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Missing keys: c,g|]}t|SrNrwrss rHr\z!_format_order..s666c!ff666rJ) stacklevelc0i|]}|tSrNrWrZrtrOs rHruz!_format_order..s!222aU222rJc0i|]}|tSrN)listr{s rHruz!_format_order..s!333ae333rJc,g|]}t|SrNrWrZlags rHr\z!_format_order..s:::SC:::rJ)r^pd DataFramer"r}rangeshapecolumnsrrd differencekeysjoinsortedrawarningswarnrrf _INT_TYPESrX) rgrOrQr exog_ordermissingextramsgkey final_ordervalues ` rH _format_orderrs  |** dBL ) )-$Qq999E$*Q-(()),,t|,,, },,t,,, E7 # #4 d))&&uzz||44EJJLL!!,,T22  "=  ? "C 499T&)@)@%)@)@)@"A"ABBCCcI ICS// !  C.  49966g66677#= =C M#3 B B B B 2 2C C& 1 1 1 1 2 E: & &4UF###2222T222 UF###3333d333 -/K;;3 =    eS ! ! ;#E#f++uqy$A$ABBK  ::E:::K   rJc ^eZdZdZ dRdddddddddSfdZedTd!ZedUd"ZedVd$ZedWd&Z edXd(Z dYd)Z e dZd,Z d[d-Z d\d]d6Zd.dd/d7d^d9Zd_d;Zd<Zd`dDZ dadbdIZe dcdddddddKdddQZxZS)er0a Autoregressive Distributed Lag (ARDL) Model Parameters ---------- endog : array_like A 1-d endogenous response variable. The dependent variable. lags : {int, list[int]} The number of lags to include in the model if an integer or the list of lag indices to include. For example, [1, 4] will only include lags 1 and 4 while lags=4 will include lags 1, 2, 3, and 4. exog : array_like Exogenous variables to include in the model. Either a DataFrame or an 2-d array-like structure that can be converted to a NumPy array. order : {int, sequence[int], dict} If int, uses lags 0, 1, ..., order for all exog variables. If sequence[int], uses the ``order`` for all variables. If a dict, applies the lags series by series. If ``exog`` is anything other than a DataFrame, the keys are the column index of exog (e.g., 0, 1, ...). If a DataFrame, keys are column names. fixed : array_like Additional fixed regressors that are not lagged. causal : bool, optional Whether to include lag 0 of exog variables. If True, only includes lags 1, 2, ... trend : {'n', 'c', 't', 'ct'}, optional The trend to include in the model: * 'n' - No trend. * 'c' - Constant only. * 't' - Time trend only. * 'ct' - Constant and time trend. The default is 'c'. seasonal : bool, optional Flag indicating whether to include seasonal dummies in the model. If seasonal is True and trend includes 'c', then the first period is excluded from the seasonal terms. deterministic : DeterministicProcess, optional A deterministic process. If provided, trend and seasonal are ignored. A warning is raised if trend is not "n" and seasonal is not False. hold_back : {None, int}, optional Initial observations to exclude from the estimation sample. If None, then hold_back is equal to the maximum lag in the model. Set to a non-zero value to produce comparable models with different lag length. For example, to compare the fit of a model with lags=3 and lags=1, set hold_back=3 which ensures that both models are estimated using observations 3,...,nobs. hold_back must be >= the maximum lag in the model. period : {None, int}, optional The period of the data. Only used if seasonal is True. This parameter can be omitted if using a pandas