p7]c@`sdZddlmZmZmZddlZddlZddlZ ddl m Z ddl m Z ddlmZmZddlmZddlmZmZmZmZdd lmZdd lmZmZmZddljj Z!ddl"j#j$Z%dd l&m'Z'ddl(j)jj*Z+d d l,m-Z-d dl.m/Z/d dl0m1Z1m2Z2e3e4krne4Z5ndZ6de+j7fdYZ8de+j9fdYZ:de!j;fdYZ<e!j=e<e:de%j>fdYZ>de!j;fdYZ?e!j=e?e>dS(s@ State Space Model Author: Chad Fulton License: Simplified-BSD i(tdivisiontabsolute_importtprint_functionN(tnorm(tlong(t pinv_extendedtBunch(tPrecisionWarning(t _get_epsilontapprox_hess_cstapprox_fprime_cst approx_fprime(tcache_readonly(taictbicthqic(tidentityi(tSimulationSmoother(tSmootherResults(tINVERT_UNIVARIATEtSOLVE_LUc O`sg}t|dkrt|dtr8|d}ntt||}x;tt|D]'}|j|j||||q`Wxz|jD]+\}}||krtd|qqWn>x;tt|D]'}|j|j ||||qWt ||fS(Nis7loglike() got multiple values for keyword argument '%s'( tlent isinstancetdicttziptrangetappendtgettitemst TypeErrortpopttuple( tnamestdefaultstargstkwargst output_argstflagstitnametvalue((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyt _handle_args(s % %tMLEModelcB`sqeZdZdBdBdBdZdZdZdZdZdBdZ dBdZ dBdZ dBd Z dBd Z d ZdBd Zd ZedZejdZedZejdZedZejdZedZejdZdBeddBdddddBedBdBdBdBdZedZdBdBdBdBdZeedBdBedBdBdZeedBdBedBdBdZd d!gZeegZd"Z eed#Z!dBd$Z"edBedBd%Z#edBed&Z$edBd'Z%d(Z&ed)Z'ed*Z(eed+Z)d d,d-d.gZ*ed/dBegZ+d0Z,d/edBed1Z-d d2d-d.gZ.ed/dBegZ/d3Z0d4Z1d5Z2ed6Z3d7Z4ed8Z5ed9Z6ed:Z7d;Z8d<Z9eed=Z:dBdBdBd>Z;dd?eed@Z<e=dBdAZ>RS(Cs[ State space model for maximum likelihood estimation Parameters ---------- endog : array_like The observed time-series process :math:`y` k_states : int The dimension of the unobserved state process. exog : array_like, optional Array of exogenous regressors, shaped nobs x k. Default is no exogenous regressors. dates : array-like of datetime, optional An array-like object of datetime objects. If a Pandas object is given for endog, it is assumed to have a DateIndex. freq : str, optional The frequency of the time-series. A Pandas offset or 'B', 'D', 'W', 'M', 'A', or 'Q'. This is optional if dates are given. **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 ---------- ssm : statsmodels.tsa.statespace.kalman_filter.KalmanFilter Underlying state space representation. Notes ----- This class wraps the state space model with Kalman filtering to add in functionality for maximum likelihood estimation. In particular, it adds the concept of updating the state space representation based on a defined set of parameters, through the `update` method or `updater` attribute (see below for more details on which to use when), and it adds a `fit` method which uses a numerical optimizer to select the parameters that maximize the likelihood of the model. The `start_params` `update` method must be overridden in the child class (and the `transform` and `untransform` methods, if needed). See Also -------- MLEResults statsmodels.tsa.statespace.kalman_filter.KalmanFilter statsmodels.tsa.statespace.representation.Representation c K`stt|jd|d|d|d|dd||_|j\|_|_|jjd|_||_ |j |dS(Ntendogtexogtdatestfreqtmissingtnonei( tsuperR*t__init__t _init_kwargst prepare_dataR+R,tshapetnobstk_statestinitialize_statespace(tselfR+R7R,R-R.R#((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR2rs   cC`swtj|jjdd}|jj}|dk rEtj|}n|jdkrm|jddf|_n||fS(sH Prepare data for use in the state space representation tordertCiiN(tnptarraytdatat orig_endogt orig_exogtNonetndimR5(R9R+R,((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR4s  cK`sN|jj}t|jd|j||_|jj||jj|_dS(s Initialize the state space representation Parameters ---------- **kwargs Additional keyword arguments to pass to the state space class constructor. iN(R+tTRR5R7tssmtbindtk_endog(R9R#R+((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR8s cC`s|jj||S(N(RDt __setitem__(R9tkeyR(((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRGscC`s|jj|S(N(RDt __getitem__(R9RH((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRIscK`s|jj||dS(sd Set the filtering method The filtering method controls aspects of which Kalman filtering approach will be used. Parameters ---------- filter_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 ----- This method is rarely used. See the corresponding function in the `KalmanFilter` class for details. N(RDtset_filter_method(R9t filter_methodR#((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRJscK`s|jj||dS(s Set the inversion method The Kalman filter may contain one matrix inversion: