M/PhHdZddlZddlZddlmZmZmZddlm Z ddl mZGddZ Gd d Z Gd d Z Gd dZdS)zI State Space Representation Author: Chad Fulton License: Simplified-BSD N)find_best_blas_typevalidate_matrix_shapevalidate_vector_shape)Initialization)toolsc eZdZdZdZdZdS) OptionWrapperc"||_||_dSN)mask_attribute mask_value)selfr rs i/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tsa/statespace/representation.py__init__zOptionWrapper.__init__s,$cXtt||jd|jzSNr)boolgetattrr r)robjobjtypes r__get__zOptionWrapper.__get__s&GC!4a884?JKKKrct||jd}t|r ||jz}n ||jz}t ||j|dSr)rr rrsetattr)rrvaluemask_attribute_values r__set__zOptionWrapper.__set__s]&sD,?CC ;; <(4?:EE(DO+;;ET(%00000rN)__name__ __module__ __qualname__rrrrrr r sD%%% LLL11111rr c,eZdZdZdZdZdZdZdS) MatrixWrapperc6||_||_d|z|_dS)N_)name attribute _attribute)rr'r(s rrzMatrixWrapper.__init__&s " /rc2t||jd}|Sr )rr))rrrmatrixs rrzMatrixWrapper.__get__+sdot44 rc.tj|d}|j|j}t |dkr||||}n||||}t||j||j |j|j<dS)NForder) npasarrayshapesr(len _set_matrix _set_vectorrr)shaperrrr7s rrzMatrixWrapper.__set__2s 5,,, 4>* u::??$$S%77EE$$S%77ET_e,,,%*[ 4>"""rc2|jdkr/|ddkr#|jd|dkr |dddf}t|j|j|d|d|j|jdkr#t j|dddddfd}|S)Nrrr-r.)ndimr7rr'nobsr1arrayr8s rr5zMatrixWrapper._set_matrix>s J!OOaA  A%(**$'NE  Iu{E!HeAh   :??HU111aaa:.c:::E rct|j|j|d|j|jdkr t j|dddfd}|S)Nrrr-r.)rr'r7r<r;r1r=r8s rr6zMatrixWrapper._set_vectorOsY Iu{E!Hch   :??HU111d7^3777E rN)rr r!rrrr5r6r"rrr$r$%s_***  1 1 1"     rr$c eZdZdZdZ eddZ eddZ eddZ eddZ ed d Z ed d Z ed d Z ddde jddddddddf dZdZdZdZdZd'dZd(dZedZedZedZedZedZdZ d)dZdZd*d Z d+d!Z d"Z!d#Z"d*d$Z#d,d&Z$dS)-Representationa> State space representation of a time series process Parameters ---------- k_endog : {array_like, int} 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 str, 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 : int, 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. Oxford University Press. Ndesignzobservation intercept obs_interceptzobservation covariance matrixobs_cov transitionzstate interceptstate_intercept selectionzstate covariance matrix state_covg.Arc i|_d}t|tjr:|}|jdr|jddks|dkr|j}|jd}||_|dkrtd||_ |dkrtd||_ ||n||_ |j |j krtd|| ||j|j f|j|j df|jdf|j|jdf|j |j df|j df|j |j df|j |j dfd|_t}|jD]T\}}|dkr t|d |ztj||d ||t||||U||_||nt$j|_|d d|_gd }|j|vr||jn|jdkrd|vr|d}n)d|vr|d}ntdd|vr|d}n)d|vr|d}ntd|d||n0t|jt0s|jtdt3|r2d|d}t7j|t:i|_i|_d|_ dS)N C_CONTIGUOUSrrzMNumber of endogenous variables in statespace model must be a positive number.z?Number of states in statespace model must be a positive number.zZDimension of state innovation `k_posdef` cannot be larger than the dimension of the state.)obsrArBrCrDrErFrGrJr&r-)dtyper/initialization)diffuseapproximate_diffuse stationaryknownconstant initial_statezSInitial state must be provided when "known" is the specified initialization method.stationary_covinitial_state_covzeInitial state covariance matrix must be provided when "known" is the specified initialization method.rQrS*Invalid state space initialization method.zUnknown keyword arguments: zT.Passing unknown keyword arguments will raise a TypeError beginning in version 0.15.)!r3 isinstancer1ndarrayflagsr7Tk_endog ValueErrorr<k_statesk_posdefbindlocalsitemsrzerosinitial_variancerprefix_statespace_mapcopypoprL initializerr4keyswarningswarn FutureWarning_representations _statespaces_time_invariant)rr[r]r^rcr<rKrArBrCrDrErFrGstatespace_classeskwargsendogscoper'r7 basic_initsrQrSmsgs rrzRepresentation.__init__s   grz * * %E N+ [^a''4199k!nG Q;;ABB B  a<<122 2  $,$8h =4= ( (KLL L   IIe    L$),|T]A6"lA. dlA6=$-; $ q1-:-:    ;,,.. 