p7]c@`sdZddlmZmZmZddlmZddlmZddl Z ddl m Z m Z mZddlmZmZmZmZmZmZdd lmZdd lmZdd lmZdd lmZdd lmZddl m!Z!ddl"m#Z#ddl$m%Z%ddl&j'j(Z)de fdYZ*de fdYZ+defdYZ,e)j-e,e+dS(sC Dynamic factor model Author: Chad Fulton License: Simplified-BSD i(tdivisiontabsolute_importtprint_function(twarn(t OrderedDictNi(tMLEModelt MLEResultstMLEResultsWrapper(t is_invertiblet prepare_exogtconstrain_stationary_univariatet!unconstrain_stationary_univariatet!constrain_stationary_multivariatet#unconstrain_stationary_multivariate(tPCA(tOLS(tVAR(tBunch(t_is_using_pandas(tlagmat(tcache_readonly(t ValueWarningt DynamicFactorcB`seZdZddededZdZdZdZ edZ dZ d Z d Z d Zd Zd ZedZedZedZdZdZeedZRS(s Dynamic factor model Parameters ---------- endog : array_like The observed time-series process :math:`y` exog : array_like, optional Array of exogenous regressors for the observation equation, shaped nobs x k_exog. k_factors : int The number of unobserved factors. factor_order : int The order of the vector autoregression followed by the factors. error_cov_type : {'scalar', 'diagonal', 'unstructured'}, optional The structure of the covariance matrix of the observation error term, where "unstructured" puts no restrictions on the matrix, "diagonal" requires it to be any diagonal matrix (uncorrelated errors), and "scalar" requires it to be a scalar times the identity matrix. Default is "diagonal". error_order : int, optional The order of the vector autoregression followed by the observation error component. Default is None, corresponding to white noise errors. error_var : boolean, optional Whether or not to model the errors jointly via a vector autoregression, rather than as individual autoregressions. Has no effect unless `error_order` is set. 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. **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 ---------- exog : array_like, optional Array of exogenous regressors for the observation equation, shaped nobs x k_exog. k_factors : int The number of unobserved factors. factor_order : int The order of the vector autoregression followed by the factors. error_cov_type : {'diagonal', 'unstructured'} 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). error_order : int The order of the vector autoregression followed by the observation error component. error_var : boolean Whether or not to model the errors jointly via a vector autoregression, rather than as individual autoregressions. Has no effect unless `error_order` is set. 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. Notes ----- The dynamic factor model considered here is in the so-called static form, and is specified: .. math:: y_t & = \Lambda f_t + B x_t + u_t \\ f_t & = A_1 f_{t-1} + \dots + A_p f_{t-p} + \eta_t \\ u_t & = C_1 u_{t-1} + \dots + C_1 f_{t-q} + \varepsilon_t where there are `k_endog` observed series and `k_factors` unobserved factors. Thus :math:`y_t` is a `k_endog` x 1 vector and :math:`f_t` is a `k_factors` x 1 vector. :math:`x_t` are optional exogenous vectors, shaped `k_exog` x 1. :math:`\eta_t` and :math:`\varepsilon_t` are white noise error terms. In order to identify the factors, :math:`Var(\eta_t) = I`. Denote :math:`Var(\varepsilon_t) \equiv \Sigma`. Options related to the unobserved factors: - `k_factors`: this is the dimension of the vector :math:`f_t`, above. To exclude factors completely, set `k_factors = 0`. - `factor_order`: this is the number of lags to include in the factor evolution equation, and corresponds to :math:`p`, above. To have static factors, set `factor_order = 0`. Options related to the observation error term :math:`u_t`: - `error_order`: the number of lags to include in the error evolution equation; corresponds to :math:`q`, above. To have white noise errors, set `error_order = 0` (this is the default). - `error_cov_type`: this controls the form of the covariance matrix :math:`\Sigma`. If it is "dscalar", then :math:`\Sigma = \sigma^2 I`. If it is "diagonal", then :math:`\Sigma = \text{diag}(\sigma_1^2, \dots, \sigma_n^2)`. If it is "unstructured", then :math:`\Sigma` is any valid variance / covariance matrix (i.e. symmetric and positive definite). - `error_var`: this controls whether or not the errors evolve jointly according to a VAR(q), or individually according to separate AR(q) processes. In terms of the formulation above, if `error_var = False`, then the matrices :math:C_i` are diagonal, otherwise they are general VAR matrices. References ---------- .. [*] Lütkepohl, Helmut. 