that of the forecast error covariance matrix. The inversion method controls how and if that inverse is performed. Parameters ---------- inversion_method : integer, optional Bitmask value to set the inversion method to. See notes for details. **kwargs Keyword arguments may be used to influence the inversion method by setting individual boolean flags. See notes for details. Notes ----- This method is rarely used. See the corresponding function in the `KalmanFilter` class for details. N(RDtset_inversion_method(R9tinversion_methodR#((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRLscK`s|jj||dS(s Set the numerical stability method The Kalman filter is a recursive algorithm that may in some cases suffer issues with numerical stability. The stability method controls what, if any, measures are taken to promote stability. Parameters ---------- stability_method : integer, optional Bitmask value to set the stability method to. See notes for details. **kwargs Keyword arguments may be used to influence the stability method by setting individual boolean flags. See notes for details. Notes ----- This method is rarely used. See the corresponding function in the `KalmanFilter` class for details. N(RDtset_stability_method(R9tstability_methodR#((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRNscK`s|jj||dS(s Set the memory conservation method By default, the Kalman filter computes a number of intermediate matrices at each iteration. The memory conservation options control which of those matrices are stored. Parameters ---------- conserve_memory : integer, optional Bitmask value to set the memory conservation method to. See notes for details. **kwargs Keyword arguments may be used to influence the memory conservation method by setting individual boolean flags. Notes ----- This method is rarely used. See the corresponding function in the `KalmanFilter` class for details. N(RDtset_conserve_memory(R9tconserve_memoryR#((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRPscK`s|jj||dS(sy Set the smoother output The smoother can produce several types of results. The smoother output variable controls which are calculated and returned. Parameters ---------- smoother_output : integer, optional Bitmask value to set the smoother output to. See notes for details. **kwargs Keyword arguments may be used to influence the smoother output by setting individual boolean flags. Notes ----- This method is rarely used. See the corresponding function in the `KalmanSmoother` class for details. N(RDtset_smoother_output(R9tsmoother_outputR#((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRRscC`s|jj||dS(sInitialize knownN(RDtinitialize_known(R9t initial_statetinitial_state_cov((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRT&scC`s|jj|dS(sInitialize approximate diffuseN(RDtinitialize_approximate_diffuse(R9tvariance((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRW*scC`s|jjdS(sInitialize stationaryN(RDtinitialize_stationary(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRY.scC`s |jjS(N(RDtinitialization(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRZ2scC`s||j_dS(N(RDRZ(R9R(((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRZ6scC`s |jjS(N(RDtinitial_variance(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR[:scC`s||j_dS(N(RDR[(R9R(((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR[>scC`s |jjS(N(RDtloglikelihood_burn(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR\BscC`s||j_dS(N(RDR\(R9R(((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR\FscC`s |jjS(N(RDt tolerance(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR]JscC`s||j_dS(N(RDR](R9R(((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR]Nstopgtlbfgsi2iicK`s|dkr|j}t}n| dkrY|dkrY|jdt|jddn| dkrnd} n| dkr|jj } n!