1 1KD%u}} D#*bhuE&M&M&M N N NT{&dE$K000!1);)G'9&8+0+F+K+K+M+M " %jj)94@@FFF  + - - OOD/ 0 0 0 0  G + +V##!::j11 F**!::o66 "LMMM6))!', !()) )rct|}|tur.||jvrtd|zt |||dS|t ur|d|dd}}||jvrtd|dzt j|j}t|d|z}gd}|j|ks4|j |vr+t|d|zj |}|j ddkr t||jdz kr|dz}|||<t |||dStd) Nrvrrr&)fdr-Drwrxry)rzr{r3r|rr~r1r=rKrcharrealastyper7r4r;) rrrrr'rrKr+ valid_typess r __setitem__zRepresentation.__setitem__sS  C<<$+%% !M#&"'((( D#u % % % % %e^^q63qrr7&D4;&& !M#&q6"*+++HUOO)ET3:..F...K<5((UZ;-F-F sTz227>>uEE|B1$$V A )E)E$#F6N D$ ' ' ' ' '()) )rc t||d<|j|d<dD]A}t||}||vs|||||<|||krtd|zB|jD]E}|dkr ||vr8t||}|jddkrtd |z|||<F|d |j|S) a Construct keyword arguments for cloning a state space model Parameters ---------- endog : array_like An observed time-series process :math:`y`. **kwargs Keyword arguments to pass to the new state space representation model constructor. Those that are not specified are copied from the specification of the current state space model. r<r[)r]r^Nz/Cannot change the dimension of %s when cloning.rJrwrzZThe `%s` matrix is time-varying. Cloning this model requires specifying an updated matrix.rL) r4r[rr\r3rhr7 setdefaultrL)rrqrprvalr'mats r _clone_kwargszRepresentation._clone_kwargss2"Uv Ly+ 4 4C$$$C&  F3K$7!s c{c!! "-/2"3444"K$$&& # #Du}}6!!dD))9R=A%%$&8:>&?@@@ #t  *D,?@@@ rc f|j|fi|}|jdi|}|||S)aw Clone a state space representation while overriding some elements Parameters ---------- endog : array_like An observed time-series process :math:`y`. **kwargs Keyword arguments to pass to the new state space representation model constructor. Those that are not specified are copied from the specification of the current state space model. Returns ------- Representation Notes ----- If some system matrices are time-varying, then new time-varying matrices *must* be provided. r")r __class__r_)rrqrpmods rclonezRepresentation.clonesI,$#E44V44dn&&v&&  rc "tj|}|jdkr|ddtjf}t |}|d}||j}|dkr |j|z}|dkr |j|z}||jkrt d||jkrt d||krt dtj|j dd||fj |g}d}d}|j D]}\}} |d kr t||} ||vrD| jd dkr2||z|jkrt ||z| d |||zf||<e|dkrt d | jd dkr|jdkrt ||ztj||} t | d kr)t!|| j| d| jd n/t#|| j| d| d| jd | jd |krt ||z| d d|f} tj| d ||f| f||<|j|fi|S)a~ Extend the current state space model, or a specific (time) subset Parameters ---------- endog : array_like An observed time-series process :math:`y`. start : int, optional The first period of a time-varying state space model to include in the new model. Has no effect if the state space model is time-invariant. Default is the initial period. end : int, optional The last period of a time-varying state space model to include in the new model. Has no effect if the state space model is time-invariant. Default is the final period. **kwargs Keyword arguments to pass to the new state space representation model constructor. Those that are not specified are copied from the specification of the current state space model. Returns ------- Representation Notes ----- This method does not allow replacing a time-varying system matrix with a time-invariant one (or vice-versa). If that is required, use `clone`. rNrzfThe `start` argument of the extension within the base model cannot be after the end of the base model.zdThe `end` argument of the extension within the base model cannot be after the end of the base model.z_The `start` argument of the extension within the base model cannot be after the `end` argument.zIModel has time-invariant %s matrix, so cannot provide an extended matrix.ziModel has time-varying %s matrix, so an updated time-varying matrix for the extension period is required.rJrw.zOExtension is being performed within-sample so cannot provide an extended matrixr:)r1 atleast_1dr;newaxisr4r<r\rconcatrqrZr3rarr7r2rrc_r) rrqstartendrpr<error_tierror_tvr'r7r updated_mats rextendzRepresentation.extends< e$$ :??!!!RZ-(E5zz =E ;)C 199I%E 77)c/C 49  ,-- - ??,-- - 3;;OPP P  djE#I68%@AA+$ ;,,..8 G8 GKD%u}}$%%C6!!9R=1$$TzDI--(D999 (+3cDj0@+@'At  "IJJJ9R=A%%$)a--$X_555!j66 u::??)