M/Ph|dZddlZddlZddlmZddlmZddl m Z m Z m ZmZmZmZddlmZmZGddZdS) zB SARIMAX specification class. Author: Chad Fulton License: BSD-3 N)_is_using_pandas)TimeSeriesModel) is_invertibleconstrain_stationary_univariate!unconstrain_stationary_univariate prepare_exogprepare_trend_specprepare_trend_data)standardize_lag_ordervalidate_basicceZdZdZ d"dZedZedZed Zed Z ed Z ed Z ed Z edZ edZedZedZedZedZedZedZedZedZdZd#dZ d$dZdZdZdZd%dZd Zd!ZdS)&SARIMAXSpecificationa% SARIMAX specification. Parameters ---------- endog : array_like, optional The observed time-series process :math:`y`. exog : array_like, optional Array of exogenous regressors. order : tuple, optional The (p,d,q) order of the model for the autoregressive, differences, and moving average components. d is always an integer, while p and q may either be integers or lists of integers. May not be used in combination with the arguments `ar_order`, `diff`, or `ma_order`. seasonal_order : tuple, optional The (P,D,Q,s) order of the seasonal component of the model for the AR parameters, differences, MA parameters, and periodicity. Default is (0, 0, 0, 0). D and s are always integers, while P and Q may either be integers or lists of positive integers. May not be used in combination with the arguments `seasonal_ar_order`, `seasonal_diff`, or `seasonal_ma_order`. ar_order : int or list of int The autoregressive order of the model. May be an integer, in which case all autoregressive lags up to and including it will be included. Alternatively, may be a list of integers specifying which lag orders are included. May not be used in combination with `order`. diff : int The order of integration of the model. May not be used in combination with `order`. ma_order : int or list of int The moving average order of the model. May be an integer or list of integers. See the documentation for `ar_order` for details. May not be used in combination with `order`. seasonal_ar_order : int or list of int The seasonal autoregressive order of the model. May be an integer or list of integers. See the documentation for `ar_order` for examples. Note that if `seasonal_periods = 4` and `seasonal_ar_order = 2`, then this implies that the overall model will include lags 4 and 8. May not be used in combination with `seasonal_order`. seasonal_diff : int The order of seasonal integration of the model. May not be used in combination with `seasonal_order`. seasonal_ma_order : int or list of int The moving average order of the model. May be an integer or list of integers. See the documentation for `ar_order` and `seasonal_ar_order` for additional details. May not be used in combination with `seasonal_order`. seasonal_periods : int Number of periods in a season. May not be used in combination with `seasonal_order`. enforce_stationarity : bool, optional Whether or not to require the autoregressive parameters to correspond to a stationarity process. This is only possible in estimation by numerical maximum likelihood. enforce_invertibility : bool, optional Whether or not to require the moving average parameters to correspond to an invertible process. This is only possible in estimation by numerical maximum likelihood. concentrate_scale : bool, optional Whether or not to concentrate the scale (variance of the error term) out of the likelihood. This reduces the number of parameters by one. This is only applicable when considering estimation by numerical maximum likelihood. dates : array_like of