| r|jjrtdn|r|jtj |}n|dkri}n|j it d6| d6| d 6| dk r| |d tapproxsHCannot use complex step derivatives when data or parameters are complex.t transformedt score_methodtapprox_complex_stepthessian_methodtmethodtfargstmaxitert full_outputtdisptcallbackt skip_hessiantcov_typetcov_kwdsN(RAt start_paramstTruet setdefaultRDt_complex_endogt ValueErrortuntransform_paramsR<R=tupdatetFalseR1R*tfitttransform_paramstparamstsmoothtmlefitt mle_retvalst mle_settings(R9RpRcRnRoRgRiRjRkRlt return_paramst optim_scoretoptim_complex_stept optim_hessianR%R#RhR|tres((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRxRsJj                  cC`sittfd6S(NRx(t MLEResultstMLEResultsWrapper(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyt _res_classessc C`s|si}|dk r%||d||dRRRDtfilterR( R9RzRcRRnRot return_ssmRtresults_wrapper_classR#R((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR sc K`stj|dd}|s-|j|}n|j|dtd||j|j_|rlttB| dRRRDR{R( R9RzRcRRnRoRRRR#R((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR{7sRcRcO`sttjtj||\}}}|s<|j|}n|j|dtd||rlttB|dtsubset((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyt from_formulasN(?t__name__t __module__t__doc__RAR2R4R8RGRIRJRLRNRPRRRTRWRYtpropertyRZtsetterR[R\R]RqRwRxRRRR{RRRRRRRRRRRRRRRRRRRRRRRRpRRRyRuRvRRt classmethodR(((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR*As/                 , ,   2+  \ W $   ?  @6  E        26RcB`s'eZdZdd+dZddZedZedZe e dZ edZ e e dZ ed Ze e d Zed Zed Ze e d ZedZe e dZedZddZedZedZedZedZedZedZedZedZdZde dZ d+dZ!d+d+e d+dZ"d d!Z#d+d+e d"Z$d d#Z%d+d+d+d$Z&d d%e e d&Z'd%d'd+d+d(Z(d)d+d+d+e d*Z)RS(,s Class to hold results from fitting a state space model. Parameters ---------- model : MLEModel instance The fitted model instance params : array Fitted parameters filter_results : KalmanFilter instance The underlying state space model and Kalman filter output Attributes ---------- model : Model instance A reference to the model that was fit. filter_results : KalmanFilter instance The underlying state space model and Kalman filter output nobs : float The number of observations used to fit the model. params : array The parameters of the model. scale : float This is currently set to 1.0 unless the model uses concentrated filtering. See Also -------- MLEModel statsmodels.tsa.statespace.kalman_filter.FilterResults statsmodels.tsa.statespace.representation.FrozenRepresentation R^c K`s!|j|_|j}tjj|||ddd|||_t|tr[||_ n d|_ |jj |_ |jj |_ |j dkr|j dkrt jdn|j |j |_|jj}|dkrdntjtj|dk|_|jj|j|jj|_|j|j|_t|dsPi|_n||_i|_|dkrwi}n|jdt|_ |jdt!|_"y&d|_#|j$d |d t|Wn[tj%j&k r$d|_#t'|j} tj(| | ftj)|_*d |jd RttsbasetTimeSeriesModelResultsR2RARRRRR6t nobs_diffuseR\RRtnobs_effectivetinitial_diffuse_state_covR<Rtdiagonaltk_diffuse_statesRztsizetfilter_concentratedtdf_modeltdf_residRRoRnt_cacheRRqt_cov_approx_complex_stepRwt_cov_approx_centeredt_rankt_get_robustcov_resultsRt LinAlgErrorRRtnantcov_params_defaulttmodelRvtsetattrtgetattrRtextendt _data_attrR( R9RRztresultsRnRoR#RtPtk_paramst extra_arraysR'((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR2sr       3            #c K`sddlm}|jdt}|r1|}n0t|j|j|jd|jd|j }||_ i|_ |j }|rd}n|j rd}nd}t|j}|dkrtjd|_d|_d |j d R?((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyt_cov_params_oims !cC`s|j|j|jS(sq (array) The variance / covariance matrix. Computed using the method from Harvey (1989). (RARR(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR6s c C`s|j|jj|jdtd|d|}t|\}}|jj|j|jdkrt j j t j ||_n| S(NRcReR( R RRRzRqRRvRRAR<RR3R<(R9ReRR=R>R?((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyt_cov_params_opgs !cC`s|j|j|jS(sy (array) The variance / covariance matrix. Computed using the outer product of gradients method. (RBRR(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR7's cC`s|jS(sj (array) The QMLE variance / covariance matrix. Alias for `cov_params_robust_oim` (R8(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pytcov_params_robust0sc C`s|jd|d|}|j|jj|jdddtd|d|}ttjtj|||\}}|jj |j|j dkrtj j tj||_ n|S(NReRRfRRc(RBR RRRzRqRR<RRvRRARR3R<(R9ReRtcov_opgR=t cov_paramsR?((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyt_cov_params_robust_oim8s  '!cC`s|j|j|jS(s (array) The QMLE variance / covariance matrix. Computed using the method from Harvey (1989) as the evaluated hessian. (RFRR(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR8Ks c C`s|jd|d|}|j|jj|jdtddd|}ttjtj|||\}}|jj |j|j dkrtj j tj||_ n|S(NReRRcRgRb(RBR RRRzRqRR<RRvRRARR3R<(R9ReRRDR=RER?