ó áp7]c@`südZddlmZmZmZddlZddlmZddl m Z m Z ddl m Z mZmZddlmZdZd Zd Zd Zd ZeeBeBeBeBZdZd Zd Zd Zd e fd„ƒYZde fd„ƒYZdS(se State Space Representation and Kalman Filter, Smoother Author: Chad Fulton License: Simplified-BSD i(tdivisiontabsolute_importtprint_functionN(t OptionWrapper(t KalmanFiltert FilterResults(treorder_missing_matrixtreorder_missing_vectortcopy_index_matrix(ttoolsiiiiitKalmanSmoothercB`sUeZdZddddddgZedeƒZedeƒZede ƒZ ede ƒZ ede ƒZedeƒZdd d gZed eƒZed eƒZed eƒZed eƒZeZd Zdddd „Zed„ƒZdddd„Z dd„Z!dd„Z"ddde#dd„Z$ddde%de#d„Z&RS(s State space representation of a time series process, with Kalman filter and smoother. 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`. results_class : class, optional Default results class to use to save filtering output. Default is `SmootherResults`. If specified, class must extend from `SmootherResults`. **kwargs Keyword arguments may be used to provide default values for state space matrices, for Kalman filtering options, or for Kalman smoothing options. See `Representation` for more details. tsmoother_statetsmoother_state_covtsmoother_state_autocovtsmoother_disturbancetsmoother_disturbance_covt smoother_alltsmoother_outputtsmooth_conventionaltsmooth_alternativetsmooth_classicalt smooth_methodicK`s…|dkrt}ntt|ƒj|||d|||dk rL|n tjjƒ|_i|_|j ||j |dS(Nt results_class( tNonetSmootherResultstsuperR t__init__R tprefix_kalman_smoother_maptcopyt_kalman_smootherstset_smoother_outputtset_smooth_method(tselftk_endogtk_statestk_posdefRtkalman_smoother_classestkwargs((sIlib/python2.7/site-packages/statsmodels/tsa/statespace/kalman_smoother.pyRgs    cC`s'|j}||jkr#|j|SdS(N(tprefixRR(R R&((sIlib/python2.7/site-packages/statsmodels/tsa/statespace/kalman_smoother.pyt_kalman_smoother~s  c K`s |dkr|j}n|dkr0|j}n|j||\}}}}|p`||jk}|s|j|} | j|j|k }n|rÏ|j|} | |j||j|||ƒ|j|>> import statsmodels.tsa.statespace.kalman_smoother as ks >>> mod = ks.KalmanSmoother(1,1) >>> mod.smoother_output 15 >>> mod.set_smoother_output(smoother_output=0) >>> mod.smoother_state = True >>> mod.smoother_output 1 >>> mod.smoother_state True N(RRR tsmoother_outputstsetattr(R RR%tname((sIlib/python2.7/site-packages/statsmodels/tsa/statespace/kalman_smoother.pyR¬s D   cK`sS|dk r||_nx4tjD])}||kr"t||||ƒq"q"WdS(sÞ Set the smoothing method The smoothing method can be used to override the Kalman smoother approach used. By default, the Kalman smoother used depends on the Kalman filter method. Parameters ---------- smooth_method : integer, optional Bitmask value to set the filter method to. See notes for details. **kwargs Keyword arguments may be used to influence the filter method by setting individual boolean flags. See notes for details. Notes ----- The smoothing method is defined by a collection of boolean flags, and is internally stored as a bitmask. The methods available are: SMOOTH_CONVENTIONAL = 0x01 Default Kalman smoother, as presented in Durbin and Koopman, 2012 chapter 4. SMOOTH_CLASSICAL = 0x02 Classical Kalman smoother, as presented in Anderson and Moore, 1979 or Durbin and Koopman, 2012 chapter 4.6.1. SMOOTH_ALTERNATIVE = 0x04 Modified Bryson-Frazier Kalman smoother method; this is identical to the conventional method of Durbin and Koopman, 2012, except that an additional intermediate step is included. SMOOTH_UNIVARIATE = 0x08 Univariate Kalman smoother, as presented in Durbin and Koopman, 2012 chapter 6, except with modified Bryson-Frazier timing. Practically speaking, these methods should all produce the same output but different computational implications, numerical stability implications, or internal timing assumptions. Note that only the first method is available if using a Scipy version older than 0.16. If the bitmask is set directly via the `smooth_method` argument, then the full method must be provided. If keyword arguments are used to set individual boolean flags, then the lowercase of the method must be used as an argument name, and the value is the desired value of the boolean flag (True or False). Note that the filter method may also be specified by directly modifying the class attributes which are defined similarly to the keyword arguments. The default filtering method is SMOOTH_CONVENTIONAL. Examples -------- >>> mod = sm.tsa.statespace.SARIMAX(range(10)) >>> mod.smooth_method 