datetime, optional If no index is given by `endog` or `exog`, an array-like object of datetime objects can be provided. freq : str, optional If no index is given by `endog` or `exog`, the frequency of the time-series may be specified here as a Pandas offset or offset string. missing : str Available options are 'none', 'drop', and 'raise'. If 'none', no nan checking is done. If 'drop', any observations with nans are dropped. If 'raise', an error is raised. Default is 'none'. Attributes ---------- order : tuple, optional The (p,d,q) order of the model for the autoregressive, differences, and moving average components. d is always an integer, while p and q may either be integers or lists of integers. seasonal_order : tuple, optional The (P,D,Q,s) order of the seasonal component of the model for the AR parameters, differences, MA parameters, and periodicity. Default is (0, 0, 0, 0). D and s are always integers, while P and Q may either be integers or lists of positive integers. ar_order : int or list of int The autoregressive order of the model. May be an integer, in which case all autoregressive lags up to and including it will be included. For example, if `ar_order = 3`, then the model will include lags 1, 2, and 3. Alternatively, may be a list of integers specifying exactly which lag orders are included. For example, if `ar_order = [1, 3]`, then the model will include lags 1 and 3 but will exclude lag 2. diff : int The order of integration of the model. ma_order : int or list of int The moving average order of the model. May be an integer or list of integers. See the documentation for `ar_order` for examples. seasonal_ar_order : int or list of int The seasonal autoregressive order of the model. May be an integer or list of integers. See the documentation for `ar_order` for examples. Note that if `seasonal_periods = 4` and `seasonal_ar_order = 2`, then this implies that the overall model will include lags 4 and 8. seasonal_diff : int The order of seasonal integration of the model. seasonal_ma_order : int or list of int The moving average order of the model. May be an integer or list of integers. See the documentation for `ar_order` and `seasonal_ar_order` for additional details. seasonal_periods : int Number of periods in a season. trend : str{'n','c','t','ct'} or iterable, optional Parameter controlling the deterministic trend polynomial :math:`A(t)`. Can be specified as a string where 'c' indicates a constant (i.e. a degree zero component of the trend polynomial), 't' indicates a linear trend with time, and 'ct' is both. Can also be specified as an iterable defining the polynomial as in `numpy.poly1d`, where `[1,1,0,1]` would denote :math:`a + bt + ct^3`. Default is to not include a trend component. ar_lags : list of int List of included autoregressive lags. If `ar_order` is a list, then `ar_lags == ar_order`. If `ar_lags = [1, 2]`, then the overall model will include the 1st and 2nd autoregressive lags. ma_lags : list of int List of included moving average lags. If `ma_order` is a list, then `ma_lags == ma_order`. If `ma_lags = [1, 2]`, then the overall model will include the 1st and 2nd moving average lags. seasonal_ar_lags : list of int List of included seasonal autoregressive lags. If `seasonal_ar_order` is a list, then `seasonal_ar_lags == seasonal_ar_order`. If `seasonal_periods = 4` and `seasonal_ar_lags = [1, 2]`, then the overall model will include the 4th and 8th autoregressive