attaches* maeigenvalues : complex array eigenvalues sorted by absolute value References ---------- formula taken from NAG manual NrrTr")rrrrr rCcomplex maeigenvaluesrrrjrrrrs rgetisinvertiblezVarmaPoly.getisinvertible;s" =AA! OODG,,QRR0GABBK 71:??!#"bj!9!9D 4"" WRY&&t,, - -ddd 3r Q##%%%rc|jdkrtd|j\}}}tj|} tj|dd|ddf}n(#tjj$rtddwxYwt|D] }tj |||||<!|S)z. this assumes no exog, todo r zapoly needs to be 3drNzmatrix not invertiblezask for implementation of pinv) r rrr empty_likerjr{ LinAlgErrorrr$)r_apolyrr*r)ra0invlags rrzVarmaPoly.reduceform]s :??344 4 % w M%  ?IMM!AfufaaaK.11EEy$ ? ? ?4=?? ? ?<< / /CVE5:..AcFFs ,A((%B r])Nr&)Nr&r) rrrrr`rrrrrrrrr9rrrrs.     + + + + ; ; ; ;&+++999&&&&: & & & &Drr__main__?gg333333皙?g?gr 皙?)rrr)rrr)rrr)rrr)rg333333?r)rrg?irr"rfig?g333333?gffffff)rr])rrrr)rrr)2rnumpyr scipyrstatsmodels.tsa.tsatoolsrrr.r6rOrRrWrYr[rrrCa21a22a23a24rTrUa31a32randomrandnutar2srjrkrsrmbhatrovrtrar23ma22ar23nsvpr#varsrrrrvp2r9rrrs:++++++\\\~1111h::::z    F8444p=p=p=p=p=p=p=p=f||||||||~ z "(rR\R\#R\D\#$ % %C "(rR\R\#R\D\#$ % %C "(rR\R\#S\D\#$ % %C "(rR\R\#R\D\#R\D\# $ % %C %q $qqq(#S4!!!8)<%<< =C "(''''''''')('''''''') * + +C a B ;s2  D )//&&a..$b/ 9 9C q6>>!Aa D GDMME T AEE!HHHJJLLLJJrNN344 28blR\#R\D\#R\D\# $ % %D 28blR\#R\C["# $ $D RX" R\#R\D\#R\D\# $%%F 4  B E$$r((OOO E"))++ E"))C.. E"   !!! E"     E"     )F  C E#        E#         mr