M/PhkddlmZddlZddlZddlZddlZddlm Z ddl m Z ddl m Z ddlmZmZmZmZddlmZddlmZmZmZmZdd lmZddlmcmcmZ dd l!m"Z"Gd d e j#Z$Gd de j%Z&dS)) OrderedDictN)norm) PandasData)cache_readonly)aicaiccbichqic)PrecisionWarning) _get_epsilon approx_fprimeapprox_fprime_csapprox_hess_cs) pinv_extended) _safe_condceZdZdZ dfd ZedZddZdZe dZ e j d Z dd Ze d Ze d Ze dd ZddZ ddZdZddZddZdZxZS)StateSpaceMLEModelz{ This is a temporary base model from ETS, here I just copy everything I need from statespace.mlemodel.MLEModel Nnonec bt|||||||_||j\|_|_t|jt|_ |jj d|_ d|_ d|_ d|_d|_d|_dS)N)endogexogdatesfreqmissingrF)super__init__ _init_kwargs prepare_datadatarr isinstancer use_pandasshapenobs_has_fixed_params _fixed_params _params_index_fixed_params_index_free_params_index)selfrrrrrkwargs __class__s j/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tsa/exponential_smoothing/base.pyrzStateSpaceMLEModel.__init__s d%dG    #!% 1 1$) < < DI$TY ;;J$Q' "'!!#' "&ctNNotImplementedError)rs r,rzStateSpaceMLEModel.prepare_data8!!r-c tr/r0)r)rrr*s r,clonezStateSpaceMLEModel.clone<s!!r-cF|D]}||jvrtd|zdS)Nz$Invalid parameter name passed: "%s".) param_names ValueError)r)r6 param_names r,_validate_can_fix_paramsz+StateSpaceMLEModel._validate_can_fix_params?sH%  J!111 :ZG2  r-c*t|jSr/)lenr6r)s r,k_paramszStateSpaceMLEModel.k_paramsFs4#$$$r-c#KjEi_ttjt jj_j}j }j }j }t| tj z}|j|tfdjD_d_ fdj D_ t!tt jjj _ dV|_ |_|_ |_ dS#|_ |_|_ |_ wxYw)a Fix parameters to specific values (context manager) Parameters ---------- params : dict Dictionary describing the fixed parameter values, of the form `param_name: fixed_value`. See the `param_names` property for valid parameter names. Examples -------- >>> mod = sm.tsa.SARIMAX(endog, order=(1, 0, 1)) >>> with mod.fix_params({'ar.L1': 0.5}): res = mod.fit() Nc@g|]}|jv |j|fS)r%.0namer)s r, z1StateSpaceMLEModel.fix_params..ts>   4---t)$/0---r-Tc*g|]}j|Sr@)r&)rBkeyr)s r,rDz1StateSpaceMLEModel.fix_params..}s.$ $ $ (+D s #$ $ $ r-)r%rzipr6nparanger=r&copyr$r'r(setkeysr9updatelist difference)r)paramscache_fixed_paramscache_has_fixed_paramscache_fixed_params_indexcache_free_params_indexall_fixed_param_namess` r, fix_paramszStateSpaceMLEModel.fix_paramsJs(   %!#D !,D$bi &>&>??""D  "/4466!%!7#'#; "&"9   T%7%<%<%>%>!?!? ?  %%&;<<< !!&)))(     ,     "&$ $ $ $ /3/A/F/F/H/H$ $ $  #'  $-(( ) ) 4 4T5M N N# #  > EEE&>Gc |||5|j|fi|}dddn #1swxYwY|S)a2 Fit the model with some parameters subject to equality constraints. Parameters ---------- constraints : dict Dictionary of constraints, of the form `param_name: fixed_value`. See the `param_names` property for valid parameter names. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. If None, the default is given by Model.start_params. **fit_kwds : keyword arguments fit_kwds are used in the optimization of the remaining parameters. Returns ------- results : Results instance Examples -------- >>> mod = sm.tsa.SARIMAX(endog, order=(1, 0, 1)) >>> res = mod.fit_constrained({'ar.L1': 0.5}) N)rVfit)r) constraints start_paramsfit_kwdsress r,fit_constrainedz"StateSpaceMLEModel.fit_constraineds0__[ ) ) 5 5$(<44844C 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 s 155c>t|dr|jSt)zP (array) Starting parameters for maximum likelihood estimation. _start_params)hasattrr_r1r<s r,rZzStateSpaceMLEModel.start_paramss% 4 ) ) &% %% %r-ct|dr|jS dtt|jD}n#t $rg}YnwxYw|S)z (list of str) List of human readable parameter names (for parameters actually included in the model). _param_namescg|]}d|zS)zparam.