$ 0A58*5*;B*?AAAA*$ 0A58*/(K4Eb4IKKK$R(4//$X_555"-c5D5j"9K "uSeCi%8+%EFt tz%**6***r绽|=c"|jj}t|t|kr.tdt|t|fzt|t|krXt|t|z }tj|j|| djtjzfj}t j|}t j|}t j||z }tj |||z <d|||z<||k}||z} d|| <ttt j |} ttt j | } | | fS)NzKGiven data (length %d) is too short to diff against model data (length %d).gF) rqrZr4r\r1rnanisnanabsinflistzipwhere) r new_endog tolerancerq nobs_appendnew_nan existing_nandiff is_revisionis_new revision_ixnew_ixs r diff_endogzRepresentation.diff_endogs`  y>>CJJ & &@ #IE ;<== = y>>CJJ & &i..3u::5KE%'9k\]]#;#=#FFGIE(9%%x vi%'((')vW| #$')W| #$i' (# F3 5 5677 c28F++,--F""rc|j|j|j|j|j|j|jf}|j |jf|z}t|dS)zO (str) BLAS prefix of currently active representation matrices Nr) _design_obs_intercept_obs_cov _transition_state_intercept _selection _state_covrqr)rarrayss rprefixzRepresentation.prefixsX L$-t}  d3T_ O  : !j]V+F"6**1--rc0tj|jS)zN (dtype) Datatype of currently active representation matrices )rprefix_dtype_maprrs rrKzRepresentation.dtypes %dk22rcV|j|jjd|jjdcxkoq|jjdcxkoZ|jjdcxkoC|jjdcxko,|jjdcxko|jjdkncS|jS)zk (bool) Whether or not currently active representation matrices are time-invariant Nr:r) rnrr7rrrrrrrs rtime_invariantzRepresentation.time_invariants   ' "1%)<)B1)E)))) #A&))))*.*:*@*C))))%+A.))))26/2G2J))))%a()))) ' 'rc@|j}||jvr |j|SdSr )rrm)rrs r _statespacezRepresentation._statespaces* T& & &$V, ,trc|jS)zN (array) Observation vector: :math:`y~(k\_endog \times nobs)` )rqrs rrJzRepresentation.obss zrc2t|tjstd|jdkr4|jdkr|jddf|_nd|jdf|_|jdkstd|jdr|jd|jkrnr|jdr|jd|jkr|j}nG|jdrtd|jdrtd td |jdstj |}tj ||_ ||_ |j jd|_ t|d r|j j|jd <d Sd S)a( Bind data to the statespace representation Parameters ---------- endog : ndarray Endogenous data to bind to the model. Must be column-ordered ndarray with shape (`k_endog`, `nobs`) or row-ordered ndarray with shape (`nobs`, `k_endog`). Notes ----- The strict requirements arise because the underlying statespace and Kalman filtering classes require Fortran-ordered arrays in the wide format (shaped (`k_endog`, `nobs`)), and this structure is setup to prevent copying arrays in memory. By default, numpy arrays are row (C)-ordered and most time series are represented in the long format (with time on the 0-th axis). In this case, no copying or re-ordering needs to be performed, instead the array can simply be transposed to get it in the right order and shape. Although this class (Representation) has stringent `bind` requirements, it is assumed that it will rarely be used directly. z-Invalid endogenous array; must be an ndarray.rrr:z9Invalid endogenous array provided; must be 2-dimensional. F_CONTIGUOUSrIzXInvalid endogenous array; column-ordered arrays must have first axis shape of `k_endog`.zTInvalid endogenous array; row-ordered arrays must have last axis shape of `k_endog`.z?Invalid endogenous array; must be ordered in contiguous memory.r3rJN)rWr1rXr\r;r[r7rYrZasfortranarray iscomplexobj_complex_endogrqr<hasattrr3)rrqs rr_zRepresentation.binds4%,, NLMM M :??|q  ${1~q1  !%+a.1 zQ/00 0 ;~ & 45;q>T\+I+I [ ( 4U[^t|-K-KGEE [ ( 4+,, ,[ ( 4+,, , 344 4{>* -%e,,E!oe44 J$Q'  4 " " 2!%!1DK    2 2rc |dkrt|jd||}n|dkrtj||||| | }n^|dkr!