2007. New Introduction to Multiple Time Series Analysis. Berlin: Springer. itdiagonalc  `s|_|_|_|_|o3|dk_|_t|\_}jdk_t |dst j |dd}n|j dkr|jdnd} tdjj_j| _j} j} jdkr| j7} | | 7} n| dkr4d} d} n| dkrOtdnj| krmtdnjdkrtd n| jd d ttj|d|d| d| | jdkrtj_nt_jjjjj t!jj"_#fd} d}| d|\_$}| d|\_%}| d|\_&}| d|\_'}| d|\_(}dS(NitordertCiisEThe dynamic factors model is only valid for multivariate time series.sGNumber of factors must be less than the number of endogenous variables.tscalarRt unstructureds3Invalid error covariance matrix type specification.tinitializationt stationarytexogtk_statestk_posdefc`s5j|}tj|||!}||7}||fS(N(t parameterstnpts_(tkeytoffsettlengtht param_slice(tself(sHlib/python2.7/site-packages/statsmodels/tsa/statespace/dynamic_factor.pyt_slices  tfactor_loadingst error_covtfactor_transitionterror_transition(RRR()tenforce_stationarityt k_factorst factor_ordert error_ordert error_varterror_cov_typeR tk_exogtmle_regressionRtNoneR"t asanyarraytndimtshapetmaxt _factor_ordert _error_ordert ValueErrort setdefaulttsuperRt__init__tFalsetssmt_time_invariantRR!t_initialize_loadingst_initialize_exogt_initialize_error_covt_initialize_factor_transitiont_initialize_error_transitiontsumtvaluestk_paramst_params_loadingst _params_exogt_params_error_covt_params_factor_transitiont_params_error_transition(R(tendogR/R0RR1R2R3R.tkwargstk_endogRR R)R%((R(sHlib/python2.7/site-packages/statsmodels/tsa/statespace/dynamic_factor.pyR@s\     "             cC`s|j|j|jd<|jdkrp|j}|j|j}tj|j|jddd||f|jdkrD|jdtn|jdkr`|jndS(NRRR(R3t_initialize_error_cov_diagonaltTrueRAt"_initialize_error_cov_unstructured(R(((sHlib/python2.7/site-packages/statsmodels/tsa/statespace/dynamic_factor.pyRF s cC`s|r dn|j|jd<|j}|j}tj|}|jdkrqd}|d||d|f}nd}|f||_dS(NiR+it state_covtobs_cov(RSR!R/R"t diag_indicesR1t_idx_error_cov(R(RRSR/tidxtmatrix((sHlib/python2.7/site-packages/statsmodels/tsa/statespace/dynamic_factor.pyR]s  cC`s|j}t||dd|jd} | |j}| d|j} t| || !| || +qW| ||j} | |j}| d|j} t| || !| || +qW| ||j               c C`sd}|j}|jdkrd}|j}|j}td|j||!d|j||||fddddd|}|jdk r|j||!|_n|j dk r|j ||||f|_ qn|S(s Estimates of unobserved factors Returns ------- out : Bunch Has the following attributes shown in Notes. Notes ----- The output is a bunch of the following format: - `filtered`: a time series array with the filtered estimate of the component - `filtered_cov`: a time series array with the filtered estimate of the variance/covariance of the component - `smoothed`: a time series array with the smoothed estimate of the component - `smoothed_cov`: a time series array with the smoothed estimate of the variance/covariance of the component - `offset`: an integer giving the offset in the state vector where this component begins itfilteredt filtered_covtsmoothedt smoothed_covR%N( R6RR/RRtfiltered_statetfiltered_state_covtsmoothed_stateRtsmoothed_state_covR(R(touttspecR%RXtres((sHlib/python2.7/site-packages/statsmodels/tsa/statespace/dynamic_factor.pyRs      (c C`sddlm}|j}tj|j|jf}|jdkrIdnd}xzt |jD]i}||j ||}xIt |jD]8}|j j |}t ||jj|||feZiZejejeZiZejejeZRS(( RRt_attrstwrapt union_dictsRt _wrap_attrst_methodst _wrap_methods(((sHlib/python2.7/site-packages/statsmodels/tsa/statespace/dynamic_factor.pyR|Js    (.Rt __future__RRRtwarningsRt collectionsRtnumpyR"tmlemodelRRRttoolsRR R R R R tstatsmodels.multivariate.pcaRt#statsmodels.regression.linear_modelRt#statsmodels.tsa.vector_ar.var_modelRtstatsmodels.tools.toolsRtstatsmodels.tools.dataRtstatsmodels.tsa.tsatoolsRtstatsmodels.tools.decoratorsRtstatsmodels.tools.sm_exceptionsRtstatsmodels.base.wrappertbasetwrapperR>RR{R|tpopulate_wrapper(((sHlib/python2.7/site-packages/statsmodels/tsa/statespace/dynamic_factor.pyts0 .^