%dr@rBis r,rDz2StateSpaceMLEModel.param_names..sOOOAaOOOr-)r`rbranger;rZr1)r)namess r,r6zStateSpaceMLEModel.param_namessu 4 ( ( $ $ OOs4;L7M7M1N1NOOO&    Ls+A AAct)z8 Not implemented for state space models r0)clsformularsubset drop_colsargsr*s r, from_formulazStateSpaceMLEModel.from_formulas "!r-cB|jdkr'|jddkrtj|d}|jre|jdr|||\}}}}nd}|jdkrt j|||}nt j|||}|S)N)axisr)indexrC)rscolumns) ndimr"rHsqueezer!_get_prediction_indexpdSeries DataFrame)r)r start_idxend_idxrg_rss r, _wrap_datazStateSpaceMLEModel._wrap_datas 9q==TZ]a//:d+++D ? Fz!} !%!;!;Iw!O!O1ay1}}yU???|DuEEE r-c|sPi}|||d<|||d<||jdd}||jdd}||||fi|} || }|S)Ncov_typecov_kwdsrXrrp) _res_classes) r)rPresult return_rawrr results_class wrapper_class result_kwargsr\s r, _wrap_resultsz StateSpaceMLEModel._wrap_resultss (M#,4 j)#,4 j)$ $ 1% 8 ; $ $ 1% 8 ; -ffFF FFC"]3''F r-c t|ddt|}d|d<d|d<t||j||S)Ng@T transformed complex_stepepsilonr*)r r;rloglike)r)rPr*rs r,_score_complex_stepz&StateSpaceMLEModel._score_complex_stepsSvr4V== $}!%~ g'-/// /r-Fc <d|d<t||j||S)NTr)r*centered)r r)r)rPapprox_centeredr*s r,_score_finite_differencez+StateSpaceMLEModel._score_finite_differences. $}VT\&&5777 7r-c 4tj|d}tjdtd|s t |ddt |}n"t |ddt |dz }t||j|||}||j z S) Nrp)ndminzkCalculation of the Hessian using finite differences is usually subject to substantial approximation errors. stacklevelrr)rr*r) rHarraywarningswarnr r r;r rnobs_effective)r)rPrr*rhessians r,_hessian_finite_differencez-StateSpaceMLEModel._hessian_finite_difference s&*** !'!"      E"61dCKK@@GG"61dCKK@@1DG(E(/)8::: $-..r-c t|ddt|}d|d<d|d<t||j||}||jz S)zy Hessian matrix computed by second-order complex-step differentiation on the `loglike` function. g@NTrrr)r r;rrr)r)rPr*rrs r,_hessian_complex_stepz(StateSpaceMLEModel._hessian_complex_step sc vr4V== $}!%~ DL'&BBB $-..r-)NNNrr/)NN)NNNN)F)__name__ __module__ __qualname____doc__r staticmethodrr4r9propertyr= contextlibcontextmanagerrVr]rZr6 classmethodrnr~rrrrr __classcell__r+s@r,rrs @F''''''4""\"""""%%X%@>@>@>D8&&X&  X 37"""["26///7777 ////.///////r-rceZdZdZdfd ZedZedZedZedZ edZ ed Z ed Z ed Z ed Zed ZedZedZedZedZdZ ddZedZd dZ d!dZdZ d"dZxZS)#StateSpaceMLEResultsa Class to hold results from fitting a state space model. Parameters ---------- model : MLEModel instance The fitted model instance params : ndarray Fitted parameters Attributes ---------- model : Model instance A reference to the model that was fit. nobs : float The number of observations used to fit the model. params : ndarray The parameters of the model. ?cL|j_|jj_t||d|jj_jj_jj_jrOjj _ tj _ nd_ g_ fdjjpgD_jj_jj_d_dS)N)scalec0g|]}|jvrd|zn|S)z %s (fixed)) fixed_paramsrAs r,rDz1StateSpaceMLEResults.__init__..Xs@   $(4+<#<#!>!@!@D  $T%7%<%<%>%> ? ?D  !