object for endog that contains a recognized frequency. missing : {"none", "drop", "raise"}, optional 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'. Notes ----- The full specification of an ARDL is .. math :: Y_t = \delta_0 + \delta_1 t + \delta_2 t^2 + \sum_{i=1}^{s-1} \gamma_i I_{[(\mod(t,s) + 1) = i]} + \sum_{j=1}^p \phi_j Y_{t-j} + \sum_{l=1}^k \sum_{m=0}^{o_l} \beta_{l,m} X_{l, t-m} + Z_t \lambda + \epsilon_t where :math:`\delta_\bullet` capture trends, :math:`\gamma_\bullet` capture seasonal shifts, s is the period of the seasonality, p is the lag length of the endogenous variable, k is the number of exogenous variables :math:`X_{l}`, :math:`o_l` is included the lag length of :math:`X_{l}`, :math:`Z_t` are ``r`` included fixed regressors and :math:`\epsilon_t` is a white noise shock. If ``causal`` is ``True``, then the 0-th lag of the exogenous variables is not included and the sum starts at ``m=1``. See the notebook `Autoregressive Distributed Lag Models <../examples/notebooks/generated/autoregressive_distributed_lag.html>`__ for an overview. See Also -------- statsmodels.tsa.ar_model.AutoReg Autoregressive model estimation with optional exogenous regressors statsmodels.tsa.ardl.UECM Unconstrained Error Correction Model estimation statsmodels.tsa.statespace.sarimax.SARIMAX Seasonal ARIMA model estimation with optional exogenous regressors statsmodels.tsa.arima.model.ARIMA ARIMA model estimation Examples -------- >>> from statsmodels.tsa.api import ARDL >>> from statsmodels.datasets import danish_data >>> data = danish_data.load_pandas().data >>> lrm = data.lrm >>> exog = data[["lry", "ibo", "ide"]] A basic model where all variables have 3 lags included >>> ARDL(data.lrm, 3, data[["lry", "ibo", "ide"]], 3) A dictionary can be used to pass custom lag orders >>> ARDL(data.lrm, [1, 3], exog, {"lry": 1, "ibo": 3, "ide": 2}) Setting causal removes the 0-th lag from the exogenous variables >>> exog_lags = {"lry": 1, "ibo": 3, "ide": 2} >>> ARDL(data.lrm, [1, 3], exog, exog_lags, causal=True) A dictionary can also be used to pass specific lags to include. Sequences hold the specific lags to include, while integers are expanded to include [0, 1, ..., lag]. If causal is False, then the 0-th lag is excluded. >>> ARDL(lrm, [1, 3], exog, {"lry": [0, 1], "ibo": [0, 1, 3], "ide": 2}) When using NumPy arrays, the dictionary keys are the column index. >>> import numpy as np >>> lrma = np.asarray(lrm) >>> exoga = np.asarray(exog) >>> ARDL(lrma, 3, exoga, {0: [0, 1], 1: [0, 1, 3], 2: 2}) NrcFnonefixedrQseasonal deterministic hold_backperiodrendog)Sequence[float] | pd.Series | ArrayLike2DlagsrPrgArrayLike2D | NonerOrhtrendLiteral['n', 'c', 'ct', 'ctt']rrQrRrrDeterministicProcess | Noner int | Nonerr Literal['none', 'drop', 'raise']rSNonec tjd|_tjd|_t |||||| | | | d t |dd|_||j_ |t|dd d } | j d |jj j d ks&tj tj| std t!|t"jrt'|j|_n)d t-| j dD|_| |_n7tj|jj j d d f|_g|_i|_i|_|||_|| \|_|_|\|_|_|jx|j_ |j_!