M/PhZHddlmZddlmZddlZddlZddlZddlm Z ddl m Z ddl m Z ddlmZddlmZmZdd lmZdd lmZdd lmZmZmZmZgd Zd6dZd7dZd8dZ d9d:d!Z d;d"Z!d#Z"d$Z#d%Z$d&Z%d'Z&d(Z'd)Z(d*Z)d+Z*d,Z+d-Z,d.Z-d/Z.d0Z/d1Z0d2Z1d.safe_is_const~s=!6!99+@qCx0@0@@! 55s/27axisr(zx is constant.z, c,g|]}t|Sstr.0rs r5 zadd_trend..s+D+D+DqCFF+D+D+Dz3x contains one or more constant columns. Column(s) z are constant.z Adding a constant with trend='z' is not allowed.rindexcolumns)rrcopyr statsmodels.tools.sm_exceptionsr.NotImplementedErrorr isinstancepdSeriesrr1 asanyarraylenvanderarangefloat64fliplrapplyr2r3ndimshaperDjoin ValueErrorrCconcat column_stack)xr rr'rD trendorderr. is_pandasnobstrendarrr6 col_constptp0 col_is_constnz_constbase_err const_colsmsgorders r5rr'sP++G w0L M M MEn.FL 211G ||vvxx #"1"+ $%3,,"1"+ C<<aclG % A6FFFFFF!"4555 D))I a # #  QAAAA M!   q66Dy !TAXRZ000*q.Hy""H ||AAAqD> e||  ! ! ! !  q11II6"-**333D19L#qtqy1H I 6)   +w&&6Q;;/HH i 33I>G!!R\22,"#)!%+D+DG+D+D+D!E!EJ6%666"ZZ%ZZZ oo%''!!""+#AAAqrrE? AAbE(<III qM Ia%jq ) ) ) qM OAgggJ ' ' Hr@r,Tc:t|d}t|d}t|dd}|d}|dkr|jd|z}|jdkr |dddf}|dd|f}|d ur|dz}ne|d ur|jd}nS|dkr|jd|zdz}||jdkr'|jd}t jd t|}t||d }t|}t||jd} |rU||vr)| | |n(| | |tj ||d|f|||d| ffS)a Returns an array with lags included given an array. Parameters ---------- x : array_like An array or NumPy ndarray subclass. Can be either a 1d or 2d array with observations in columns. col : int or None `col` can be an int of the zero-based column index. If it's a 1d array `col` can be None. lags : int The number of lags desired. drop : bool Whether to keep the contemporaneous variable for the data. insert : bool or int If True, inserts the lagged values after `col`. If False, appends the data. If int inserts the lags at int. Returns ------- array : ndarray Array with lags Examples -------- >>> import statsmodels.api as sm >>> data = sm.datasets.macrodata.load() >>> data = data.data[['year','quarter','realgdp','cpi']] >>> data = sm.tsa.add_lag(data, 'realgdp', lags=2) Notes ----- Trims the array both forward and backward, so that the array returned so that the length of the returned array is len(`X`) - lags. The lags are returned in increasing order, ie., t-1,t-2,...,t-lags lagsdroprXr-)rRNrr,TFz number of variables, inserting at the last positionBoth)trim)rrr rSrRwarningswarnr rrpoprCr1rW) rXcolrfrginsertcontempins_idxndlags first_cols last_colss r5add_lagrtsN D& ! !D T6 " "D1c"""A { Qwwgaj3v{{ aaagJ3iG ~~' 5'!* A::WQZ&(1,F AGAJ  WQZF M!     GT / / /FJw ++I 0 *   NN:++C00 1 1 1 1 MM)//#.. / / / ?AdeeZ/0&!DEE9 2 is not implemented until it is neededrr7)N)rrRintTrGrSmeanr1rMrNfloatlinalgpinvdot)rXrdr8r[residtrendsbetas r5detrendrs, UG $ $E D& ! !Dv{{s4yyA~~ C !! >    71:D zzAFFFNN"29U4[[11UQY???y~~f%%))!,,BF64(((v{{s4yyA~~ Lr@forwardexmaxlagrwri.Literal['forward', 'backward', 'both', 'none']originalLiteral['ex', 'sep', 'in'] use_pandasboolreturnKNDArray | DataFrame | tuple[NDArray, NDArray] | tuple[DataFrame, DataFrame]cPt|d}t|d}t|ddd}t|dd }|}t|d d d }t |d o|}|dn|}|}|r|dvrt dd}|j\}} |dvr| }||krt dtj ||z| |dzzf} tdt|dzD]%} || || z ||z| z | || z z| || z dzzf<&|dvrd} n|dvr|} nt d|dvrt| } n|} |r|}t|trLd|jD}tt!