lags. seasonal_ma_lags : list of int List of included seasonal moving average lags. If `seasonal_ma_order` is a list, then `seasonal_ma_lags == seasonal_ma_order`. See the documentation to `seasonal_ar_lags` for examples. max_ar_order : int Largest included autoregressive lag. max_ma_order : int Largest included moving average lag. max_seasonal_ar_order : int Largest included seasonal autoregressive lag. max_seasonal_ma_order : int Largest included seasonal moving average lag. max_reduced_ar_order : int Largest lag in the reduced autoregressive polynomial. Equal to `max_ar_order + max_seasonal_ar_order * seasonal_periods`. max_reduced_ma_order : int Largest lag in the reduced moving average polynomial. Equal to `max_ma_order + max_seasonal_ma_order * seasonal_periods`. enforce_stationarity : bool Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. This is only possible in estimation by numerical maximum likelihood. enforce_invertibility : bool Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. This is only possible in estimation by numerical maximum likelihood. concentrate_scale : bool Whether or not to concentrate the variance (scale term) out of the log-likelihood function. This is only applicable when considering estimation by numerical maximum likelihood. is_ar_consecutive is_ma_consecutive is_integrated is_seasonal k_exog_params k_ar_params k_ma_params k_seasonal_ar_params k_seasonal_ma_params k_params exog_names ar_names ma_names seasonal_ar_names seasonal_ma_names param_names Examples -------- >>> SARIMAXSpecification(order=(1, 0, 2)) SARIMAXSpecification(endog=y, order=(1, 0, 2)) >>> spec = SARIMAXSpecification(ar_order=1, ma_order=2) SARIMAXSpecification(endog=y, order=(1, 0, 2)) >>> spec = SARIMAXSpecification(ar_order=1, seasonal_order=(1, 0, 0, 4)) SARIMAXSpecification(endog=y, order=(1, 0, 0), seasonal_order=(1, 0, 0, 4)) NnoneTcp| |_||_||_||_|du}|dup|dup|du}|du}|dup | dup| dup| du}|r|rt d|r|rt d|r|dn|}|dn|}|dn|}|||f}n|sd}|r|dn|}| dn| } | dn| } | dn| } || | | f}n|sd}t |dkrt dt |dkrt d |r|d dkrt d |d t |d krt d |d dkrt d |d t |d krt d|ddkrt dt|ddt |d t|ddf}t|ddt |d t|ddt |df}|rZ|dd krt d|ddks|d dks |ddkr|ddkrt d||_|\|_ |_ |_ ||_ |\|_ |_|_|_t#|j t$r |j |_n4t)jd |j d z|_t#|j t$r |j |_n4t)jd |j d z|_t#|j t$r |j |_n4t)jd |j d z|_t#|jt$r |j|_n4t)jd |jd z|_|jr |jdnd|_|jr |jdnd|_|jr |jdnd|_|jr |jdnd|_|j|j|jzz|_|j|j|jzz|_tA|j}tAt)j!|j|jz}|"|}|r%t |dkrt d|ztA|j}tAt)j!|j|jz}|"|}|r%t |dkrt d|z| |_#tI| \|_%}tM|d} |r|t |j%dkru|j%dd krdt)j'|}!t)j(|!d}"|"dk}#|#|!ddkz}$|$}%t)j)|%rt dt)j*|j%d kd|_+t |j+|_,t |j+dkrd|_-d|_.nt)j/|j+t)jt |j+kr%|j+d|_-|j+d|_.n|j+|_-|j+d|_.ta|\|_1}|du}&|2|gn-t)j2t |t(j3z}|t |nt |}'|j-x|4|'|}(||(}n]| rGtkj6|(|j7|8}(tkj9|(|gd }nt(j:|(|f}tw||||||_<|&rdn |j<j=|_=|j<j>|_>|rQ|&sO|j=j?d kr?|j=j@d d kr)t dt|j=j@z|&rdn*t)j)t)jB|j=|_CdS)NzCCannot specify both `order` and either of `ar_order` or `ma_order`.zpCannot specify both `seasonal_order` and any of `seasonal_ar_order`, `seasonal_ma_order`, or `seasonal_periods`.r)rrr)rrrrz9`order` argument must be an iterable with three elements.zA`seasonal_order` argument must be an iterable with four elements.rz%Cannot specify negative differencing.z'Cannot specify fractional differencing.z.Cannot specify negative seasonal differencing.z0Cannot specify fractional seasonal differencing.z-Cannot specify negative seasonal periodicity.ARMAz seasonal ARz seasonal MAz,Seasonal periodicity must be greater than 1.zXMust include nonzero seasonal