1 >>> mod.filter_conventional True >>> mod.filter_univariate = True >>> mod.smooth_method 17 >>> mod.set_smooth_method(filter_univariate=False, filter_collapsed=True) >>> mod.smooth_method 33 >>> mod.set_smooth_method(smooth_method=1) >>> mod.filter_conventional True >>> mod.filter_univariate False >>> mod.filter_collapsed False >>> mod.filter_univariate = True >>> mod.smooth_method 17 N(RRR tsmooth_methodsR5(R RR%R6((sIlib/python2.7/site-packages/statsmodels/tsa/statespace/kalman_smoother.pyRös P   c K`s]|j||d||\}}}} } | s6| rEtdƒ‚n|j|} | ƒ| S(NR&sgPassed settings forced re-creation of the Kalman filter. Please run `_filter` before running `_smooth`.(R3t ValueErrorR( R RRR&t complex_steptresultsR%R-R0R.R/tsmoother((sIlib/python2.7/site-packages/statsmodels/tsa/statespace/kalman_smoother.pyt_smoothLs$  c K`sy|j|}|j|ƒ}|j|ƒ|j|ƒ|dkrP|j}n|j|d||} |j| ƒ|S(s½ Apply the Kalman smoother to the statespace model. Parameters ---------- smoother_output : int, optional Determines which Kalman smoother output calculate. Default is all (including state, disturbances, and all covariances). results : class or object, optional If a class, then that class is instantiated and returned with the result of both filtering and smoothing. If an object, then that object is updated with the smoothing data. If None, then a SmootherResults object is returned with both filtering and smoothing results. run_filter : bool, optional Whether or not to run the Kalman filter prior to smoothing. Default is True. prefix : string The prefix of the datatype. Usually only used internally. Returns ------- SmootherResults object R:N(t_filterRtupdate_representationt update_filterRRR<tupdate_smoother( R RRR:t run_filterR&R9R%R)R;((sIlib/python2.7/site-packages/statsmodels/tsa/statespace/kalman_smoother.pytsmoothbs     N('t__name__t __module__t__doc__R4RtSMOOTHER_STATER tSMOOTHER_STATE_COVR tSMOOTHER_DISTURBANCERtSMOOTHER_DISTURBANCE_COVRtSMOOTHER_STATE_AUTOCOVR t SMOOTHER_ALLRR7tSMOOTH_CONVENTIONALRtSMOOTH_ALTERNATIVERtSMOOTH_CLASSICALRtSMOOTH_UNIVARIATEtsmooth_univariateRRRRtpropertyR'R3RRR,R<tTrueRB(((sIlib/python2.7/site-packages/statsmodels/tsa/statespace/kalman_smoother.pyR "s6   & J V  Rc B`s–eZdZddddddddd d d g ZejZejeZ e d „Z d „Z d„Z ed„ƒZed„ƒZed„ƒZRS(s  Results from applying the Kalman smoother and/or filter to a state space model. Parameters ---------- model : Representation A Statespace representation Attributes ---------- nobs : int 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. dtype : dtype Datatype of representation matrices prefix : str BLAS prefix of representation matrices shapes : dictionary of name:tuple A dictionary recording the shapes of each of the representation matrices as tuples. endog : array The observation vector. design : array The design matrix, :math:`Z`. obs_intercept : array The intercept for the observation equation, :math:`d`. obs_cov : array The covariance matrix for the observation equation :math:`H`. transition : array The transition matrix, :math:`T`. state_intercept : array The intercept for the transition equation, :math:`c`. selection : array The selection matrix, :math:`R`. state_cov : array The covariance matrix for the state equation :math:`Q`. missing : array of bool An array of the same size as `endog`, filled with boolean values that are True if the corresponding entry in `endog` is NaN and False otherwise. nmissing : array of int An array of size `nobs`, where the ith entry is the number (between 0 and k_endog) of NaNs in the ith row of the `endog` array. time_invariant : bool Whether or not the representation matrices are time-invariant initialization : str Kalman filter initialization method. initial_state : array_like The state vector used to initialize the Kalamn filter. initial_state_cov : array_like The state covariance matrix used to initialize the Kalamn filter. filter_method : int Bitmask representing the Kalman filtering method inversion_method : int Bitmask representing the method used to invert the forecast error covariance matrix. stability_method : int Bitmask representing the methods used to promote numerical stability in the Kalman filter recursions. conserve_memory : int Bitmask representing the selected memory conservation