B Zؚ@sdZddlmZmZmZddlmZddlmZddl Z ddl Z ddl mZmZddlmZmZmZdd lmZmZmZmZdd lmZdd lmZdd lmZddlm m!Z"dd l#m$Z$m%Z%GdddeZ&GdddeZ'GdddeZ(e")e(e'dS)zs Vector Autoregressive Moving Average with eXogenous regressors model Author: Chad Fulton License: Simplified-BSD )divisionabsolute_importprint_function)warn) OrderedDictN)INVERT_UNIVARIATESOLVE_LU)MLEModel MLEResultsMLEResultsWrapper) is_invertible prepare_exog!constrain_stationary_multivariate#unconstrain_stationary_multivariate)Bunch)_is_using_pandas) var_model)EstimationWarning ValueWarningcsbeZdZdZdfdd Zed d Zed d ZeddZddZ ddZ fddZ Z S)VARMAXu 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 : {'nc', 'c'}, optional Parameter controlling the deterministic trend polynomial. Can be specified as a string where 'c' indicates a constant intercept and 'nc' indicates no intercept term. 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 : {'nc', 'c'}, optional Parameter controlling the deterministic trend polynomial. Can be specified as a string where 'c' indicates a constant intercept and 'nc' indicates no intercept term. 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 = \nu + 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 informationl. 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. Nrrc unstructuredFTc  s|_|_|_|_|_|_t|d_t|d_tjdk_ |dkr`t d|dkrpt djdkrjdkrt djdkrjdkrt d t t |\_}jdk_t|dst|}tjd} | j_|jd} | } | j} | d d | d ttBttj|f|| | d | jdks\j dkrddj_t_j j jd<j djjd<j djjd<j jjd<jdkrֈj jd<n*jdkrtj j ddjd<j jjd<t!j"_#jdkrFt$j%j&fjd<t'j }djd|<jdkrt'jdj }|dj |df}djd|<t'jdj }|d| dj |d| j f}djd|<t'j }djd|<|d| j |df}jdkr@djd|<jdkrnjdkrntj(dd| f_)n&jdkrtj(dd| ddf_)jdkrtj(dd| ddf_*ntj(dd| | df_*jdkrdt'j _+njdkrt,j _-jr*dt'j _.fdd }d}|d|\_/}|d|\_0}|d|\_1}|d|\_2}|d|\_3}|d|\_4}dS)!Nrrr)rnczInvalid trend specification.)diagonalrz3Invalid error covariance matrix type specification.zNInvalid VARMAX(p,q) specification; at least one p,q must be greater than zero.zcEstimation of VARMA(p,q) models is not generically robust, due especially to identification issues.Zinitialization stationaryZinversion_method)exogk_statesk_posdefFtrendarmaZ regressionr state_covrobs_covZstate_intercept)Zdesign) transition)Z selectionr&)r$)r%cs,j|}tj|||}||7}||fS)N) parametersnps_)keyoffsetlengthZ param_slice)self@lib/python3.7/site-packages/statsmodels/tsa/statespace/varmax.py_slices zVARMAX.__init__.._slice)5error_cov_typemeasurement_errorenforce_stationarityenforce_invertibilityorderr intk_ark_mak_trend ValueErrorrrrk_exogmle_regressionrr(Z asanyarraymaxZ_k_ordershape setdefaultrr superr__init__ssmZ_time_invariantrr'k_endogsumvaluesk_paramszerosrnobsZ diag_indicesr)_idx_state_intercept_idx_transition_idx_state_covZ tril_indices_idx_lower_state_cov _idx_obs_cov _params_trend _params_ar _params_ma_params_regression_params_state_cov_params_obs_cov)r-endogrr5r r1r2r3r4kwargsZ _min_k_arrCrridxr0r+) __class__)r-r/rAvs                     zVARMAX.