periodicity if including seasonal AR, MA, or differencing.zlInvalid model: autoregressive lag(s) %s are in both the seasonal and non-seasonal autoregressive components.zlInvalid model: moving average lag(s) %s are in both the seasonal and non-seasonal moving average components.)axiszuA constant trend was included in the model specification, but the `exog` data already contains a column of constants.)indexcolumns)exogdatesfreqmissingz8SARIMAX models require univariate `endog`. Got shape %s.)Denforce_stationarityenforce_invertibilityconcentrate_scale trend_offset ValueErrorlenintr orderar_orderdiffma_orderseasonal_orderseasonal_ar_order seasonal_diffseasonal_ma_orderseasonal_periods isinstancelistar_lagsnparangetolistma_lagsseasonal_ar_lagsseasonal_ma_lags max_ar_order max_ma_ordermax_seasonal_ar_ordermax_seasonal_ma_ordermax_reduced_ar_ordermax_reduced_ma_ordersetarray intersectiontrendr trend_polyr asanyarrayptpanywhere trend_termsk_trend trend_order trend_degreeallrk_exogzerosnanconstruct_trend_datapd DataFramerconstruct_trend_namesconcatc_r_modelendogrndimshapestrisnan _has_missing))selfrVrr&r*r'r(r)r+r,r-r.rArr r!r"rrrvalidate_specification has_orderhas_specific_orderhas_seasonal_orderhas_specific_seasonal_orderr1r6duplicate_ar_lagsr5r7duplicate_ma_lags_exog_is_pandasxptp0 col_is_constnz_const col_const faux_endognobs trend_datas) c/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tsa/arima/specification.py__init__zSARIMAXSpecification.__init__s %9!%:"!2(% &d23d$6F3&d2 +47'8'D(D'4D'@(D'8'D(D(8t'C $  ;+ ;:;; ;  8"= 8788 8  $,qq(H 11$D$,qq(HtX.EE E ' *&.4E !.!6AAMM&.4E &-3C //1ACNN# *)N u::??*++ + ~  ! # #455 5 " 2Qx!|| !HIIIQx3uQx==(( !JKKKa 1$$ "2333a Cq(9$:$::: "2333a 1$$ "1222 "%(D 1 1 aMM !%(D 1 13 "."3] C C q! " " !."3] C C q! " " $ " 3a A%% ",---"a''>!+<+A+A"1%**q0AQ0F0F "2333  27/ ty$-,"0  !3T5K  dmT * * D=DLL9Q (9::AACCDL dmT * * D=DLL9Q (9::AACCDL d,d 3 3 C$($:D ! ! !T3a788??AA  ! d,d 3 3 C$($:D ! ! !T3a788??AA  !15 CDL,,!04 CDL,,!*.)> ED !" % %A "*.)> ED !" % %A "    &)> > ? !    &)> > ? ! dl##rx(=>>!%!6 788#001ABB ! 2c*;&<&>!%!6 788#001ABB ! 2c*;&<&TTT[-> K$  # C: C !## (8(;a(?(?*,/ 0@,A,ABCC C @DDBF28DJ+?+?$@$@ cN|jdkot|jt S)z (bool) Is autoregressive lag polynomial consecutive. I.e. does it include all lags up to and including the maximum lag. r)r:r/r'r0r\s rnis_ar_consecutivez&SARIMAXSpecification.is_ar_consecutive+*a/4t}d333 5rpcN|jdkot|jt S)z (bool) Is moving average lag polynomial consecutive. I.e. does it include all lags up to and including the maximum lag. r)r;r/r)r0rrs rnis_ma_consecutivez&SARIMAXSpecification.is_ma_consecutivertrpc.|jdkp |jdkS)zq (bool) Is the model integrated. I.e. does it have a nonzero `diff` or `seasonal_diff`. r)r(r,rrs rn is_integratedz"SARIMAXSpecification.is_integratedsy1}6 2Q 66rpc|jdkS)z3(bool) Does the model include a seasonal component.r)r.rrs rn is_seasonalz SARIMAXSpecification.is_seasonals$))rpc*t|jS)z?(int) Number of parameters associated with exogenous variables.)r$ exog_namesrrs rn k_exog_paramsz"SARIMAXSpecification.k_exog_paramss4?