M/Ph44dZddlZddlZddlmZmZddlmZddl m Z ddl m Z ddl mZddlmZdd lmZdd lmZmZdd lmZdd lmZdd lmZ ddZdS)zk Feasible generalized least squares for regression with SARIMA errors. Author: Chad Fulton License: BSD-3 N) add_constantBunch)OLS)arma_innovations)diff) yule_walker)burg)hannan_rissanen) innovationsinnovations_mle) statespace)SARIMAXSpecification) SARIMAXParamsrrrrrrr2:0yE>r c  ||}tj}|ddkp |ddk} || }n|r| rtd|r%|tj|nt |}t ||||} | j}| j}| jrXtj dt|| j | j | j }t|| j | j | j }tj||f} | || i} t!||} | }|j}|j}t)| }||_| jdkrtj| j|_| jdkrtj| j|_| jdkrtj| j|_| j dkrtj| j!|_"|j#|_$|j}|j}|j}|j"}|j$}dg}dg}|g}|d nd}d}d }tKd|dzD]}|}|d krtM|f| j'd d | \}}n|d kr'|| d tQ|| j'd \}}n|dkr/|| dtS|| j*d \} }| d}n|dkrtW|f| j'| j*d d| \}}n|dkrdntj,|||||f}!| j-dd| j-df}"| j.dd| j.d| j.df}#|dkrt_|f|"|#d |!d| \}}nta|f|"|#d |!d| \}}|j}|j}|j}|j"}|j$}|1||j2stdtgj3| ||d\}$}%|$dddf}&|$ddddf}'t!|&|'}(|(})|)j}|tj4||z }t)| }||_| jdkr||_| jdkr||_| jdkr||_| j dkr||_"||_$|1|tj5||z }*|1|*|tj6|*|krd}n|tj d|z|d}to| |||||| |d}+||+fS)a Estimate ARMAX parameters by GLS. Parameters ---------- endog : array_like Input time series array. exog : array_like, optional Array of exogenous regressors. If not included, then `include_constant` must be True, and then `exog` will only include the constant column. order : tuple, optional The (p,d,q) order of the ARIMA model. Default is (0, 0, 0). seasonal_order : tuple, optional The (P,D,Q,s) order of the seasonal ARIMA model. Default is (0, 0, 0, 0). include_constant : bool, optional Whether to add a constant term in `exog` if it's not already there. The estimate of the constant will then appear as one of the `exog` parameters. If `exog` is None, then the constant will represent the mean of the process. Default is True if the specified model does not include integration and False otherwise. n_iter : int, optional Optionally iterate feasible GSL a specific number of times. Default is to iterate to convergence. If set, this argument overrides the `max_iter` and `tolerance` arguments. max_iter : int, optional Maximum number of feasible GLS iterations. Default is 50. If `n_iter` is set, it overrides this argument. tolerance : float, optional Tolerance for determining convergence of feasible GSL iterations. If `iter` is set, this argument has no effect. Default is 1e-8. arma_estimator : str, optional The estimator used for estimating the ARMA model. This option should not generally be used, unless the default method is failing or is otherwise unsuitable. Not all values will be valid, depending on the specified model orders (`order` and `seasonal_order`). Possible values are: * 'innovations_mle' - can be used with any specification * 'statespace' - can be used with any specification * 'hannan_rissanen' - can be used with any ARMA non-seasonal model * 'yule_walker' - only non-seasonal consecutive autoregressive (AR) models * 'burg' - only non-seasonal, consecutive autoregressive (AR) models * 'innovations' - only non-seasonal, consecutive moving average (MA) models. The default is 'innovations_mle'. arma_estimator_kwargs : dict, optional Arguments to pass to the ARMA estimator. Returns ------- parameters : SARIMAXParams object Contains the parameter estimates from the final iteration. other_results : Bunch Includes eight components: `spec`, `params`, `converged`, `differences`, `iterations`, `arma_estimator`, 'arma_estimator_kwargs', and `arma_results`. Notes ----- The primary reference is [1]_, section 6.6. In particular, the implementation follows the iterative procedure described in section 6.6.2. Construction of the transformed variables used to compute the GLS estimator described in section 6.6.1 is done via an application of the innovations algorithm (rather than explicit construction of the transformation matrix). Note that if the specified model includes integration, both the `endog` and `exog` series will be differenced prior to estimation and a warning will be issued to alert the user. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. Nrz1Cannot include a constant in an integrated model.)exogorderseasonal_orderztProvided `endog` and `exog` series have been differenced to eliminate integration prior to GLS parameter estimation.)k_diffk_seasonal_diffseasonal_periods)specFc.|rtd|dS)Nz/arma_estimator_kwargs not supported for method ) ValueError)kwargsmethods d/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tsa/arima/estimators/gls.py_check_arma_estimator_kwargsz)gls.._check_arma_estimator_kwargss1  J&JJ   r)ar_orderdemeanr r )ma_orderr%r )r$r&r%r )rrr% start_params)rrinclude_constantr*zRoots of the autoregressive parameters indicate that data isnon-stationary. GLS cannot be used with non-stationary parameters. You should consider differencing the model dataor applying a nonlinear transformation (e.g., natural log).T) ar_params ma_params normalizezFeasible GLS failed to converge in %d iterations. Consider increasing the maximum number of iterations using the `max_iter` argument or reducing the required tolerance using the `tolerance` argument.)rparams converged differences iterationsarma_estimatorarma_estimator_kwargs arma_results)8npinfr ones_likerrendogr is_integratedwarningswarnr seasonal_diffrc_validate_estimatorrfitr/residr exog_params max_ar_orderzeros k_ar_paramsr,max_seasonal_ar_orderk_seasonal_ar_paramsseasonal_ar_params max_ma_order k_ma_paramsr-max_seasonal_ma_orderk_seasonal_ma_paramsseasonal_ma_paramsscalesigma2rangerr$r r r&r r_rrr r append is_stationaryrdotabsallr),r9rrrr+n_itermax_iter tolerancer3r4 integratedr augmentedmod_olsres_olsrBrApr,rHr-rMrOr5r1 parametersr0ir"prevp_armares_armaoutr* tmp_ordertmp_seasonal_ordertmp_uxmod_glsres_gls difference other_resultss, r!glsros`F qA6!2Q!6J)> NjNLMMMK&*lr|E""" T8J8J D/= ? ? ?D JE 9D  <  / 0 0 0U49%)%7&*&;===D$($6%)%:<<<eTk"I N+++$ "%GkkmmG.K ME 4   AAM 1ht/00  !A%%!x(ABB 1ht/00  !A%%!x(ABB}AH I- I- XF6L&KJTI A 1hl # #p?p? ] * ** ) $ e ) )' ) ) FHHv % % ( ()> G G G#EDM+0 2 2 2 FHH } , , ( ()> N N N' /4666MCWFF 0 0 0. 7 $   7 7 5 7 7 FHHQBE)Y*<*bfZ)%;<<>I E > M36> > ? ? ? 2A"(!6$    M m r#) NrrNNrrr N)__doc__numpyr6r;statsmodels.tools.toolsrr#statsmodels.regression.linear_modelrstatsmodels.tsa.innovationsr statsmodels.tsa.statespace.toolsr,statsmodels.tsa.arima.estimators.yule_walkerr%statsmodels.tsa.arima.estimators.burgr 0statsmodels.tsa.arima.estimators.hannan_rissanenr ,statsmodels.tsa.arima.estimators.innovationsr r +statsmodels.tsa.arima.estimators.statespacer #statsmodels.tsa.arima.specificationrstatsmodels.tsa.arima.paramsrror#r!r~s8 77777777333333888888111111DDDDDD666666LLLLLL""""""""BBBBBBDDDDDD666666;GCG@Daaaaaar#