%D  "D     .4"    JO  +  r-ctr/r0r<s r,rz#StateSpaceMLEResults.nobs_effectivecr2r-c |j|jz Sr/)rdf_modelr<s r,df_residzStateSpaceMLEResults.df_residgs"T]22r-cBt|j|j|jS)z6 (float) Akaike Information Criterion )rllfrrr<s r,rzStateSpaceMLEResults.aick 48T0$-@@@r-cBt|j|j|jS)zS (float) Akaike Information Criterion with small sample correction )rrrrr<s r,rzStateSpaceMLEResults.aiccrs DHd14=AAAr-cBt|j|j|jS)z5 (float) Bayes Information Criterion )r rrrr<s r,r zStateSpaceMLEResults.bicyrr-ctr/r0r<s r, fittedvaluesz!StateSpaceMLEResults.fittedvaluess "!r-cBt|j|j|jS)z< (float) Hannan-Quinn Information Criterion )r rrrr<s r,r zStateSpaceMLEResults.hqicsDHd14=AAAr-ct)zY (float) The value of the log-likelihood function evaluated at `params`. r0r<s r,rzStateSpaceMLEResults.llfs "!r-cXtjtj|jS)z- (float) Mean absolute error )rHmeanabsresidr<s r,maezStateSpaceMLEResults.maes wrvdj))***r-c |j|jz S)z, (float) Mean squared error )sser#r<s r,msezStateSpaceMLEResults.mses x$)##r-cDtj|jtjz}tj|t }d||j<|tj|jz}tj tj |j|dz||<|S)z (array) The p-values associated with the z-statistics of the coefficients. Note that the coefficients are assumed to have a Normal distribution. )dtypeTrr) rH zeros_likezvaluesnan ones_likeboolr(isnanrsfr)r)pvaluesmasks r,rzStateSpaceMLEResults.pvaluess- --6|G4000(,T $% $,''''t|D'9 : :;;a? r-ctr/r0r<s r,rzStateSpaceMLEResults.residr2r-c:tj|jdzS)z/ (float) Sum of squared errors rr)rHsumrr<s r,rzStateSpaceMLEResults.sses vdjAo&&&r-c |j|jz S)z@ (array) The z-statistics for the coefficients. )rPbser<s r,rzStateSpaceMLEResults.zvaluess {TX%%r-c ||dkrd}nM|dkr|j}n?|j|\}}}t|tr|j}|dz }|dkr |j|z}||jkrt d|S)z?Returns a valid numeric start index for predictions/simulationsNstartrendrpz/Cannot anchor simulation outside of the sample.)r#r_get_index_locr slicerr7)r)anchorilocr}s r,_get_prediction_start_indexz0StateSpaceMLEResults._get_prediction_start_indexs >Vw..DD u__9DD226::JD!Q$&& "z AID !889t#D $)  NOO O r-TFc |j|j|jddd||z}t |jdkrt j|j|j}t |j|j krt||\}}nt j t j g}}t j |t j z}|||<nt|\}}|j |jdd|j6t jt j||_| S)NTapprox)rPrincludes_fixedmethodapprox_complex_steprr)rr)rrrrPr;rrHix_r(r=rrrrMrlinalg matrix_rankdiag)r)rrevaluated_hessianrtmpsingular_valuesneg_covs r,_cov_params_approxz'StateSpaceMLEResults._cov_params_approxs4!/$*2D2D; 3+ 3E3 3   t ! !A % %6$143JKKD4$%% 55)67H7N)O)O&oo')vx_m$566?GGDMM)67H)I)I &Wo $+4MMM : ..rw/G/GHHDJxr-cB||j|jS)z (array) The variance / covariance matrix. Computed using the numerical Hessian approximated by complex step or finite differences methods. )r_cov_approx_complex_step_cov_approx_centeredr<s r,cov_params_approxz&StateSpaceMLEResults.cov_params_approxs' &&  )4+D   r-Nc|d}|jtd|dks|dkrDddlm}t |dr*t j|j|j}|j |z }n|j }g}|Bt|j dd}|rtd |z|d z}ntd |d z}|dkrd d gndd g}t|j jD]|} t |dr|jj| |d} n|j} || ||dk} |t j| dd|fj}t j|}nt+d|S)a" Ljung-Box test for no serial correlation of standardized residuals Null hypothesis is no serial correlation. Parameters ---------- method : {'ljungbox', 'boxpierce', 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 min(10, nobs//5) for non-seasonal time series and min (2*m, nobs//5) for seasonal time series. Returns ------- output : ndarray 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. See Also -------- statsmodels.stats.diagnostic.acorr_ljungbox Ljung-Box test for serial correlation. Notes ----- For