###rpc*t|jS)z9(int) Number of autoregressive (non-seasonal) parameters.)r$r1rrs rn k_ar_paramsz SARIMAXSpecification.k_ar_params4<   rpc*t|jS)z9(int) Number of moving average (non-seasonal) parameters.)r$r5rrs rn k_ma_paramsz SARIMAXSpecification.k_ma_paramsrrpc*t|jS)z3(int) Number of seasonal autoregressive parameters.)r$r6rrs rnk_seasonal_ar_paramsz)SARIMAXSpecification.k_seasonal_ar_params4()))rpc*t|jS)z3(int) Number of seasonal moving average parameters.)r$r7rrs rnk_seasonal_ma_paramsz)SARIMAXSpecification.k_seasonal_ma_paramsrrpcl|j|jz|jz|jz|jz}|js|dz }|S)z'(int) Total number of model parameters.r)r}rrrrr!)r\k_paramss rnrzSARIMAXSpecification.k_paramssL&)99Dz1SARIMAXSpecification.ar_names..3331 333rp)r1rrs rnar_nameszSARIMAXSpecification.ar_names43dl3333rpc$d|jDS)z@(list of str) Names of (non-seasonal) moving average parameters.cg|]}d|zS)zma.L%drrs rnrz1SARIMAXSpecification.ma_names..rrp)r5rrs rnma_nameszSARIMAXSpecification.ma_namesrrpc8|jfd|jDS)z:(list of str) Names of seasonal autoregressive parameters.c g|] }d|zz S)zar.S.L%drrrss rnrz:SARIMAXSpecification.seasonal_ar_names..$"DDD a!e$DDDrp)r.r6r\rs @rnseasonal_ar_namesz&SARIMAXSpecification.seasonal_ar_names *  !DDDDd.CDDDDrpc8|jfd|jDS)z:(list of str) Names of seasonal moving average parameters.c g|] }d|zz S)zma.S.L%drrs rnrz:SARIMAXSpecification.seasonal_ma_names..*rrp)r.r7rs @rnseasonal_ma_namesz&SARIMAXSpecification.seasonal_ma_names&rrpc|j|jz|jz|jz|jz}|js|d|S)z,(list of str) Names of all model parameters.sigma2)r|rrrrr!append)r\namess rn param_namesz SARIMAXSpecification.param_names,sR4=04=@'(*.*@A% # LL " " " rpc"hd}|jdk}|jdk}|jdk}|jr|dg|jr |jdks|jr"|jdkr|ddg|s |jr|r|d|s |j r|r*|d|d|r|d|jd us|j r|d|S) a (list of str) Estimators that could be used with specification. Note: does not consider the presense of `exog` in determining valid estimators. If there are exogenous variables, then feasible Generalized Least Squares should be used through the `gls` estimator, and the `valid_estimators` are the estimators that could be passed as the `arma_estimator` argument to `gls`. >burg statespace innovations yule_walkerhannan_rissaneninnovations_mlerrrrrrrF) r8r9r.r[intersection_updaterr rvdiscardrsr!)r\ estimatorshas_arhas_ma has_seasonals rnvalid_estimatorsz%SARIMAXSpecification.valid_estimators5sqJJJ "a'"a',1    ;  * *L> : : : & N4+>> spec = SARIMAXSpecification(order=(1, 0, 2)) >>> spec.validate_estimator('yule_walker') ValueError: Yule-Walker estimator does not support moving average components. >>> spec.validate_estimator('burg') ValueError: Burg estimator does not support moving average components. >>> spec.validate_estimator('innovations') ValueError: Burg estimator does not support autoregressive components. >>> spec.validate_estimator('hannan_rissanen') # returns None >>> spec.validate_estimator('innovations_mle') # returns None >>> spec.validate_estimator('statespace') # returns None >>> spec.validate_estimator('not_an_estimator') ValueError: "not_an_estimator" is not a valid estimator. rz Yule-WalkerBurg InnovationszHannan-RissanenzInnovations MLEz State space)rrrrrrrz8%s estimator does not support missing values in `endog`.)rrzG%s estimator cannot enforce a stationary autoregressive lag polynomial.zH%s estimator cannot enforce an invertible moving average lag polynomial.)rrz2%s estimator does not support seasonal components.zB%s estimator does not support non-consecutive autoregressive lags.z8%s estimator does not support moving average components.rz;Innovations estimator does not support seasonal components.zKInnovations estimator does not support non-consecutive moving average lags.zAInnovations estimator does not support autoregressive components.rz?Hannan-Rissanen estimator does not support seasonal components.rFzInnovations MLE estimator does not support non-stationary autoregressive components, but `enforce_stationarity` is set to FalsezeInnovations MLE estimator does not support concentrating the scale out of the log-likelihood functionz"%s" is not a valid estimator.N) r8r9r.r[r#rr rsrvr!)r\ estimatorrrr has_missingtitless rnvalidate_estimatorz'SARIMAXSpecification.validate_estimatorbs d"a'"a',1 ' )(00'     $ $ L "79? 