||j}t|jd|}n7|dkrt|jd}n|d krt|jd }t |tst d ||_dS) z,Create an Initialization object if necessaryrPrU componentsaPstarPinfAR0Q0rNNapproximate_diffuse_variancerOrMrV)rr]from_componentsrcrWr\rL) rrLrrQrSrrrrrrs rrgzRepresentation.initialize6s W $ $+DM75=;IKKKNN| + ++;5tqRB@@@NN 4 4 4+3/3/D,+ 4-IKKKNN| + ++DM<HHNN y ( (+DM9EEN..99 KIJJ J,rctj|d}tj|d}|j|jfks+t d|jt |jfz|j|j|jfks1t d|j|jt |jfz|d||dS)a Initialize the statespace model with known distribution for initial state. These values are assumed to be known with certainty or else filled with parameters during, for example, maximum likelihood estimation. Parameters ---------- constant : array_like Known mean of the initial state vector. stationary_cov : array_like Known covariance matrix of the initial state vector. r-r.zJInvalid dimensions for constant state vector. Requires shape (%d,), got %szSInvalid dimensions for stationary covariance matrix. Requires shape (%d,%d), got %srPrUN)r1r2r7r]r\r{rg)rrQrSs rinitialize_knownzRepresentation.initialize_knownRs :hc222N#>>>~$-!111="mS-@-@ABCC C# t}'EEEG"mT]!."67799:: : ('5  7 7 7 7 7rcF||j}|d|dS)a Initialize the statespace model with approximate diffuse values. Rather than following the exact diffuse treatment (which is developed for the case that the variance becomes infinitely large), this assigns an arbitrary large number for the variance. Parameters ---------- variance : float, optional The variance for approximating diffuse initial conditions. Default is 1e6. NrNr)rcrg)rvariances rinitialize_approximate_diffusez-Representation.initialize_approximate_diffusers=  ,H -5=  ? ? ? ? ?rc >|d||||||dS)aa Initialize the statespace model with component matrices Parameters ---------- a : array_like, optional Vector of constant values describing the mean of the stationary component of the initial state. Pstar : array_like, optional Stationary component of the initial state covariance matrix. If given, should be a matrix shaped `k_states x k_states`. The submatrix associated with the diffuse states should contain zeros. Note that by definition, `Pstar = R0 @ Q0 @ R0.T`, so either `R0,Q0` or `Pstar` may be given, but not both. Pinf : array_like, optional Diffuse component of the initial state covariance matrix. If given, should be a matrix shaped `k_states x k_states` with ones in the diagonal positions corresponding to states with diffuse initialization and zeros otherwise. Note that by definition, `Pinf = A @ A.T`, so either `A` or `Pinf` may be given, but not both. A : array_like, optional Diffuse selection matrix, used in the definition of the diffuse initial state covariance matrix. If given, should be a `k_states x k_diffuse_states` matrix that contains the subset of the columns of the identity matrix that correspond to states with diffuse initialization. Note that by definition, `Pinf = A @ A.T`, so either `A` or `Pinf` may be given, but not both. R0 : array_like, optional Stationary selection matrix, used in the definition of the stationary initial state covariance matrix. If given, should be a `k_states x k_nondiffuse_states` matrix that contains the subset of the columns of the identity matrix that correspond to states with a non-diffuse initialization. Note that by definition, `Pstar = R0 @ Q0 @ R0.T`, so either `R0,Q0` or `Pstar` may be given, but not both. Q0 : array_like, optional Covariance matrix associated with stationary initial states. If given, should be a matrix shaped `k_nondiffuse_states x k_nondiffuse_states`. Note that by definition, `Pstar = R0 @ Q0 @ R0.T`, so either `R0,Q0` or `Pstar` may be given, but not both. Notes ----- The matrices `a, Pstar, Pinf, A, R0, Q0` and the process for initializing the state space model is as given in Chapter 5 of [1]_. For the definitions of these matrices, see equation (5.2) and the subsequent discussion there. References ---------- .. [1] Durbin, James, and Siem Jan Koopman. 