||jdkrt dnt#|jg}d|D}t|D]5}t#|dz|fd|D6t| d | |j|} | j| d }|dvr||}||d}n"| | | |d f}|dkr| | | d |f}|dkr||fS|S) a, Create 2d array of lags. Parameters ---------- x : array_like Data; if 2d, observation in rows and variables in columns. maxlag : int All lags from zero to maxlag are included. trim : {'forward', 'backward', 'both', 'none', None} The trimming method to use. * 'forward' : trim invalid observations in front. * 'backward' : trim invalid initial observations. * 'both' : trim invalid observations on both sides. * 'none', None : no trimming of observations. original : {'ex','sep','in'} How the original is treated. * 'ex' : drops the original array returning only the lagged values. * 'in' : returns the original array and the lagged values as a single array. * 'sep' : returns a tuple (original array, lagged values). The original array is truncated to have the same number of rows as the returned lagmat. use_pandas : bool If true, returns a DataFrame when the input is a pandas Series or DataFrame. If false, return numpy ndarrays. Returns ------- lagmat : ndarray The array with lagged observations. y : ndarray, optional Only returned if original == 'sep'. Notes ----- When using a pandas DataFrame or Series with use_pandas=True, trim can only be 'forward' or 'both' since it is not possible to consistently extend index values. Examples -------- >>> from statsmodels.tsa.tsatools import lagmat >>> import numpy as np >>> X = np.arange(1,7).reshape(-1,2) >>> lagmat(X, maxlag=2, trim="forward", original='in') array([[ 1., 2., 0., 0., 0., 0.], [ 3., 4., 1., 2., 0., 0.], [ 5., 6., 3., 4., 1., 2.]]) >>> lagmat(X, maxlag=2, trim="backward", original='in') array([[ 5., 6., 3., 4., 1., 2.], [ 0., 0., 5., 6., 3., 4.], [ 0., 0., 0., 0., 5., 6.]]) >>> lagmat(X, maxlag=2, trim="both", original='in') array([[ 5., 6., 3., 4., 1., 2.]]) >>> lagmat(X, maxlag=2, trim="none", original='in') array([[ 1., 2., 0., 0., 0., 0.], [ 3., 4., 1., 2., 0., 0.], [ 5., 6., 3., 4., 1., 2.], [ 0., 0., 5., 6., 3., 4.], [ 0., 0., 0., 0., 5., 6.]]) rrriTrbackwardbothnoneoptionalr&r)rsepinr%rXr-N)rRr/r)rrzEtrim cannot be 'none' or 'backward' when used on Series or DataFramesr)rrzmaxlag should be < nobsr,)rr)rrztrim option not validc,g|]}t|Sr:r;r=s r5r?zlagmat..s333AQ333r@zSColumns names must be distinct after conversion to string (if not already strings).c,g|]}t|Sr:r;)r>rms r5r?zlagmat..s1113s88111r@c:g|]}t|dzzS)z.L.r;)r>rmlag_strs r5r?zlagmat..s)LLL3CHHu,w6LLLr@rB)rrr7r)rrrr r lowerrUrSr1zerosrangerwrLrHrrDsetr<nameextendrCilocrg)rXrrirrorigrZdropidxr[nvarlmkstartobsstopobs x_columnsrDlagrfleadsrs @r5rr)sRfh ' 'F:|44J  7    D 8Z9LMMMH D1c...A t,,;I\66tD ::<>""agaj00 01 QV I11y111== N NC#'llG NNLLLL)LLL M M M M r(7(|17G D D Dwxyy! } $ $OE99YQ9//D(7"GHH,- u  x''12E5U{ r@c (t|d}t|dd}t|ddd}||}t||}t|d}|jd kr$|rt j|}n2|dddf}n%|jd ks |jd krtd |j\}} |r|rt|j ddd f||d d} | j ddd|d zfg} td | D]N} t|j dd| f||d d} | | j dd||d zfOt j | d S|rtj|}t|ddd f||d ddd|d zfg} td | D]A} | t|dd| f||d dd||d zfBtj| S)a Generate lagmatrix for 2d array, columns arranged by variables. Parameters ---------- x : array_like Data, 2d. Observations in rows and variables in columns. maxlag0 : int The first variable all lags from zero to maxlag are included. maxlagex : {None, int} The max lag for all other variables all lags from zero to maxlag are included. dropex : int Exclude first dropex lags from other variables. For all variables, except the first, lags from dropex to maxlagex are included. trim : str The trimming method to use. * 'forward' : trim invalid observations in front. * 'backward' : trim invalid initial observations. * 'both' : trim invalid observations on both sides. * 'none' : no trimming of observations. use_pandas : bool If true, returns a DataFrame when the input is a pandas Series or DataFrame. If false, return numpy ndarrays. Returns ------- ndarray The array with lagged observations, columns ordered by variable. Notes ----- Inefficient implementation for unequal lags, implemented for convenience. maxlag0maxlagexT)rrirrNr,rr-z'Only supports 1 and 2-dimensional data.r)rirrr7)rir)rrmaxr rRrIrrUrSrrrappendrVr1rKrW) rXrrdropexrirrrZr[rrflagslirs r5rrsLw **G*t<< > > >ya((((  M!   qAwTD999!!!]w{]:JKF1d^^   1QQQT7F = = =6HqL((     ?6 " ""r@c,|dS)NF)ravelmats r5rrs 99S>>r@cj|jtt|SN)rxtake _triu_indicesrLrs r5rrs$ 5::mCHH-- . ..r@c@tj|\}}||z|zSr)r1 tril_indicesr!rowscolss r5 _tril_indicesr####JD$ !8d?r@c@tj|\}}||z|zSr)r1 triu_indicesrs r5rr(rr@c@tj|\}}||z|zSr)r1 diag_indicesrs r5 _diag_indicesr-rr@cttjt|}||zt|ksJ|||fdS)Nrrd)rwr1sqrtrLreshape)vrs r5rr2sN BGCFFOOA q5CFF???? 99aV39 ' ''r@c Tddtjddt|zzzz}ttj|}tj||f}||tj|<||jz}|tj|xxdzcc<|S)Ng?rAr,r-) r1rrLrwroundrrrxr)rrresults r5rr8s "rwq1s1vv:~... /D rx~~  D XtTl # #F$%F2?4 ! fh F 2?4 !!!Q&!!! Mr@ct|d}tj||dzzdz}tjd|DjS)z Create duplication matrix D_n which satisfies vec(S) = D_n vech(S) for symmetric matrix S Returns ------- D_n : ndarray r!r,r-cPg|]#}t|$Sr:)rr)r>rXs r5r?z&duplication_matrix..Rs(4441VAYY__&&444r@)rr1eyearrayrx)r!tmps r5rrGsQ CA &a!e! " "C 844444 5 5 77r@ct|d}ttjtj||f}tj||z|dkS)z Create the elimination matrix L_n which satisfies vech(M) = L_n vec(M) for any matrix M Parameters ---------- Returns ------- r!r)rrr1trilonesr)r! vech_indicess r5rrUsR CArwrw1v//00L 6!a%==* ++r@ct|d}t|d}tj||z}tj||z||fd}||dS)z Create the commutation matrix K_{p,q} satisfying vec(A') = K_{p,q} vec(A) Parameters ---------- p : int q : int Returns ------- K : ndarray (pq x pq) pqrrrr7)rr1rrNrrr)rrKindicess r5rres{ CACA q1u AiA&&1vS&99G 66'--//6 * **r@c 2tj|dz }tj|dz }tdt|D]J}||}t|D]!