ó áp7]c@s dZddlmZddlZddlmZddlmZd„Z dd„Z dd „Z d d d d d „Z d d d d „Zd „Zd„Zdefd„ƒYZdefd„ƒYZedkrœejddgddggddgddgggƒZejddgddggddgddgggƒZejddgddggddgddgggƒZejddgddggddgddggddgddgggƒZejejdƒddd…dd…fdejdƒddd…dd…ffZejdddgdddgdddggdddgdddgdddgggƒZejjdd ƒZ e ee ƒZ!ej"j#ee!dƒe!d!dƒZ$e$d j%dd d ƒZ&ee&ƒZ'ee!ƒZ(e(j)dƒe(j*ƒe(j*d"ƒd#ejddgddggddgddggddgddgggƒZ+ejddgddggd$dgdd%gggƒZ,ejddgddggd&dgd$dggd%dgddgggƒZ-ee+e,ƒZ.e/e0e.ƒƒe/e.j1ƒƒe/e.j1eƒƒe/e.j2ƒƒe/e.j3ƒƒe/e.j4ƒƒee-ƒZ5e/e5j3ƒƒe/e5j4ƒƒndS('s8 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 didn't 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 iÿÿÿÿ(tprint_functionN(tsignal(tlagmatc Csëtj|ƒ}tj|ƒ}|jdkrF|dd…df}n|jdkrdtdƒ‚n|jd}|jd}|d}|jdkr½tj||dd…dfddƒS|jdkr~t|jƒdkr÷tj||ddƒStj |jd|d|fƒ}x\t |ƒD]N}tj|dd…|f|dd…|fddƒ|dd…|f3 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 iNisx array has to be 1d or 2ditmodetvalidi( tnptasarraytndimtNonet ValueErrortshapeRtconvolvetmintzerostrange( txtatnvartnlagstntrimtresulttityftyvalid((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pyt varfilter&s,9   &$L++ic CsÉ|j\}}}||kr+tdƒntj|d||fƒ}|d|ddd…dd…f<|d |d|…dd…dd…f<|dkrGx¤td|dƒD]Œ}tj||fƒ}xOtd|ƒD]>} |tj||  ||| dd…dd…fƒ7}qßW|||dd…dd…f>> 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]]) ( RtarrayR temptytfillR RRtlentslicettuple( Rtfronttbacktaxist fillvalueR tshapearrtouttstartindtendindtktmyslice((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pytpadoneös   6c Cs¢tj|jƒ}||c||8>> 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.]]) ( RR,R R RRR/R0R1( RR2R3R4R R6R8R9R:R;((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pyttrimones  6cCsI|j\}}}tjtj||ƒddd…dd…f| fS(s?make reduced lagpolynomial into a right side lagpoly array N(R Rtr_teyeR(RRRtnvarex((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pytar2full5scCs |d S(sconvert full (rhs) lagpolynomial into a reduced, left side lagpoly array this is mainly a reminder about the definition i((R((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pytar2lhs<st_VarcBsAeZdZd„Zd„Zd„Zd„Zddd„ZRS(s<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]]]) cCs"||_|j\|_|_dS(N(tyR RR(tselfRD((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pyt__init__Vs cCsä||_|j}t|j|ddddƒ}|dd…d|…f|_|dd…|d…f|_tjj|j|jddƒ}||_ |dj |||ƒ|_ t |j ƒ|_ |d |_|d |_dS( s¯estimate parameters using ols Parameters ---------- nlags : integer 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 ttrimtbothtoriginaltinNtrcondiÿÿÿÿiii(RRRRDtyredtxredRtlinalgtlstsqt estresultstreshapetarlhsRAtarhattrsstxredrank(RERRtlmattres((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pytfitZs  !  cCs1t|dƒs*t|j|jƒ|_n|jS(s:calculate estimated timeseries (yhat) for sample tyhat(thasattrRRDRSRY(RE((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pytpredictƒscCsa|jdddd…ftjjtj|jj|jƒƒdd…dd…df|_dS(sÔ 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( RTRRRNtinvRRMtTtparamcov(RE((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pytcovmatŒsicCs@|dkr'tj||jfƒ}nt|j|d|jƒS(s£calculates 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 R'N(RRR