((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyt_cov_params_robust_approxTs  '!cC`s|j|j|jS(s (array) The QMLE variance / covariance matrix. Computed using the numerical Hessian as the evaluated hessian. (RGRR(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR9hs tstandardcC`s|j}|j}|dkr6t||}nY|dkr|jjjddkrjtdn|jjdddddf}|dkrtjtjj |dd |j |j }q|d krtjtjj |d|j tj |j |j }q|d krttjtjj |dd |j tj tj |j |j }qtd n td |S(sk Information criteria Parameters ---------- criteria : {'aic', 'bic', 'hqic'} The information criteria to compute. method : {'standard', 'lutkepohl'} The method for information criteria computation. Default is 'standard' method; 'lutkepohl' computes the information criteria as in Lütkepohl (2007). See Notes for formulas. Notes ----- The `'standard'` formulas are: .. math:: AIC & = -2 \log L(Y_n | \hat \psi) + 2 k \\ BIC & = -2 \log L(Y_n | \hat \psi) + k \log n \\ HQIC & = -2 \log L(Y_n | \hat \psi) + 2 k \log \log n \\ where :math:`\hat \psi` are the maximum likelihood estimates of the parameters, :math:`n` is the number of observations, and `k` is the number of estimated parameters. Note that the `'standard'` formulas are returned from the `aic`, `bic`, and `hqic` results attributes. The `'lutkepohl'` formuals are (Lütkepohl, 2010): .. math:: AIC_L & = \log | Q | + \frac{2 k}{n} \\ BIC_L & = \log | Q | + \frac{k \log n}{n} \\ HQIC_L & = \log | Q | + \frac{2 k \log \log n}{n} \\ where :math:`Q` is the state covariance matrix. Note that the Lütkepohl definitions do not apply to all state space models, and should be used with care outside of SARIMAX and VARMAX models. References ---------- .. [*] Lütkepohl, Helmut. 2007. *New Introduction to Multiple Time* *Series Analysis.* Berlin: Springer. RHt lutkepohliisZCannot compute Lütkepohl statistics for models with time-varying state covariance matrix.NiR iRRsInvalid information criterias/Invalid information criteria computation method( tlowerRRt state_covR5RtR<tsqueezeRtslogdetRR tlog(R9tcriteriaRgtouttcov((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyt info_criteriaqs,/    %   # cC`sB|j}|jddkr5|dddf}n |j}|S(sW (array) The predicted values of the model. An (nobs x k_endog) array. iiN(RR5RC(R9t fittedvalues((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRSs   cC`st|j|j|jS(s< (float) Hannan-Quinn Information Criterion (RR;R R(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRscC`s |jjS(sY (float) The value of the log-likelihood function evaluated at `params`. (Rtllf_obs(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRTscC`s|j|jjjS(sY (float) The value of the log-likelihood function evaluated at `params`. (RTRR\R(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR;scC`s |jjS(sj (float) The number of observations during which the likelihood is not evaluated. (RR\(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR\scC`stjtj|jdS(s (array) The p-values associated with the z-statistics of the coefficients. Note that the coefficients are assumed to have a Normal distribution. i(RtsfR<tabstzvalues(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pytpvaluesscC`sB|j}|jddkr5|dddf}n |j}|S(sI (array) The model residuals. An (nobs x k_endog) array. iiN(RR5RC(R9tresid((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRYs   cC`s|j|jS(s@ (array) The z-statistics for the coefficients. (Rztbse(R9((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRWscC`s|dkrd}n|dkrddlm}tj|j|j}g}xlt|jj D]I}|j j ||df}tj |}|j |||qbWn tdtj|S(sV Test for normality of standardized residuals. Null hypothesis is normality. Parameters ---------- method : string {'jarquebera'} or None The statistical test for normality. Must be 'jarquebera' for Jarque-Bera normality test. If None, an attempt is made to select an appropriate test. Notes ----- Let `d` = max(loglikelihood_burn, nobs_diffuse); this test is calculated ignoring the first `d` residuals. In the case of missing data, the maintained hypothesis is that the data are missing completely at random. This test is then run on the standardized residuals excluding those corresponding to missing observations. See Also -------- statsmodels.stats.stattools.jarque_bera t jarqueberai(t jarque_beraNsInvalid normality test method.