__init__cCs dttfiS)Nfit) VARMAXResultsVARMAXResultsWrapper)r-r.r.r/ _res_classesszVARMAX._res_classescCsDtj|jtjd}t|j}y |}Wnt k rBYnX|j ddj }|j dkrf|j nd}tt|rtjt|dd}||}|dk r||}td}|j dkrtj||j}|t||j8}g}|jdkr|jnd}t|}|j|d|jd} t| jj}|jdkrl|dddf} |jdkrf|ddddf}ng}n|jdkr|}ng}| j}|jdkr|jr||j|j|jj|j|j|jj} t dgt!| } | st"d g} |j#dkr~t|}|j|j#dd d}t|jj} |j$r~| |j|j#|jj|j|j|j#j} t dgt!| }|s~t"d |jdkr| ||j%<|||j&<| ||j'<|j(r|||j)<|j*d kr| j+,||j-<n.|j*d kr tj.| j+}||j/||j-<|j0r@|j#dkr0|j+,||j1<n| j+,||j1<|S)N)dtypeZbackfill)methodrr)Zaxis)ZmaxlagsZicr rz`Non-stationary starting autoregressive parameters found with `enforce_stationarity` set to True.rz`Non-invertible starting moving-average parameters found with `enforce_stationarity` set to True.rr)2r(rGrFZfloat64pdZ DataFramerTcopyZ interpolate TypeErrorZfillnarEr;ranyZisnanZlinalgZpinvdotTr7rVARrXr arrayparamsravelZresidr3reshaperCr listr:r8r4rNrOrPr<rQr1Zsigma_urrRZcholeskyrLr2rS)r-rfrTrmask exog_params ar_paramsr7Zmod_arZres_arZ trend_paramscoefficient_matricesr ma_paramsZmod_maZres_maZ invertibleZ cov_factorr.r.r/ start_paramss                 zVARMAX.start_paramscsg}jdkr*|fddtjD7}|fddtjD7}|fddtjD7}|fddtjD7}jdkr|fddtjD7}n&jd kr|fd dtjD7}jr|fd dtjD7}|S) Nrcsg|]}dj|qS)zconst.%s) endog_names).0i)r-r.r/ sz&VARMAX.param_names..c sJg|]B}tjD]2}tjD]"}d|dj|j|fq qqS)z L%d.%s.%sr)ranger7rCrp)rqjrrk)r-r.r/rssc sJg|]B}tjD]2}tjD]"}d|dj|j|fq qqS)z L%d.e(%s).%sr)rtr8rCrp)rqrurrrv)r-r.r/rsscs4g|],}tjD]}dj|j|fqqS)z beta.%s.%s)rtr;Z exog_namesrp)rqrrru)r-r.r/rssrcsg|]}dj|qS)z sigma2.%s)rp)rqrr)r-r.r/rssrcsLg|]D}t|dD]2}||kr.dj|ndj|j|fqqS)rz sqrt.var.%szsqrt.cov.%s.%s)rtrp)rqrrru)r-r.r/rsscsg|]}dj|qS)zmeasurement_variance.%s)rp)rqrr)r-r.r/rss)r rtrCr1r2)r- param_namesr.)r-r/rws6          zVARMAX.param_namescCstj|dd}tj|j|jd}||j||j<|jdkr|jr|jdkr`t ||j d}n@|jdkrtj|j dj|jd}||j ||j <t ||j}||j|j|j|j}t||\}}|||j<n||j||j<|jdkrJ|jrJtj|j|jd}||j|j|j|j}t||\}}|||j<n||j||j<||j||j<|jdkr||j d||j <n|jdkr||j ||j <|jr||jd||j<|S) aZ Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation Parameters ---------- unconstrained : array_like Array of unconstrained parameters used by the optimizer, to be transformed. Returns ------- constrained : array_like Array of constrained parameters which may be used in likelihood evalation. Notes ----- Constrains the factor transition to be stationary and variances to be positive. r)ndmin)r\rrr!rr$)r(rerGr>r\rNr7r3r1diagrRrBrLrbrcrOrhrCrrgr8r4eyerPrQr2rS)r- unconstrained constrainedr$state_cov_lower coefficientsrmvariancer.r.r/transform_paramss>       zVARMAX.transform_paramscCstj|dd}tj|j|jd}||j||j<|jdkr|jr|jdkr\t ||j }n@|jdkrtj|j dj|jd}||j ||j <t ||j}||j|j|j|j}t||\}}|||j<n||j||j<|jdkrF|jrFtj|j|jd}||j|j|j|j}t||\}}|||j<n||j||j<||j||j<|jdkr||j d||j <n|jdkr||j ||j <|jr||jd||j<|S) a Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer. Parameters ---------- constrained : array_like Array of