p7]c@`shdZddlmZmZmZddlmZddlmZddl Z ddl Z ddl mZddlmZddlmZddljjZdd lmZmZd d lmZmZd d lmZmZm Z d d l!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'defdYZ(defdYZ)de fdYZ*ej+e*e)dS(ss Vector Autoregressive Moving Average with eXogenous regressors model Author: Chad Fulton License: Simplified-BSD i(tdivisiontabsolute_importtprint_function(twarn(t OrderedDictN(tBunch(t_is_using_pandas(t var_model(tEstimationWarningt ValueWarningi(tINVERT_UNIVARIATEtSOLVE_LU(tMLEModelt MLEResultstMLEResultsWrapper(t is_invertiblet prepare_exogt!constrain_stationary_multivariatet#unconstrain_stationary_multivariatetprepare_trend_spectprepare_trend_datatVARMAXcB`steZdZd d ddeeedZedZedZ edZ d Z d Z d Z RS(s Vector Autoregressive Moving Average with eXogenous regressors model Parameters ---------- endog : array_like The observed time-series process :math:`y`, , shaped nobs x k_endog. exog : array_like, optional Array of exogenous regressors, shaped nobs x k. order : iterable The (p,q) order of the model for the number of AR and MA parameters to use. trend : str{'n','c','t','ct'} or iterable, optional Parameter controlling the deterministic trend polynomial :math:`A(t)`. Can be specified as a string where 'c' indicates a constant (i.e. a degree zero component of the trend polynomial), 't' indicates a linear trend with time, and 'ct' is both. Can also be specified as an iterable defining the polynomial as in `numpy.poly1d`, where `[1,1,0,1]` would denote :math:`a + bt + ct^3`. Default is a constant trend component. error_cov_type : {'diagonal', 'unstructured'}, optional The structure of the covariance matrix of the error term, where "unstructured" puts no restrictions on the matrix and "diagonal" requires it to be a diagonal matrix (uncorrelated errors). Default is "unstructured". measurement_error : boolean, optional Whether or not to assume the endogenous observations `endog` were measured with error. Default is False. enforce_stationarity : boolean, optional Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. Default is True. enforce_invertibility : boolean, optional Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. Default is True. kwargs Keyword arguments may be used to provide default values for state space matrices or for Kalman filtering options. See `Representation`, and `KalmanFilter` for more details. Attributes ---------- order : iterable The (p,q) order of the model for the number of AR and MA parameters to use. trend : str{'n','c','t','ct'} or iterable Parameter controlling the deterministic trend polynomial :math:`A(t)`. Can be specified as a string where 'c' indicates a constant (i.e. a degree zero component of the trend polynomial), 't' indicates a linear trend with time, and 'ct' is both. Can also be specified as an iterable defining the polynomial as in `numpy.poly1d`, where `[1,1,0,1]` would denote :math:`a + bt + ct^3`. error_cov_type : {'diagonal', 'unstructured'}, optional The structure of the covariance matrix of the error term, where "unstructured" puts no restrictions on the matrix and "diagonal" requires it to be a diagonal matrix (uncorrelated errors). Default is "unstructured". measurement_error : boolean, optional Whether or not to assume the endogenous observations `endog` were measured with error. Default is False. enforce_stationarity : boolean, optional Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. Default is True. enforce_invertibility : boolean, optional Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. Default is True. Notes ----- Generically, the