|j|j_"d|_|jr;d|j#D}tI|d k|_tJ|_&tN|_(dS)NrrrF)rrrgrrrr old_namesrQT)strictrrkrlrzfixed must be an (nobs, m) array where nobs matches the number of observations in the endog variable, and allvalues must be finitecg|]}d|S)zz.rNrZis rHr\z!ARDL.__init__..ms+%%%!"HHH%%%rJr]c,g|]}t|SrNre)rZvals rHr\z!ARDL.__init__..sAAASCAAArJ))r_empty_x_ysuper__init__r#_causaldata orig_fixedr"rrallisfiniterar^rrr}r _fixed_namesr_fixed_blocks_namesrf_order_construct_regressors_construct_variable_names _endog_name _exog_names param_namesxnamesynamesvaluesrer1_results_classARDLResultsWrapper_results_wrapper)rGrrrgrOrrrQrrrrr fixed_arrmin_lagsrDs rHrz ARDL.__init__>sd (6""(4..   '  !$??? $   "5'!DDDIq!TY_%:1%===RV I&&FF=!, %.. $($7$7!!%%&+IOA,>&?&?%%%!$DKK(DIO$9!$,>,@,@AAAHx==1,DL) 2rJNDArray | pd.DataFrame | Nonec|jjS)z*The fixed data used to construct the model)rrrFs rHrz ARDL.fixedsy##rJc|jS)z'Flag indicating that the ARDL is causal)rrFs rHrQz ARDL.causals |rJlist[int] | Nonec"|jsdn|jS)z-The autoregressive lags included in the modelN)_lagsrFs rHar_lagsz ARDL.ar_lagss :5tt4:5rJric|jS)z5The lags of exogenous variables included in the model)rrFs rHdl_lagsz ARDL.dl_lagss {rJtuple[int, ...]c|jsdn tt|j}|g}|jD]3}|/|tt|4t |S)zThe order of the ARDL(p,q)r)rrXmaxrrappendtuple)rGar_order ardl_orderrs rHrzARDL.ardl_orders}!J@11CDJ,@,@Z K&&(( 2 2D!!#c$ii..111Z   rJcltj|jjd|jz df|_dS)z)Place holder to let AutoReg init completerN)r_rrr _hold_backrrFs rH_setup_regressorszARDL._setup_regressorss-(DJ,Q/$/A1EFFrJrdict[Hashable, np.ndarray]c|siSd}|D]!}|tt||}"t|tjst |ddd}i}|D]z}|| t|t jr$t|tsJ|dd|f}n||}t||d}||}|dd|f||<{|S)z6Transform exogenous variables and orders to regressorsrNrgrkrlinoriginal) rrr^rrr"r_ndarrayrXr/) rgrO max_orderr exog_lagsrrp lagged_colrs rH _format_exogzARDL._format_exogs  I <<>> 5 5CC)44 $ -- >dF1===D  1 1CSz!$ ++ !#s+++++111c6l3iY>>>J:D'40IcNNrJcBt|jj||jS)z(Validate and standardize the model order)rr orig_exogr)rGrOs rHrfzARDL._check_ordersTY0%FFFrJ nonrobustTcov_typer=cov_kwdsdict[str, Any]use_t)tuple[np.ndarray, np.ndarray, np.ndarray]c|jjddkr;tjdtjdtjdfSt |j|j}||||}|}|j}|dkr3|s1|jjd}|jjd}|||z z } || z}|j ||j fS)Nr]rrrrrrr) rrr_rrrfit cov_paramsrparamsnormalized_cov_params) rGrrrols_modols_resrnobsrtscales rH_fitz ARDL._fits 7= q 8D>>28F#3#3RXf5E5EE Edgtw''++  ''))   { " "5 "7=#D a AD1H%E % J~z7+HHHrJrr1c||||\}}}t|||||}t|S)aQ Estimate the model parameters. Parameters ---------- cov_type : str The covariance estimator to use. The most common choices are listed below. Supports all covariance estimators that are available in ``OLS.fit``. * 'nonrobust' - The class OLS covariance estimator that assumes homoskedasticity. * 'HC0', 'HC1', 'HC2', 'HC3' - Variants of White's (or Eiker-Huber-White) covariance estimator. `HC0` is the standard implementation. The other make corrections to improve the finite sample performance of the heteroskedasticity robust covariance estimator. * 'HAC' - Heteroskedasticity-autocorrelation robust covariance estimation. Supports cov_kwds. - `maxlags` integer (required) : number of lags to use. - `kernel` callable or str (optional) : kernel currently available kernels are ['bartlett', 