}||xx||||z dz zzcc<"|d||d|<K|S)z Transforms params to induce stationarity/invertability. Parameters ---------- params : array_like The AR coefficients Reference --------- Jones(1980) r-r,N)r1tanhrrL)params newparamsrjakiters r5_ar_transparamsrzs ##I '&1*  C 1c&kk " "   aL1XX 7 7E JJJ!iE A 66 6JJJJBQB "1" r@cj|}|}tt|dz ddD]Q}||}t|D](}||||||z dz zzd|dzz z ||<)|d||d|<Rdtj|z}|S)z Inverse of the Jones reparameterization Parameters ---------- params : array_like The transformed AR coefficients r,rrAr-N)rErrLr1arctanh)rrrrr invarcoefss r5_ar_invtransparamsrs[[]]F ++--C 3v;;?Ar * * 1I1XX  E -!fQY].C*CCAF CJJ!Wrr RZ'''J r@c dtj| z dtj| zz }dtj| z dtj| zz }tdt |D]J}||}t|D]!}||xx||||z dz zz cc<"|d||d|<K|S)z Transforms params to induce stationarity/invertability. Parameters ---------- params : ndarray The ma coeffecients of an (AR)MA model. Reference --------- Jones(1980) r,N)r1exprErrL)rrrrbrs r5_ma_transparamsrsbffWoo%!bffWoo*=>DDFFI w Aw$7 8 > > @ @C1c&kk " "   aL1XX 7 7E JJJ!iE A 66 6JJJJBQB "1" r@cP|}tt|dz ddD]Q}||}t|D](}||||||z dz zz d|dzz z ||<)|d||d|<Rtjd|z d|zz  }|S)z Inverse of the Jones reparameterization Parameters ---------- params : ndarray The transformed MA coefficients r,rrAr-N)rErrLr1log)macoefsrrrr invmacoefss r5_ma_invtransparamsrs ,,..C 3w<irrXs r5r?z&unintegrate_levels..s.EEErwq!a%((+EEEr@rrA)rr1asarrayr)rXrs``r5unintegrate_levelsrsT* CA "1"A :EEEEEU1a__EEE F FFr@cDt|dd}t|dkrI|d}tt jtj||f|S|d}t jtj||fS)ay After taking n-differences of a series, return the original series Parameters ---------- x : array_like The n-th differenced series levels : list A list of the first-value in each differenced series, for [first-difference, second-difference, ..., n-th difference] Returns ------- y : array_like The original series de-differenced Examples -------- >>> x = np.array([1, 3, 9., 19, 8.]) >>> levels = unintegrate_levels(x, 2) >>> levels array([ 1., 2.]) >>> unintegrate(np.diff(x, 2), levels) array([ 1., 3., 9., 19., 8.]) Nr,rAr)listrLrl unintegrater1cumsumr_)rXlevelsx0s r5rrs|4&\\!!!_F 6{{Q ZZ^^29RU2q5\22F;;; B 9RU2q5\ " ""r@freqstr | offsets.DateOffsetct|tjst|}t|tjsJ|j}d}|dvs||rdS|dks|drdS|dks|drd S|d ks|d rd S|d krdS|dkrdS|dkrdStd|)a$ Convert a pandas frequency to a periodicity Parameters ---------- freq : str or offset Frequency to convert Returns ------- int Periodicity of freq Notes ----- Annual maps to 1, quarterly maps to 4, monthly to 12, weekly to 52. )zA-zAS-zY-zYS-zYE-)AYr,Q)zQ-QSQEM)zM-MSME WzW-4DBHzDfreq {} not understood. Please report if you think this is in error.) rHr DateOffsetr rule_codeupper startswithrUformat)r yearly_freqss r5rrs$ dG. / / dG. / //// >   ! !D4L zT__\::q (:;;q (:;;r --r q q r &&,fTll   r@)rFr)Nr,FT)r,r)rrF) rrwrirrrrrrr)NrrF)rrrrw)3 __future__rstatsmodels.compat.pythonrrjnumpyr1pandasrIrpandas.tseriesrpandas.tseries.frequenciesrtypingrstatsmodels.tools.datar r rFr statsmodels.tools.typingr statsmodels.tools.validationr rrr__all__rrtrrrrrrrrrrrrrrrrrrrrr:r@r5r&s"""""",,,,,,""""""000000AAAAAAAA888888,,,,,,   @ @ @ @ FMPMPMPMP`,,,,bAJ04! TTTTTpEJT#T#T#T#n///   (((    8 8 8 , , , +++*.,2*GGG4###D* * * * * * r@