VARMAX model is specified (see for example chapter 18 of [1]_): .. math:: y_t = A(t) + A_1 y_{t-1} + \dots + A_p y_{t-p} + B x_t + \epsilon_t + M_1 \epsilon_{t-1} + \dots M_q \epsilon_{t-q} where :math:`\epsilon_t \sim N(0, \Omega)`, and where :math:`y_t` is a `k_endog x 1` vector. Additionally, this model allows considering the case where the variables are measured with error. Note that in the full VARMA(p,q) case there is a fundamental identification problem in that the coefficient matrices :math:`\{A_i, M_j\}` are not generally unique, meaning that for a given time series process there may be multiple sets of matrices that equivalently represent it. See Chapter 12 of [1]_ for more information. Although this class can be used to estimate VARMA(p,q) models, a warning is issued to remind users that no steps have been taken to ensure identification in this case. References ---------- .. [1] Lütkepohl, Helmut. 2007. New Introduction to Multiple Time Series Analysis. Berlin: Springer. iitct unstructuredc  `s|_|_|_|_|_|_t|d_t|d_|dkrwt dnjdkrjdkrt dnjdkrjdkrt dt n|_t j\_ _j jdkoj ddk_t|\_}jdk_t|dsftj|}ntjd} | j_|jd} | } | j} | jdd | jd ttBttj |d |d | d | | jdksjdkr.j r.t!j"_#nt$_%j&jj%d<j&djj%d<j&djj%d<j&jj%d<jdkrj&j%d    cC`sjtj|dd}tj|jd|j}||j||j<|jdkr2|jr2|jdkrtj ||j }n]|jdkrtj|j djd|j}||j ||j     c K`stt|j||}|jru||jj|j|jj}t j |j d|}|j|j |j RQtnanR[R8R\R9RvRUR2R^RVRRRERXR3R_RY( R0RRaRt intercepttzeroRRR R!R((s@lib/python2.7/site-packages/statsmodels/tsa/statespace/varmax.pyRsB       "    N(ii(t__name__t __module__t__doc__RARItTrueRHtpropertyRgRRRRR(((s@lib/python2.7/site-packages/statsmodels/tsa/statespace/varmax.pyRs_ ? S MRecB`sVeZdZdddZddedddZddedZe jje_RS(s Class to hold results from fitting an VARMAX model. Parameters ---------- model : VARMAX instance The fitted model instance Attributes ---------- specification : dictionary Dictionary including all attributes from the VARMAX model instance. coefficient_matrices_var : array Array containing autoregressive lag polynomial coefficient matrices, ordered from lowest degree to highest. coefficient_matrices_vma : array Array containing moving average lag polynomial coefficients, ordered from lowest degree to highest. See Also -------- statsmodels.tsa.statespace.kalman_filter.FilterResults statsmodels.tsa.statespace.mlemodel.MLEResults topgc K`stt|j||||||ti |jjd6|jjd6|jjd6|jjd6|jj d6|jj d6|jj d6|jj d6|jj d 6|jjd 6|_d|_d|_|jj d kr?tj|j|jj}|jj}|jj } |j|| |jj||| j|_n|jj d krtj|j|jj} |jj}|jj } | j|| |jj||| j|_ndS( NR2R3R4R5R6R8R9RR<R?i(RGReRHRtmodelR2R3R4R5R6R8R9RR<R?t specificationRAtcoefficient_matrices_vartcoefficient_matrices_vmaR+R~RR[RLRR|R\( R0RRtfilter_resultstcov_typetcov_kwdsRaRRLR8RR9((s@lib/python2.7/site-packages/statsmodels/tsa/statespace/varmax.pyRHs6                cK`s|dkr|jjd}n|jj|||dt\}}} } d} | r|jj|jjdkr|jjjj d| } t j | |jj f} |jjdkrS|dkrt dnt j|}| |jjf}|j |ks+t dt|t|j fnt j|jjjj|jfj}nt| d|d|jjd|jjd|jjd |jjd |jjd |jj}|j|j|d jd kr|d dd|jd f} n|d dddf} x|jjj D]}|dkr7qnt!|j"|}|j dd krt#|j dkr|dd| df||eZiZejejeZiZejejeZRS(( RRt_attrstwrapt union_dictsRt _wrap_attrst_methodst _wrap_methods(((s@lib/python2.7/site-packages/statsmodels/tsa/statespace/varmax.pyRfs    (,Rt __future__RRRtwarningsRt collectionsRtpandasRptnumpyR+tstatsmodels.tools.toolsRtstatsmodels.tools.dataRtstatsmodels.tsa.vector_arRtstatsmodels.base.wrappertbasetwrapperRtstatsmodels.tools.sm_exceptionsRR t kalman_filterR R tmlemodelR R RttoolsRRRRRRRReRftpopulate_wrapper(((s@lib/python2.7/site-packages/statsmodels/tsa/statespace/varmax.pyts(  .1