'uniform'], default is Bartlett. - `use_correction` bool (optional) : If true, use small sample correction. cov_kwds : dict, optional A dictionary of keyword arguments to pass to the covariance estimator. `nonrobust` and `HC#` do not support cov_kwds. use_t : bool, optional A flag indicating that inference should use the Student's t distribution that accounts for model degree of freedom. If False, uses the normal distribution. If None, defers the choice to the cov_type. It also removes degree of freedom corrections from the covariance estimator when cov_type is 'nonrobust'. Returns ------- ARDLResults Estimation results. See Also -------- statsmodels.tsa.ar_model.AutoReg Ordinary Least Squares estimation. statsmodels.regression.linear_model.OLS Ordinary Least Squares estimation. statsmodels.regression.linear_model.RegressionResults See ``get_robustcov_results`` for a detailed list of available covariance estimators and options. Notes ----- Use ``OLS`` to estimate model parameters and to estimate parameter covariance. rr)rr1rrGrrrrrnorm_cov_paramsress rHrzARDL.fits\~/3ii/8/ / + O &*oU   "#&&&rJtuple[np.ndarray, np.ndarray]c:|jrt|jnd|_t|jj|jd\}}t |tjsJt |tjsJ||c|_ |_ |j j dt|jkr'd|jD}|j dd|f|_ |jj }|||j|_d}|jD]#}t||t|nd}$t|j||_|j|_|j |j|j|jd|_|j|j g}|d|jD|jgzz }tj|} |t1|j|_|j|jkrt5d | |jd} | j d| j dkr,t5d | j dd | j dd |jj|jd| fS) %Construct and format model regressorsrseprr]cg|]}|dz Sr]rNrs rHr\z.ARDL._construct_regressors..3s666Ca666rJNrrgrrcg|]}|SrNrN)rZexs rHr\z.ARDL._construct_regressors..Fs / / /Rb / / /rJDhold_back must be >= the maximum lag of the endog and exog variablesThe number of regressors () including deterministics, lags of the endog, lags of the exogenous, and fixed regressors is larger than the sample available for estimation ().)rr_maxlagr/rrr^r_r _endog_reg_endogrrcrrr_exogr_deterministics in_sample_deterministic_regrr column_stackrXrra) rGrrrlag_locsr exog_maxlagrxregs rHrzARDL._construct_regressors&s +/*;s4:! # IOT\E    F&"*-----*bj11111'16$ ?  #s4: 6 6664:666H"oaaak:DOI' &&y$+>>  ;%%'' O OCks3s888ANNKK4<55 "&"6"@"@"B"B_J!4[     $do 6 / /4:,,.. / / /4;- ??oa    !$,//DO ?T\ ) ) $/##$ 9Q<#)A, & &4SYq\44$'9Q<444  yt001366rJc|jjfd|jD}|jj}i}|jD]O}t |t jrd|nt||j|}fd|D||<P|||j j |j d|_ t|j j }||z }|D] }|||z }||j z }|fS)Construct model variables namescg|] }d| Sz.LrN)rZry_names rHr\z2ARDL._construct_variable_names..\s'@@@f++++@@@rJrcg|] }d| Sr rN)rZrbases rHr\z2ARDL._construct_variable_names..fs'@@@C$//#//@@@rJr )rrrrrr^r_rr=rrrrr}) rGendog_lag_namesrg exog_namesrrx_namesr#r!s @@rHrzARDL._construct_variable_namesYs!@@@@TZ@@@y" ; A AC$ ++  3yy3xx;s#D@@@@4@@@JsOO%!4<&    t.677?" ' 'C z# &GG4$$wrJstartrXendnum_oosexog_oos fixed_oos np.ndarraycdd}||jkrdn |j|z } |dz|jjdkr@|>|.pad_xsBaxx A9bgsAh77;<< .s"A"A"As37"A"A"ArJrc6g|]}tj|SrN)r_asarray)rZarrs rHr\z'ARDL._forecasting_x..s ???#bjoo???rJ)rr,r.rXrSr,) rrrrrrrgr_r:r1rrr out_of_samplerconcathstackr2r3rr/rrr^rrrrrextendrr)rGr'r(r)rgr*rr+r4r.adjusted_startdetoos_detrr endog_regrs rH_forecasting_xzARDL._forecasting_xus = = = = DO++aa51H !Gtz'* * *t|  !8!