statespace models: 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. NljungboxWCannot compute test statistic when standardized forecast errors have not been computed. boxpiercer)acorr_ljungboxloglikelihood_burnseasonal_periodsrr rrpfilter_results)lagsrz'Invalid serial correlation test method.)standardized_forecasts_errorr7statsmodels.stats.diagnosticrr`rHmaximumr nobs_diffuser#rgetattrrminrfk_endograppendasarrayTc_r1) r)rrrdroutputrcolsrexresultss r,test_serial_correlationz,StateSpaceMLEResults.test_serial_correlationsZ >F  , 4HII I Z  6[#8#8 C C C C C Ct122 5Jt68IJJ "&Q!%!4F|#*4:7I1#M#M #8q#33^q5HIIDDr>Q#677D#{22Aq66AD4:-.. > >4!122:+HKABBOAA9A(.DV{-B bj11!!!T':<====U6]FF%'122 2 r- two-sidedc|d}|jtd|dkrt|dr9|jjdz}t j|j|j}|j|z }nH|jdz}|j dkr*t j |}|tj ddf}|j }d}t j |}g}g}t|jjD]} t!t j|dz } || | df} | t j| } t'| || ||| zf} | t j| } t'| dkr%t)jd | zd tj} dkr%t)jd | zd tj} t j| t j| z } |rdd lmfd }fd}nddlmfd}fd}|}|dvr || }nS|dvrd| z } || }n>|dvr+dt j|| || z}ntd|| ||tj||f}nt?d|S)a 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 : {'breakvar', 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 : str, 'increasing', 'decreasing' or 'two-sided' This specifies the alternative for the p-value calculation. Default is two-sided. use_f : bool, 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 : ndarray 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. NbreakvarrrrrrprrzgEarly subset of data for variable %d has too few non-missing observations to calculate test statistic.rzgLater subset of data for variable %d has too few non-missing observations to calculate test statistic.)fc2|Sr/cdftest_statistics denom_dofr numer_dofs r,z>StateSpaceMLEResults.test_heteroskedasticity..s'I:?:?r-c2|Sr/rrs r,rz>StateSpaceMLEResults.test_heteroskedasticity..s'I:?:?r-)chi2c6|zSr/rrr rrs r,rz>StateSpaceMLEResults.test_heteroskedasticity..s!!O3Y:@:@r-c6|zSr/rr"s r,rz>StateSpaceMLEResults.test_heteroskedasticity..s!!O3Y:@:@r-)reinc increasing)r dec decreasingr)2z2-sidedrzInvalid alternative.z'Invalid heteroskedasticity test method.) rr7r`rrHrrrr#rur newaxisrrfrrintroundrr;rrrr scipy.statsrr lowerminimumrr r1)r)r alternativeuse_f squared_residr rrp_valuesreh numer_resid denom_residtest_statistic pval_lower pval_upperp_valuer r rrrs @@@@r,test_heteroskedasticityz,StateSpaceMLEResults.test_heteroskedasticityXsd >F  , 4HII I Z  t-.. 'DaGJt68IJJ "&Q $ A1 D  %**$&J}$=$=M$1"*aaa-$@M!%!4J}55M OH4:-..9 )9 )!!34455+ArssF3 )28K+@+@*@A  ,, +AqQwJ7 )28K+@+@*@A  ,, q==M#?AB#C./$$$$ #%&Kq==M#?AB#C./$$$$ #%&K!# !4!4rvk7J7J!J @------"?"?"?"?"?"?J"?"?"?"?"?"?JJ100000"@"@"@"@"@"@J"@"@"@"@"@"@J*//11 "<<<(j88GG $>>>%'.%8N(j88GG $AAA"*" >22" >22##GG %%;<<<&&~666((((U?H45FF%'122 2 r-c|d}|jtd|dkrddlm}t |dr t j|j|j}nd}g}t|j j D]i}t |dr|j j||df}n|j}t j |}||||jntdt j|S) a Test for normality of standardized residuals. Null hypothesis is normality. Parameters ---------- method : {'jarquebera', 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. See Also -------- statsmodels.stats.stattools.jarque_bera The Jarque-Bera test of normality. Notes ----- For statespace models: 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. N jarqueberarr) jarque_berar fiter_resultszInvalid normality test method.)rr7statsmodels.stats.stattoolsr=r`rHrrrrfrrrrrr1r)r)rr=r r rerrs r,test_normalityz#StateSpaceMLEResults.test_normality s58 >!F  , 4HII I \ ! ! ? ? ? ? ? ?t122 Jt68IJJF4:-.. 