(RAtstatsmodels.stats.stattoolsR\R<tmaximumR\R RRRFRRtisnanRRR=(R9RgR\tdtoutputR&RYtmask((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyttest_normality s    s two-sidedc`s|dkrd}n|dkr|jjd}tj|j|j}|j|}g}g}x2t|j j D]} t tj |d} || | df} | tj | } t| || ||| f} | tj | } t| dkr.tjd| tj} ndkrWtjd| tj} ntj| tj| } |rddlmfd }fd }n:dd lmfd }fd }|j}|dkr|| }nb|dkr<d| } || }n=|dkrmdtj|| || }n td|j| |j|quWtj||f}n td|S(s Test for heteroskedasticity of standardized residuals Tests whether the sum-of-squares in the first third of the sample is significantly different than the sum-of-squares in the last third of the sample. Analogous to a Goldfeld-Quandt test. The null hypothesis is of no heteroskedasticity. Parameters ---------- method : string {'breakvar'} or None The statistical test for heteroskedasticity. Must be 'breakvar' for test of a break in the variance. If None, an attempt is made to select an appropriate test. alternative : string, 'increasing', 'decreasing' or 'two-sided' This specifies the alternative for the p-value calculation. Default is two-sided. use_f : boolean, optional Whether or not to compare against the asymptotic distribution (chi-squared) or the approximate small-sample distribution (F). Default is True (i.e. default is to compare against an F distribution). Returns ------- output : array An array with `(test_statistic, pvalue)` for each endogenous variable. The array is then sized `(k_endog, 2)`. If the method is called as `het = res.test_heteroskedasticity()`, then `het[0]` is an array of size 2 corresponding to the first endogenous variable, where `het[0][0]` is the test statistic, and `het[0][1]` is the p-value. Notes ----- The null hypothesis is of no heteroskedasticity. That means different things depending on which alternative is selected: - Increasing: Null hypothesis is that the variance is not increasing throughout the sample; that the sum-of-squares in the later subsample is *not* greater than the sum-of-squares in the earlier subsample. - Decreasing: Null hypothesis is that the variance is not decreasing throughout the sample; that the sum-of-squares in the earlier subsample is *not* greater than the sum-of-squares in the later subsample. - Two-sided: Null hypothesis is that the variance is not changing throughout the sample. Both that the sum-of-squares in the earlier subsample is not greater than the sum-of-squares in the later subsample *and* that the sum-of-squares in the later subsample is not greater than the sum-of-squares in the earlier subsample. For :math:`h = [T/3]`, the test statistic is: .. math:: H(h) = \sum_{t=T-h+1}^T \tilde v_t^2 \Bigg / \sum_{t=d+1}^{d+1+h} \tilde v_t^2 where :math:`d` = max(loglikelihood_burn, nobs_diffuse)` (usually corresponding to diffuse initialization under either the approximate or exact approach). This statistic can be tested against an :math:`F(h,h)` distribution. Alternatively, :math:`h H(h)` is asymptotically distributed according to :math:`\chi_h^2`; this second test can be applied by passing `asymptotic=True` as an argument. See section 5.4 of [1]_ for the above formula and discussion, as well as additional details. TODO - Allow specification of :math:`h` References ---------- .. [1] Harvey, Andrew C. 1990. *Forecasting, Structural Time Series* *Models and the Kalman Filter.* Cambridge University Press. tbreakvariiNsgEarly subset of data for variable %d has too few non-missing observations to calculate test statistic.sgLater subset of data for variable %d has too few non-missing observations to calculate test statistic.i(tfc`sj|S(N(tcdf(ttest_statistics(t denom_dofRet numer_dof(sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pytsc`sj|S(N(RU(Rg(RhReRi(sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRjs(tchi2c`sj|S(N(Rf(Rg(RkRhRi(sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRjsc`sj|S(N(RU(Rg(RkRhRi(sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRjsR&tinct increasingR`tdect decreasingg?t2s2-sideds two-sidedsInvalid alternative.s'Invalid heteroskedasticity test method.(R&RlRm(R`RnRo(Rps2-sideds two-sided(RARRR<R^R\R R6RRRFtinttroundR_RRRRRt scipy.statsReRkRJtminimumRtRtc_R(R9Rgt alternativetuse_ft squared_residR`R Rgtp_valuesR&tht numer_residt denom_residttest_statistict pval_lowert pval_uppertp_valueRa((RkRhReRisBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyttest_heteroskedasticity9s`R                      c C`s'|d krd}n|dks-|dkrddlm}tj|j|j}|j|}g}|d krtd|d}nxzt |j j D]f}||j j ||d|d|dk}|dkr|j|dd!q|j|dqWtj|}n td |S( s} Ljung-box test for no serial correlation of standardized residuals Null hypothesis is no serial correlation. Parameters ---------- method : string {'ljungbox','boxpierece'} or None The statistical test for serial correlation. If