constrained parameters used in likelihood evalution, to be transformed. Returns ------- unconstrained : array_like Array of unconstrained parameters used by the optimizer. r)rx)r\rrrr$g?)r(rerGr>r\rNr7r3r1ryrRrBrLrbrcrOrhrCrrgr8r4rzrPrQr2rS)r-r|r{r$r}r~Zunconstrained_matricesrr.r.r/untransform_paramss>       zVARMAX.untransform_paramsc sVtt|j|f|}|jrh||j|j|jj}t |j |}|j dkrX|||j 7}|j|j|j<n|j dkr||j |j|j<||j|j|j|j}||j|j|j|j}t j||f|j|j<|jdkr||j|j|j<nH|jdkr8t j|jdj|jd}||j||j<t ||j|jd<|jrR||j|j|j<dS)Nrrrr$)r\) r@rupdater<rQrhrCr;rcr(rbrr rNrBrIrOr7rPr8c_rJr1rRrKrGr>r\rLr2rSrM)r-rfrUrk interceptr"r#r})rWr.r/rbs0        z VARMAX.update)NrrrFTT) __name__ __module__ __qualname____doc__rApropertyr[rorwrrr __classcell__r.r.)rWr/rsX  r 9SMrcsHeZdZdZd fdd Zdfdd Zdfd d Zejje_ZS)rYa 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 opgc stt|j||||f|tj|_tf|jj|jj |jj |jj |jj |jj |jj|jj|jj|jjd |_d|_d|_|jj dkrt|j|jj}|jj}|jj }||||j|||j|_|jjdkrt|j|jj} |jj}|jj} | || |j||| j|_dS)N) r1r2r3r4r5r7r8r r9r;r)r@rYrAr(infZdf_residrmodelr1r2r3r4r5r7r8r r9r; specificationZcoefficient_matrices_varZcoefficient_matrices_vmarerfrOrCrhrcrP) r-rrffilter_resultsZcov_typerUrlrCr7rnr8)rWr.r/rAs8  zVARMAXResults.__init__NFc s|dkr|jjd}|jj|||dd\}}} } | r|jj|jjdkr|jjjjd| } t | |jj f} |jjdkr|dkrt dt |}| |jjf} |j| kst dt | t |jftj|jjjj|jfj}t| ||jj|jj|jj|jj|jj|jjd}||jx|jjD]|}|dkr>q,t|j|}|jd d kr,t|jd kr|dd| df||<n |dddd| df||<q,Wn"|jjdkr|dk rt d t!t"t#|j$f|||||d |S)aO In-sample prediction and out-of-sample forecasting Parameters ---------- start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. Default is the the zeroth observation. end : int, str, or datetime, optional Zero-indexed observation number at which to end forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. Default is the last observation in the sample. exog : array_like, optional If the model includes exogenous regressors, you must provide exactly enough out-of-sample values for the exogenous variables if end is beyond the last observation in the sample. dynamic : boolean, int, str, or datetime, optional Integer offset relative to `start` at which to begin dynamic prediction. Can also be an absolute date string to parse or a datetime type (these are not interpreted as offsets). Prior to this observation, true endogenous values will be used for prediction; starting with this observation and continuing through the end of prediction, forecasted endogenous values will be used instead. kwargs Additional arguments may required for forecasting beyond the end of the sample. See `FilterResults.predict` for more details. Returns ------- forecast : array Array of out of sample forecasts. NrT)Zsilentz~Out-of-sample forecasting in a model with a regression component requires additional exogenous values via the `exog` argument.zPProvided exogenous values are not of the appropriate shape. 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