method. tolerance : float The tolerance at which the Kalman filter determines convergence to steady-state. loglikelihood_burn : int The number of initial periods during which the loglikelihood is not recorded. converged : bool Whether or not the Kalman filter converged. period_converged : int The time period in which the Kalman filter converged. filtered_state : array The filtered state vector at each time period. filtered_state_cov : array The filtered state covariance matrix at each time period. predicted_state : array The predicted state vector at each time period. predicted_state_cov : array The predicted state covariance matrix at each time period. kalman_gain : array The Kalman gain at each time period. forecasts : array The one-step-ahead forecasts of observations at each time period. forecasts_error : array The forecast errors at each time period. forecasts_error_cov : array The forecast error covariance matrices at each time period. loglikelihood : array The loglikelihood values at each time period. collapsed_forecasts : array If filtering using collapsed observations, stores the one-step-ahead forecasts of collapsed observations at each time period. collapsed_forecasts_error : array If filtering using collapsed observations, stores the one-step-ahead forecast errors of collapsed observations at each time period. collapsed_forecasts_error_cov : array If filtering using collapsed observations, stores the one-step-ahead forecast error covariance matrices of collapsed observations at each time period. standardized_forecast_error : array The standardized forecast errors smoother_output : int Bitmask representing the generated Kalman smoothing output scaled_smoothed_estimator : array The scaled smoothed estimator at each time period. scaled_smoothed_estimator_cov : array The scaled smoothed estimator covariance matrices at each time period. smoothing_error : array The smoothing error covariance matrices at each time period. smoothed_state : array The smoothed state at each time period. smoothed_state_cov : array The smoothed state covariance matrices at each time period. smoothed_state_autocov : array The smoothed state lago-one autocovariance matrices at each time period: :math:`Cov(\alpha_{t+1}, \alpha_t)`. smoothed_measurement_disturbance : array The smoothed measurement at each time period. smoothed_state_disturbance : array The smoothed state at each time period. smoothed_measurement_disturbance_cov : array The smoothed measurement disturbance covariance matrices at each time period. smoothed_state_disturbance_cov : array The smoothed state disturbance covariance matrices at each time period. Rtscaled_smoothed_estimatortscaled_smoothed_estimator_covtsmoothing_errortsmoothed_statetsmoothed_state_covtsmoothed_state_autocovt smoothed_measurement_disturbancetsmoothed_state_disturbancet$smoothed_measurement_disturbance_covtsmoothed_state_disturbance_covcC`shtt|ƒj||ƒx-|jD]"}t||t||dƒƒq#Wd|_d|_d|_ dS(sø Update the results to match a given model Parameters ---------- model : Representation The model object from which to take the updated values. only_options : boolean, optional If set to true, only the smoother and filter options are updated, and the state space representation is not updated. Default is False. Notes ----- This method is rarely required except for internal usage. N( RRR>t_smoother_optionsR5tgetattrRt_smoothed_forecastst_smoothed_forecasts_errort_smoothed_forecasts_error_cov(R tmodelt only_optionsR6((sIlib/python2.7/site-packages/statsmodels/tsa/statespace/kalman_smoother.pyR>%s    c C`s7g}|js|jr(|jdƒn|js:|jrJ|jdƒn|jrc|jdƒn|jr||jdƒn|jr•|jdƒn|jr´|dddg7}n|jrÐ|d d g7}ntj|jƒd k}xœ|j D]‘}|d krqò||krs|dkr’t ||dƒ}|dk rj|rjtj t ||jd |jƒƒ}ntj |dtƒ}t|||ƒqƒ|d krEt ||dƒ}|dk r|rt||jdtdtd |jƒ}t|j||jdtdtdtd |jƒntj |dtƒ}t|||ƒqƒt||tj t ||dƒdtƒƒqòt||dƒqòWd|_d|_d|_|jd krtj |jdtƒ|_tj |jdtƒ|_tj |jdtƒ|_nd}d}d|krB|jdd…||…f|_nd|kr||jdd…dd…||…f|_nd|_d|_d|_|jr3|jj dkr3|j!|j"9_!|j#|j"9_#|j$|j"9_$|j%|j"9_%|j|j"_|j|j"_|j&|j"_&ndS(s Update the smoother results Parameters ---------- smoother : KalmanSmoother The model object from which to take the updated values. Notes ----- This method is rarely required except for internal usage. 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