None, an attempt is made to select an appropriate test. lags : None, int or array_like If lags is an integer then this is taken to be the largest lag that is included, the test result is reported for all smaller lag length. If lags is a list or array, then all lags are included up to the largest lag in the list, however only the tests for the lags in the list are reported. If lags is None, then the default maxlag is 12*(nobs/100)^{1/4} Returns ------- output : array An array with `(test_statistic, pvalue)` for each endogenous variable and each lag. The array is then sized `(k_endog, 2, lags)`. If the method is called as `ljungbox = res.test_serial_correlation()`, then `ljungbox[i]` holds the results of the Ljung-Box test (as would be returned by `statsmodels.stats.diagnostic.acorr_ljungbox`) for the `i` th endogenous variable. Notes ----- Let `d` = max(loglikelihood_burn, nobs_diffuse); this test is calculated ignoring the first `d` residuals. Output is nan for any endogenous variable which has missing values. See Also -------- statsmodels.stats.diagnostic.acorr_ljungbox tljungboxt boxpiercei(tacorr_ljungboxi(itlagsis'Invalid serial correlation test method.N(RAtstatsmodels.stats.diagnosticRR<R^R\R R6tminRRRFRRRRuR( R9RgRRR`R RaR&R!((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyttest_serial_correlations&+      c K`s|dkr|jjd}n|jj|||\}}}}t|ttfrv|jj|\}}}n|jj |||d||} t t || d|S(s In-sample prediction and out-of-sample forecasting Parameters ---------- start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., 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, i.e., the last forecast is end. 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. 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 in-sample predictions and / or out-of-sample forecasts. An (npredict x k_endog) array. iit row_labelsN( RARt_indext_get_prediction_indexRtbytestunicodet_get_index_locRtpredicttPredictionResultsWrappertPredictionResults( R9tstarttendtdynamictindexR#t out_of_sampletprediction_indext_tprediction_results((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pytget_prediction" s$ $ icK`sKt|ttfr)|j|d}n|}|jd|jd||S(s Out-of-sample forecasts Parameters ---------- steps : int, str, or datetime, optional If an integer, the number of steps to forecast from the end of the sample. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, steps must be an integer. Default **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. A (steps x k_endog) array. iRR(RRqRR6R(R9RR#R((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyt get_forecast[ scK`s|j||||}|jS(s In-sample prediction and out-of-sample forecasting Parameters ---------- start : int, str, or datetime, optional Zero-indexed observation number at which to start forecasting, i.e., 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, i.e., the last forecast is end. 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. 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 in-sample predictions and / or out-of-sample forecasts. An (npredict x k_endog) array. (Rtpredicted_mean(R9RRRR#R((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRu s$cK`sKt|ttfr)|j|d}n|}|jd|jd||S(s Out-of-sample forecasts Parameters ---------- steps : int, str, or datetime, optional If an integer, the number of steps to forecast from the end of the sample. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, steps must be an integer. Default **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. A (steps x k_endog) array. iRR(RRqRR6R(R9RR#R((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pytforecast sc C`s\|jjr|jnd}|jjj|&|jj|j||||}WdQX|S(s Simulate a new time series following the state space model Parameters ---------- nsimulations : int The number of observations to simulate. If the model is time-invariant this can be any number. If the model is time-varying, then this number must be less than or equal to the number measurement_shocks : array_like, optional If specified, these are the shocks to the measurement equation, :math:`\varepsilon_t`. If unspecified, these are automatically generated using a pseudo-random number generator. If specified, must be shaped `nsimulations` x `k_endog`, where `k_endog` is the same as in the state space model. state_shocks : array_like, optional