2012. Time Series Analysis by State Space Methods: Second Edition. Oxford University Press. rrNrg)rrrrrrrs rinitialize_componentsz$Representation.initialize_componentss9t  TQ2      rc0|ddS)z@ Initialize the statespace model as stationary. rONrrs rinitialize_stationaryz$Representation.initialize_stationarys  %%%%%rc0|ddS)z= Initialize the statespace model as diffuse. rMNrrs rinitialize_diffusez!Representation.initialize_diffuses  """""rc ||j}tj|}||jvri|j|<|jD]e}|dkr)|j||j||<1t|d|z||j||<fn|jD]r}|j||}|dkrt|d|z|}|j |j kr|dd|dd<b||j||<s||j vrG|j |}|jj d|j j dk p|j j d|j j dk p|j j d|j j dk p|jj d|jj dk p|jj d|jj dk pt|jj d|jj dk pM|jj d|jj dk p&|jj d|jj dk }nd}|r||j vr|j |=|j|}||j|d|j|d|j|d|j|d|j|d |j|d |j|d |j|d |j |<|||fS) NrJr&rr:TrArBrCrDrErFrG)rrrrlr3rhrJrrr7rmrqrArBrCrDrErFrGrd) rrrKr+existingnewsscreateclss r_initialize_representationz)Representation._initialize_representations >[F&v. . . .,.D !& )+**,,  U??..)&1&99  cFl33::5AA)&1&99 +**,, D D08@U??!$f 55<>>E$*1-1C1I!1LLLEJ$Q'4<+=a+@@@EM'*do.CA.FFF E '-a0)/234 EL&q)T^-A!-DDDEL&q)T^-A!-DDD FF  ***%f-,V4C(+%f-e4%f-h7%f-o>%f-i8%f-l;%f-.?@%f-k:%f-k: ) )D f %uf$$rFc||j}t|jtrD|jjst d|j||j|dSt d)NzInitialization is incomplete.) complex_stepz!Statespace model not initialized.)rrWrLr initialized RuntimeErrorrmrg)rrrs r_initialize_statez Representation._initialize_states >[F d)> : : D&2 D"#BCCC  f % 0 01D>J 1 L L L L LBCC Cr)NN)r) NNNNNNNNNr )NNNNNN)NF)%rr r!__doc__rqr$rArBrCrDrErFrGr1float64rrrrrrrpropertyrrKrrrJr_rgrrrrrrrr"rrr@r@\s~~@ E]8X . .F"M"9?KKMm;YGGG|\::J$m$57HIIO k;77I 7EEI 48"%ARZD$ $$D }$}$}$}$~$)$)$)L')')')R---^6|+|+|+|+|####4 . .X .33X3  ( (X (X X O2O2O2bGKEI26----8777@????(FJ*.;;;;z&&& ### F%F%F%F%PDDDDDDrr@c*eZdZdZgdZeZdZdZdS)FrozenRepresentationa Frozen Statespace Model Takes a snapshot of a Statespace 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 : ndarray The observation vector. design : ndarray The design matrix, :math:`Z`. obs_intercept : ndarray The intercept for the observation equation, :math:`d`. obs_cov : ndarray The covariance matrix for the observation equation :math:`H`. transition : ndarray The transition matrix, :math:`T`. state_intercept : ndarray The intercept for the transition equation, :math:`c`. selection : ndarray The selection matrix, :math:`R`. state_cov : ndarray 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 : Initialization object 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. )modelrrKr<r[r]r^rrqrArBrCrDrErFrGmissingnmissingr3rLrRrTrccf|jD]}t||d||dSr ) _attributesrupdate_representationrrr's rrzFrozenRepresentation.__init__qsE$ & &D D$ % % % % ""5)))))rc||_|j|_|j|_|j|_|j|_|j|_|j|_|j|_|j|_|j |_ |j |_ |j |_|j |_|j |_|j |_|j |_t1j|j|jjd|_t1j|j|jjd|_t;|j|_|jD]&}|dkr tA||j!|j|<'|jj!|jd<|j"|_"|j"|#t1j|j|jj$d|_$t1j|j|jj%d|_%t1j|j|jj&d|_&dSdS)zUpdate model RepresentationT)rerJN)'rrrKr<r[r]r^rrqrrerArrBrrCrrDrrErrFrrGr1r=rmrrdictr3rhrr7rLrrRrTinitial_diffuse_state_covrs rrz*FrozenRepresentation.update_representationysp l [ J }   #2[ m((** "16688~**,, +0022$5::<<)..00)..00x 24; ? G%)+++ !3DK!@!I&*,,, 5<(( K$$&& : :Du}} 'd 3 3 9DK  !Z- E$2   +  # # % % %!#"4;/=D"J"J"JD %'X"4;/A&N&N&ND "-/X"4;/I...D * * * , +rN)rr r!r_model_attributesrrrr"rrrr(sV>>~$K***22222rr)rrinumpyr1rrrrrLrr r$r@rr"rrrsD+*****11111111(44444444nIDIDIDIDIDIDIDIDXCCCCCCCCCCr