9J"KLLL = = = 1$$)B$ "C#))#4"5666 1$$)C$ "C#))#4"5666 / / / E "0282C"DEEE) 6 "I#))#4"5666 E "0282C"DEEE E E- ' ' : "9:::) J "IJJJ @ "?@@@ @ @+ + + : "9::: : :+ + +(E11 "OPPP% = "<=== = =, & & D= IJJ JrpFc t||j|d}|j|j|j|j|jg}gd}|js*|d|dtj |}tt|tj ||}d|vr|d|d<|S)a, Split parameter array by type into dictionary. Parameters ---------- params : array_like Array of model parameters. allow_infnan : bool, optional Whether or not to allow `params` to contain -np.inf, np.inf, and np.nan. Default is False. Returns ------- split_params : dict Dictionary with keys 'exog_params', 'ar_params', 'ma_params', 'seasonal_ar_params', 'seasonal_ma_params', and (unless `concentrate_scale=True`) 'sigma2'. Values are the parameters associated with the key, based on the `params` argument. Examples -------- >>> spec = SARIMAXSpecification(ar_order=1) >>> spec.split_params([0.5, 4]) {'exog_params': array([], dtype=float64), 'ar_params': array([0.5]), 'ma_params': array([], dtype=float64), 'seasonal_ar_params': array([], dtype=float64), 'seasonal_ma_params': array([], dtype=float64), 'sigma2': 4.0} zjoint parameters) allow_infnantitle) exog_params ar_params ma_paramsseasonal_ar_paramsseasonal_ma_paramsrr)r rr}rrrrr!rr2cumsumdictzipsplititem)r\paramsrixrouts rn split_paramsz!SARIMAXSpecification.split_paramss>  -9&8::: $"2D4D')BD===% # IIaLLL LL " " " Yr]]3ubhvr223344 s??M..00CM rpc d|j|fd|j|fd|j|fd|j|fd|j|fdt |j |fg}g}|D]\} } } | dkru| td | ztj tj | } | j | fkstd | | | j fz| | tj |S) a Join parameters into a single vector. Parameters ---------- exog_params : array_like, optional Parameters associated with exogenous regressors. Required if `exog` is part of specification. ar_params : array_like, optional Parameters associated with (non-seasonal) autoregressive component. Required if this component is part of the specification. ma_params : array_like, optional Parameters associated with (non-seasonal) moving average component. Required if this component is part of the specification. seasonal_ar_params : array_like, optional Parameters associated with seasonal autoregressive component. Required if this component is part of the specification. seasonal_ma_params : array_like, optional Parameters associated with seasonal moving average component. Required if this component is part of the specification. sigma2 : array_like, optional Innovation variance parameter. Required unless `concentrated_scale=True`. Returns ------- params : ndarray Array of parameters. Examples -------- >>> spec = SARIMAXSpecification(ar_order=1) >>> spec.join_params(ar_params=0.5, sigma2=4) array([0.5, 4. ]) zexogenous variableszAR termszMA termszseasonal AR termszseasonal MA termsvariancerNz;Specification includes %s, but no parameters were provided.zISpecification included %d %s, but parameters with shape %s were provided.)r}rrrrr%r!r#r2 atleast_1dsqueezerXr concatenate) r\rrrrrr definitions params_listrkrs rn join_paramsz SARIMAXSpecification.join_paramss7N#D$6 D )9 5 )9 5 $";" $ $";" $ !7788& AC  + + + E1f1uu>$&BDI&JKKKrz&'9'9::|t++$&P()5&,'?