If specified, these are the shocks to the state equation, :math:`\eta_t`. If unspecified, these are automatically generated using a pseudo-random number generator. If specified, must be shaped `nsimulations` x `k_posdef` where `k_posdef` is the same as in the state space model. initial_state : array_like, optional If specified, this is the state vector at time zero, which should be shaped (`k_states` x 1), where `k_states` is the same as in the state space model. If unspecified, but the model has been initialized, then that initialization is used. If unspecified and the model has not been initialized, then a vector of zeros is used. Note that this is not included in the returned `simulated_states` array. Returns ------- simulated_obs : array An (nsimulations x k_endog) array of simulated observations. N( RRRRARRDt fixed_scaleRRz(R9RRRRURtsim((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR s &ic K`s_|jjr|jnd}|jjj|)|jj|j|||||}WdQX|S(s Impulse response function Parameters ---------- steps : int, optional The number of steps for which impulse responses are calculated. Default is 1. Note that the initial impulse is not counted as a step, so if `steps=1`, the output will have 2 entries. impulse : int or array_like If an integer, the state innovation to pulse; must be between 0 and `k_posdef-1`. Alternatively, a custom impulse vector may be provided; must be shaped `k_posdef x 1`. orthogonalized : boolean, optional Whether or not to perform impulse using orthogonalized innovations. Note that this will also affect custum `impulse` vectors. Default is False. cumulative : boolean, optional Whether or not to return cumulative impulse responses. Default is False. **kwargs If the model is time-varying and `steps` is greater than the number of observations, any of the state space representation matrices that are time-varying must have updated values provided for the out-of-sample steps. For example, if `design` is a time-varying component, `nobs` is 10, and `steps` is 15, a (`k_endog` x `k_states` x 5) matrix must be provided with the new design matrix values. Returns ------- impulse_responses : array Responses for each endogenous variable due to the impulse given by the `impulse` argument. A (steps + 1 x k_endog) array. Notes ----- Intercepts in the measurement and state equation are ignored when calculating impulse responses. N( RRRRARRDRRRz(R9RRRRR#RR((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR s +i cC`sddlm}m}||||}tj|j|j}|jj||df}|j d} t |j dr|j j dk r|j j |j} ntjt|} | j| || jd| d| ddd| j| d| d| jd |tj|} |j d } y| j| d td d Wn*tk r| j| dtd d nXddlm} m} | | }d!d"f}tj|d|d} | j| || d d| j| | j| d d| j|| j| jd|j d} ddlm }|| ddd| | jd|j d} ddl!m"}||d| d|| jd | j#dd|S(#s  Diagnostic plots for standardized residuals of one endogenous variable Parameters ---------- variable : integer, optional Index of the endogenous variable for which the diagnostic plots should be created. Default is 0. lags : integer, optional Number of lags to include in the correlogram. Default is 10. fig : Matplotlib Figure instance, optional If given, subplots are created in this figure instead of in a new figure. Note that the 2x2 grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Notes ----- Produces a 2x2 plot grid with the following plots (ordered clockwise from top left): 1. Standardized residuals over time 2. Histogram plus estimated density of standardized residulas, along with a Normal(0,1) density plotted for reference. 3. Normal Q-Q plot, with Normal reference line. 4. Correlogram See Also -------- statsmodels.graphics.gofplots.qqplot statsmodels.graphics.tsaplots.plot_acf i(t _import_mpltcreate_mpl_figNiR-italphag?sStandardized residualitdensitytlabeltHisttnormed(t gaussian_kdeRg\(\ig\(\?itKDEsN(0,1)s Histogram plus estimated densityi(tqqplottlinetstaxs Normal Q-Qi(tplot_acfRt Correlogramg\(\g\(\@($tstatsmodels.graphics.utilsRRR<R^R\R RRt add_subplotRR>R-RAt _mpl_reprtarangeRtplotthlinestset_xlimt set_titleR_thistRqtAttributeErrorRsRRtlinspacetpdftlegendtstatsmodels.graphics.gofplotsRtstatsmodels.graphics.tsaplotsRtset_ylim(R9tvariableRtfigtfigsizeRRR`RYRtxtresid_nonmissingRRtkdetxlimRR((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pytplot_diagnostics sL#$!         