8 8411> /L122EE!=E' kk%+667777 8&&FGG Gxr-皙?c  ddlm}|j}|d}|d}|jjrS|jj}||} d| j| j| jfzg} |d} | dd| j| j| jfzzgz } n&t|dt|j zg} | |j j } | d } n3#t$r&tjtjgd zg} YnwxYw |d } nH#t$r;tjtjgd zgd d d } YnwxYw |d } n3#t$r&tjtjgdzg} YnwxYwt)|t*s|g}dg}|d|dgft/d t1|D]#}|dd||zgf$|ddd| dgfd| d gfgz }d|j gfdd|jzgfg}t5|dr |dd|jzgf|dd|jzgfdd|jzgfdd|jzgfgz }t5|d r4|j,|jj r |d!d|j!zgfn |d!d|j!zgft5|d"r|d#|j"gfd$}d%|| ddddffd&|| ddd dffd'|| dddffd(|| ddd ffg}d)|| dddffd*|| ddd ffd+|| ddd ffd,|| ddd-ffg}|}|#||||.t1|j$dkr |r|%|||j&d/0|#|||d.g}t5|d"r)d1|j'vr ||j'd1|j(t1|j$t1|j)z krx|*}t1|j)dkr'tj+|j,|j,}||}|d2t[|z|rDd3t]|D}|/dd4|0||S)5a 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 : str 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 r)SummaryNzStatespace Model Resultsz%02d-%02d-%02dz- z - r)rrrrrpr<r)zDep. Variable:NzModel:z+ )zDate:N)zTime:NzSample:zNo. Observations:zLog Likelihoodz%#5.3frsquaredz R-squared:z%#8.3fAICBICHQICrScalerzCovariance Type:cBdd|DgS)Nz, cg|]}|dS)z.2fr@rds r,rDzBStateSpaceMLEResults.summary....s111a!zz111r-)join)rs r,rz.StateSpaceMLEResults.summary..s' II115111 2 2$ r-zLjung-Box (Q):zProb(Q):zHeteroskedasticity (H):zProb(H) (two-sided):zJarque-Bera (JB):z Prob(JB):zSkew:z Kurtosis:r)gleftgrighttitleF)alphaxnameuse_t descriptionzmCovariance matrix is singular or near-singular, with condition number %6.3g. Standard errors may be unstable.c*g|]\}}d|dzd|S)[rpz] r@)rBretexts r,rDz0StateSpaceMLEResults.summary..s>(/4#AE##T##r-z Warnings:)1statsmodels.iolib.summaryrCr _index_dates_indexmonthdayyearstrr#r+rr: ExceptionrHrrrreshaper@r rNrrfr;rr`rFrr r rfilter_concentratedrradd_table_2colsrPadd_table_paramsr6rrr cov_paramsrr(r enumerateinsert add_extra_txt)r)rQrrP model_namedisplay_paramsrCrixr samplehetlbjbtop_leftre top_right format_str diagn_left diagn_rightsummaryetextrdrs r,rtzStateSpaceMLEResults.summaryBs< 655555  =.E =E : " :"B5 A&!'15!&)AABF2A t.!'15!&1IIIJ JFF%jj%#di.."89F  1J +..j.AACC + + +(RVHqL>**CCC + ;--Z-@@BB ; ; ;BF8a<.))11!Q::BBB ; *$$L$99BB * * *BF8a<.))BBB **d++ &$J,-JqM?3444q#j//** : :A OOR$A"6!78 9 9 9 9    $ &)    !49+ . 48 34 5  4 $ $ I   lX -E,FG H H H X() * X() * h*+ ,  4) * * A'3+?4  'Htz,A+B!CDDD   g4:(='>? @ @ @ 4 $ $ C OO/$-A B B B  zz"QQQ2X,77 8 Bqqq!RxL11 2 & 3qqq!t9(=(= > #ZZAAAqD %:%: ;  !**R1X"6"6 7 **R1X.. / jjAAAqD** + **R1X.. /  ')) %     t{  a  N   $ $E)9 %      ;b     4 $ $ 7$-)G)G LL}5 6 6 6 :T[))C0A,B,BB C C**J4$%%))vd5t7NOO'- LL)*556     )3<  ^ YYYYv;F&*ppppd6 6 6 t \\\\\\\\r-r)' collectionsrrrnumpyrHpandasrxr,rstatsmodels.base.datarstatsmodels.tools.decoratorsrstatsmodels.tools.eval_measuresrrr r statsmodels.tools.sm_exceptionsr statsmodels.tools.numdiffr r rrstatsmodels.tools.toolsrstatsmodels.tsa.base.tsa_modeltsabase tsa_modeltsbase statsmodels.tsa.statespace.toolsrTimeSeriesModelrTimeSeriesModelResultsrr@r-r,rs######,,,,,,777777@@@@@@@@@@@@<<<<<< 211111////////////777777V/V/V/V/V//V/V/V/rm m m m m 68m m m m m r-