&@AAA ""6***~k***rpc||}|jr|jr9tjd|d f}t |st d|jr9tjd|d f}t |st d|jr~|j r8tjd|df}t |st d|j r8tjd|df}t |st d |j s|d d krt d d Sd S)a Validate parameter vector by raising ValueError on invalid values. Parameters ---------- params : array_like Array of model parameters. Notes ----- Primarily checks that the parameters have the right shape and are not NaN or infinite. Also checks if parameters are consistent with a stationary process if `enforce_stationarity=True` and that they are consistent with an invertible process if `enforce_invertibility=True`. Finally, checks that the variance term is positive, unless `concentrate_scale=True`. Examples -------- >>> spec = SARIMAXSpecification(ar_order=1) >>> spec.validate_params([-0.5, 4.]) # returns None >>> spec.validate_params([-0.5, -2]) ValueError: Non-positive variance term. >>> spec.validate_params([-1.5, 4.]) ValueError: Non-stationary autoregressive polynomial. rrz)Non-stationary autoregressive polynomial.rz2Non-stationary seasonal autoregressive polynomial.rz)Non-invertible moving average polynomial.rz2Non-invertible seasonal moving average polynomial.rrzNon-positive variance term.N) rrrr2r_rr#rr rrr!)r\rar_polyseasonal_ar_polyma_polyseasonal_ma_polys rnvalidate_paramsz$SARIMAXSpecification.validate_paramsQs8""6**  $ 5 5%F;$7#7 78$W--5$&4555( 5#%5V4H-I,I)I#J $%5665$&4555  % 5 5%6+#6 67$W--5$&4555( 5#%5F3G,H)H#I $%5665$&4555% @h1$$ !>??? @ @$$rpc,||}i}|jr |d|d<|jr+|jrt |d|d<n |d|d<|jr,|jrt |d |d<n |d|d<|jr+|jrt |d|d<n |d|d<|jr,|jrt |d |d<n |d|d<|j s|ddz|d<|j di|S) a] Constrain parameter values to be valid through transformations. Parameters ---------- unconstrained : array_like Array of model unconstrained parameters. Returns ------- constrained : ndarray Array of model parameters transformed to produce a valid model. Notes ----- This is usually only used when performing numerical minimization of the log-likelihood function. This function is necessary because the minimizers consider values over the entire real space, while SARIMAX models require parameters in subspaces (for example positive variances). Examples -------- >>> spec = SARIMAXSpecification(ar_order=1) >>> spec.constrain_params([10, -2]) array([-0.99504, 4. ]) rrrrrrrr) rr}rr constrainrr rrr!r)r\ unconstrainedrs rnconstrain_paramsz%SARIMAXSpecification.constrain_paramss8))-88    A$1-$@F= !   A( A&/ k0J&K&K{##&3K&@{#   A) A'0{1K'L'L&L{##&3K&@{#  $ 9( 9m,@ABB+,,""67+,  $ 9) 9}-ABCCC+,,""67+,% :,X69F8 t))&)))rpc,||}i}|jr |d|d<|jr+|jrt |d|d<n |d|d<|jr,|jrt |d |d<n |d|d<|jr+|jrt |d|d<n |d|d<|jr,|jrt |d |d<n |d|d<|j s|ddz|d<|j di|S) a Reverse transformations used to constrain parameter values to be valid. Parameters ---------- constrained : array_like Array of model parameters. Returns ------- unconstrained : ndarray Array of parameters with constraining transformions reversed. Notes ----- This is usually only used when performing numerical minimization of the log-likelihood function. This function is the (approximate) inverse of `constrain_params`. Examples -------- >>> spec = SARIMAXSpecification(ar_order=1) >>> spec.unconstrain_params([-0.5, 4.]) array([0.57735, 2. ]) rrrrrrg?r) rr}rr unconstrainrr rrr!r)r\ constrainedrs rnunconstrain_paramsz'SARIMAXSpecification.unconstrain_paramss4'' 44    ?$/ $>F= !   ?( ?&1+k2J&K&K{##&1+&>{#   ?) ?&1;{3K2K&L&L{##&1+&>{#  $ 7( 7 ,@ ABB+,, 45+,  $ 7) 7-A!B BCC+,, 45+,% :*84c9F8 t))&)))rpc|jd}n;t|jtt j|j||}|S)N)rIr rBr%r2sum)r\rloffsetrms rnrOz)SARIMAXSpecification.construct_trend_datasJ   #JJ+RVDO%<%rs 333333:::::::::::::::::::::: NMMMMMMMXBXBXBXBXBXBXBXBXBXBrp