g?cC`sddlm}|j}|d$kr.d}n|d$krCd}n|jjr|jj}||} d| j| j| jfg} |d} | dd| j| j| jfg7} nt |dt |j g} |d$kr|j j }ny|j dd } Wn-tk r7tjtjgd g} nXy|jdd } Wn<tk rtjtjgd gjd d d } nXy|jdd } Wn-tk rtjtjgdg} nXt|ts|g}nd7g}|jd|dgfx;td t|D]$}|jdd||gfq'W|d8d9d| dgfd| d gfg7}d|j gfdd|jgfg}t|dr|jdd|jgfn|dd|jgfdd|jgfdd|jgfg7}|j d$k rT|j j!rT|jdd|j"gfnt|d r|jd!|j#gfnd"}d#|| d$d$ddffd%|| d$d$d dffd&|| d$d$dffd'|| d$d$d ffg}d(|| d$d$dffd)|| d$d$d ffd*|| d$d$d ffd+|| d$d$d,ffg}|}|j$|d-|d.|d/|t|j%dkr|r|j&|d0|d1|j'j(d2t)n|j$|d-|d.|d/dg}t|d rWd3|j*krW|j|j*d3n|j+t|j%kr|jd4tj,j-|j.n|rgt/|D]"\}}d5j0|d |^q}|j1dd6|j2|n|S(:s Summarize the Model Parameters ---------- alpha : float, optional Significance level for the confidence intervals. Default is 0.05. start : int, optional Integer of the start observation. Default is 0. model_name : string The name of the model used. Default is to use model class name. Returns ------- summary : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary i(tSummarysStatespace Model Resultss%02d-%02d-%02dis- s - RgRdiRiR[isDep. Variable:sModel:ts+ sDate:sTime:sSample:sNo. Observations:sLog Likelihoods%#5.3ftrsquareds R-squared:s%#8.3ftAICtBICtHQICtScaleRnsCovariance Type:cS`s,djg|D]}dj|^q gS(Ns, s{0:.2f}(tjoinR5(R=R&((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRj ssLjung-Box (Q):NsProb(Q):sHeteroskedasticity (H):sProb(H) (two-sided):sJarque-Bera (JB):s Prob(JB):sSkew:s Kurtosis:itglefttgrightttitleRtxnametuse_tR&smCovariance matrix is singular or near-singular, with condition number %6.3g. Standard errors may be unstable.s [{0}] {1}s Warnings:(sDep. Variable:N(sDate:N(sTime:N(3tstatsmodels.iolib.summaryRRRAt _index_datesRtmonthtdaytyeartstrR6R2RRt ExceptionR<R=RRtreshapeRcRtlistRRRR;RRR RRRRRRntadd_table_2colsRztadd_table_paramsR>RRwRoRRtcondRERR5tinsertt add_extra_txt(R9RRRt model_nametdisplay_paramsRRtixR`tsamplethettlbtjbttop_leftR&t top_rightt format_strt diagn_leftt diagn_righttsummarytetextttext((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRp s         *    /    "    ""%%  2N(*RRRRAR2RR R RRqRwR@R4RAR6RBR7RCRFR8RGR9RRRSRRTR;R\RXRYRWRcRRRRRRRRRR(((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRsZ  ^ l           O   , K  8 ' ,  1[ RcB`seZidd6dd6dd6dd6dd6dd6dd6dd 6ZejejjeZid d 6d d 6d d6Zejejj eZ RS(tcolumnsRWRQR4RR6R7RCR9R8R-RtynamesRR( RRt_attrstwrapt union_dictsR tTimeSeriesResultsWrappert _wrap_attrst_methodst _wrap_methods(((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR s"   RcB`sJeZdZd dZedZdddZddddZRS( s* Parameters ---------- prediction_results : kalman_filter.PredictionResults instance Results object from prediction after fitting or filtering a state space model. row_labels : iterable Row labels for the predicted data. Attributes ---------- c C`sQ|jjdkrCtj|jdddfd|jj}n!tj|jjd|jj}td|j j d|d||_||_ |j j }|j ddkr|dddf}n |j}|j j}|j ddkr|ddddf}n |j}tt|j||dd d |d tdS( NiiR'RR>R+t predict_datestdistRRtlink(RRFtpdtSeriesR+t endog_namest DataFrameRCRR>R2RRR5RRR1RR2R(R9RRRR+Rt var_pred_mean((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR2 s(     cC`sF|jjdkr'tj|j}ntj|jjj}|S(Ni(RRBR<tsqrtRCR(R9tse_mean((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR: stendpointg?cK`stt|j|||}|jdk rtj|d|j}|jjj }t |t ksr|g}ng|D]}d|^qyg|D]}d|^q}||_ n|S(NRslower %ssupper %s( R1Rtconf_intRRARRRR>RttypeRR(R9RgRtkwdsRRR'R ((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRB s  itallc C`sAddlm}tj|jd|}|}|jjdkrx|jjj }|j|d<|j |dRRR5RRRtkeysRR'( R9R+twhatRR tci_meant to_includetynameRFR((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyt summary_frameW s$     N( RRRRAR2RRRR(((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyR s  RcB`sGeZidd6dd6dd6ZejeZiZejeZRS(R-RRtt_values(RRRRRRRR(((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pyRu s (@Rt __future__RRRRtnumpyR<tpandasRRsRtstatsmodels.compat.pythonRtstatsmodels.tools.toolsRRtstatsmodels.tools.sm_exceptionsRtstatsmodels.tools.numdiffRR R R tstatsmodels.tools.decoratorsR tstatsmodels.tools.eval_measuresR RRtstatsmodels.base.wrappertbasetwrapperRtstatsmodels.genmod._predictiontgenmodt _predictiontpredt!statsmodels.genmod.families.linksRtstatsmodels.tsa.base.tsa_modelttsat tsa_modelR RRtkalman_smootherRt kalman_filterRRRRRR)tTimeSeriesModelR*R RtResultsWrapperRtpopulate_wrapperRR(((sBlib/python2.7/site-packages/statsmodels/tsa/statespace/mlemodel.pytsL   "    h