RR+RSRD(REthorizR&((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pytforecast£s N( t__name__t __module__t__doc__RFRXR[R_RRa(((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pyRCDs   ) t VarmaPolycBs}eZdZd d„Zd dd„Zd dd„Zd ddd„Zd„Zd„Z d d „Z d d „Z d „Z RS( s¼class to keep track of Varma polynomial format Examples -------- ar23 = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[-0.6, 0. ], [ 0.2, -0.6]], [[-0.1, 0. ], [ 0.1, -0.1]]]) ma22 = np.array([[[ 1. , 0. ], [ 0. , 1. ]], [[ 0.4, 0. ], [ 0.2, 0.3]]]) cCsõ||_||_|j\}}}||||_|_|_|dd|…ftj|ƒkjƒ |_ |jdkr¡tj|ƒd|_t |_ n#|dtj|ƒkjƒ |_ |jd|_ ||k|_|d |_dS(Ni.i(N.(RtmaR RtnvarallRRR?tallt isstructuredRtTruet isindependenttmalagsthasexogtarm1(RERRfRRgR((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pyRFÏs  / #RcCsd|dk r|}n<|dkr-|j}n$|dkrE|j}n tdƒ‚|jd|jƒS(s4stack lagpolynomial vertically in 2d array RRfsno array or name giveniÿÿÿÿN(RRRfR RQRg(RERtname((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pytvstackßs       cCss|dk r|}n<|dkr-|j}n$|dkrE|j}n tdƒ‚|jddƒjd|jƒjS(s6stack lagpolynomial horizontally in 2d array RRfsno array or name giveniiiÿÿÿÿN(RRRfR tswapaxesRQRgR](RERRo((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pythstackîs       tverticalcCsª|dk r|}n<|dkr-|j}n$|dkrE|j}n tdƒ‚|jd|jƒ}|j\}}tj|d|ƒ}||dd…d|…f<|S(sDstack lagpolynomial vertically in 2d square array with eye RRfsno array or name giveniÿÿÿÿR:N( RRRfR RQRgR RR?(RERRot orientationtastackedtlenpkRtamat((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pyt stacksquareýs       cCs9tj|jd|jdfdƒ}|jd|jƒS(s;stack ar and lagpolynomial vertically in 2d array iiiÿÿÿÿ(Rt concatenateRRfRQRg(RER((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pytvstackarma_minus1s&cCsEtj|jd|jdfdƒ}|jddƒjd|jƒS(sustack ar and lagpolynomial vertically in 2d array this is the Kalman Filter representation, I think iiiiÿÿÿÿ(RRyRRfRqRQRg(RER((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pythstackarma_minus1s&cCsŸ|dk r|}n1|jr8|j|jƒd }n|jd }|j|ƒ}tjtjj|ƒƒddd…}||_ tj |ƒdkj ƒS(sAcheck whether the auto-regressive lag-polynomial is stationary Returns ------- isstationary : boolean *attaches* areigenvalues : complex array eigenvalues sorted by absolute value References ---------- formula taken from NAG manual iNiÿÿÿÿ( RRit reduceformRRxRtsortRNteigvalst areigenvaluestabsRh(RERRwtev((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pytgetisstationary s   ( cCsÌ|dk r|}n/|jr7|j|jƒd}n |jd}|jddkrstjgtjƒ|_t S|j |ƒ}tj tj j |ƒƒddd…}||_tj|ƒdkjƒS(sAcheck whether the auto-regressive lag-polynomial is stationary Returns ------- isinvertible : boolean *attaches* maeigenvalues : complex array eigenvalues sorted by absolute value References ---------- formula taken from NAG manual iiNiÿÿÿÿ(RRkR|RfR RR,tcomplext maeigenvaluesRjRxR}RNR~R€Rh(RERRwR((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pytgetisinvertible=s    ( cCsÌ|jdkrtdƒ‚n|j\}}}tj|ƒ}y/tjj|dd|…dd…fƒ}Wn&tjjk r–tddƒ‚nXx.t|ƒD] }tj |||ƒ||R?ta31ta32trandomtrandntuttar2sRNRORWRQtbhatRStvRXRatar23tma22tar23nstvpRtvarsRpR{R‚R…tvp2(((s<lib/python2.7/site-packages/statsmodels/tsa/varma_process.pyts”  _ 4 =#  s¿           [   $