ó áp7]c@`sÆdZddlmZmZmZddlZddlmZm Z m Z ddl m Z ddl mZdefd „ƒYZd efd „ƒYZd efd „ƒYZdefd„ƒYZdS(sI State Space Representation Author: Chad Fulton License: Simplified-BSD i(tdivisiontabsolute_importtprint_functionNi(tfind_best_blas_typetvalidate_matrix_shapetvalidate_vector_shape(tInitialization(ttoolst OptionWrappercB`s#eZd„Zd„Zd„ZRS(cC`s||_||_dS(N(tmask_attributet mask_value(tselfR R ((sHlib/python2.7/site-packages/statsmodels/tsa/statespace/representation.pyt__init__s cC`s tt||jdƒ|j@ƒS(Ni(tbooltgetattrR R (R tobjtobjtype((sHlib/python2.7/site-packages/statsmodels/tsa/statespace/representation.pyt__get__scC`sVt||jdƒ}t|ƒr1||jB}n||j@}t||j|ƒdS(Ni(RR R R tsetattr(R Rtvaluetmask_attribute_value((sHlib/python2.7/site-packages/statsmodels/tsa/statespace/representation.pyt__set__s  (t__name__t __module__R RR(((sHlib/python2.7/site-packages/statsmodels/tsa/statespace/representation.pyRs  t MatrixWrappercB`s5eZd„Zd„Zd„Zd„Zd„ZRS(cC`s#||_||_d||_dS(Nt_(tnamet attributet _attribute(R RR((sHlib/python2.7/site-packages/statsmodels/tsa/statespace/representation.pyR &s  cC`st||jdƒ}|S(N(RRtNone(R RRtmatrix((sHlib/python2.7/site-packages/statsmodels/tsa/statespace/representation.pyR+scC`sŽtj|ddƒ}|j|j}t|ƒdkrO|j|||ƒ}n|j|||ƒ}t||j|ƒ|j |j|js$1cC`s[t|j|j|d|jƒ|jdkrWtj|dd…dfddƒ}n|S(NiiRR (RRR'R)R(R!R*R(R RRR'((sHlib/python2.7/site-packages/statsmodels/tsa/statespace/representation.pyR&Os ((RRR RRR%R&(((sHlib/python2.7/site-packages/statsmodels/tsa/statespace/representation.pyR%s    tRepresentationc B`sgeZdZdZeddƒZeddƒZeddƒZeddƒZ eddƒZ ed d ƒZ ed d ƒZ dd d e jddddddddd„ Zd„Zd„Zed„ƒZed„ƒZed„ƒZed„ƒZed„ƒZd„Zdddd„Zd„Zdd„Zd„Zd„Zdd„Zded„Z RS(sI State space representation of a time series process Parameters ---------- k_endog : array_like or integer The observed time-series process :math:`y` if array like or the number of variables in the process if an integer. k_states : int The dimension of the unobserved state process. k_posdef : int, optional The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation. Must be less than or equal to `k_states`. Default is `k_states`. initial_variance : float, optional Initial variance used when approximate diffuse initialization is specified. Default is 1e6. initialization : Initialization object or string, optional Initialization method for the initial state. If a string, must be one of {'diffuse', 'approximate_diffuse', 'stationary', 'known'}. initial_state : array_like, optional If `initialization='known'` is used, the mean of the initial state's distribution. initial_state_cov : array_like, optional If `initialization='known'` is used, the covariance matrix of the initial state's distribution. nobs : integer, optional If an endogenous vector is not given (i.e. `k_endog` is an integer), the number of observations can optionally be specified. If not specified, they will be set to zero until data is bound to the model. dtype : np.dtype, optional If an endogenous vector is not given (i.e. `k_endog` is an integer), the default datatype of the state space matrices can optionally be specified. Default is `np.float64`. design : array_like, optional The design matrix, :math:`Z`. Default is set to zeros. obs_intercept : array_like, optional The intercept for the observation equation, :math:`d`. Default is set to zeros. obs_cov : array_like, optional The covariance matrix for the observation equation :math:`H`. Default is set to zeros. transition : array_like, optional The transition matrix, :math:`T`. Default is set to zeros. state_intercept : array_like, optional The intercept for the transition equation, :math:`c`. Default is set to zeros. selection : array_like, optional The selection matrix, :math:`R`. Default is set to zeros. state_cov : array_like, optional The covariance matrix for the state equation :math:`Q`. Default is set to zeros. **kwargs Additional keyword arguments. Not used directly. It is present to improve compatibility with subclasses, so that they can use `**kwargs` to specify any default state space matrices (e.g. `design`) without having to clean out any other keyword arguments they might have been passed. Attributes ---------- nobs : int The number of observations. k_endog : int The dimension of the observation series. k_states : int The dimension of the unobserved state process. k_posdef : int The dimension of a guaranteed positive definite covariance matrix describing the shocks in the measurement equation. shapes : dictionary of name:tuple A dictionary recording the initial shapes of each of the representation matrices as tuples. initialization : str Kalman filter initialization method. Default is unset. initial_variance : float Initial variance for approximate diffuse initialization. Default is 1e6. Notes ----- A general state space model is of the form .. math:: y_t & = Z_t \alpha_t + d_t + \varepsilon_t \\ \alpha_t & = T_t \alpha_{t-1} + c_t + R_t \eta_t \\ where :math:`y_t` refers to the observation vector at time :math:`t`, :math:`\alpha_t` refers to the (unobserved) state vector at time :math:`t`, and where the irregular components are defined as .. math:: \varepsilon_t \sim N(0, H_t) \\ \eta_t \sim N(0, Q_t) \\ The remaining variables (:math:`Z_t, d_t, H_t, T_t, c_t, R_t, Q_t`) in the equations are matrices describing the process. Their variable names and dimensions are as follows Z : `design` :math:`(k\_endog \times k\_states \times nobs)` d : `obs_intercept` :math:`(k\_endog \times nobs)` H : `obs_cov` :math:`(k\_endog \times k\_endog \times nobs)` T : `transition` :math:`(k\_states \times k\_states \times nobs)` c : `state_intercept` :math:`(k\_states \times nobs)` R : `selection` :math:`(k\_states \times k\_posdef \times nobs)` Q : `state_cov` :math:`(k\_posdef \times k\_posdef \times nobs)` In the case that one of the matrices is time-invariant (so that, for example, :math:`Z_t = Z_{t+1} ~ \forall ~ t`), its last dimension may be of size :math:`1` rather than size `nobs`. References ---------- .. [*] Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods: Second Edition. 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