<&>?@@E E : Duc$*ooEEEI HHYqqq"A"Adj"A"A"AAB C C C ?122  A$)-r|<< O|D$)2E2MNNN$$T4;77D HH????? @ @ @ ;q>A   HHUOOO _Q   " T_ %&&zrJrr-int | str | dt.datetime | pd.Timestamp | Nonedynamicc `|||||\}}}}}} fd} jjjd|| |djjd}|| |djjd}|| |djd}|%| t j|d jd}jjd sjsd} nnj s t j ntj } j r@td j D} t| | } | | krj r|td j r-|jd| z| krtd | | z d| djjd r|tdjjd r'|jd| krtd| d| dj~||| rzt j| jjd ft j}t%jjt&jr%t'j|jjj}||| ||||} |dur |d z|z }n;||}|}|jkrt3|j|z }t j| jdt j}| d||z|d|<jjd }t7||jdD]X}t9j D]3\}}||z }||kr ||}nj||z}|| |||zf<4| ||z||<Y|||d z| zdS) In-sample prediction and out-of-sample forecasting. Parameters ---------- params : array_like The fitted model 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. Unlike standard python slices, end is inclusive so that all the predictions [start, start+1, ..., end-1, end] are returned. dynamic : {bool, int, str, datetime, Timestamp}, optional Integer offset relative to `start` at which to begin dynamic prediction. 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. Datetime-like objects are not interpreted as offsets. They are instead used to find the index location of `dynamic` which is then used to to compute the offset. exog : array_like A replacement exogenous array. Must have the same shape as the exogenous data array used when the model was created. exog_oos : array_like An array containing out-of-sample values of the exogenous variables. Must have the same number of columns as the exog used when the model was created, and at least as many rows as the number of out-of-sample forecasts. fixed : array_like A replacement fixed array. Must have the same shape as the fixed data array used when the model was created. fixed_oos : array_like An array containing out-of-sample values of the fixed variables. Must have the same number of columns as the fixed used when the model was created, and at least as many rows as the number of out-of-sample forecasts. Returns ------- predictions : {ndarray, Series} Array of out of in-sample predictions and / or out-of-sample forecasts. c:t|tjrst|tjst|dt |jt jjjkrt|dnt||dd}|j dks|j d|j dkrt|d|j d|r1|j d|j dkrt|d d |S) Nz; must be a DataFrame when the original exog was a DataFramez0 must have the same columns as the original exogrkF)rmoptionalr]z< must have the same number of columns as the original data, rz9 must have the same number of rows as the original data (r) r^rrrbrrrrrar"rmr)r;nameorigexactnrGs rH check_exogz ARDL.predict..check_exogsd$ -- D!#r|44#***#+&&&1D1L*M*MMM$N !dUCCCx1}} !  1 = = 66&*jm66 1A66 ,,&',,,JrJrNrgTr*Frr+r]c,g|]}t|SrNrrYs rHr\z ARDL.predict..sEEE1AEEErJzoexog_oos must be provided when out-of-sample observations require values of the exog not in the original samplezexog_oos must have at least z observations to produce z, forecasts based on the model specification.zEfixed_oos must be provided when predicting out-of-sample observationszfixed_oos must have at least z forecasts.r8)_prepare_predictionrrrrrr_r:rrinfrerrrargr2r3r^rrrrD_parse_dynamicrrrr enumerate_wrap_prediction)rGrr'r(rFrgr*rr+r)rO max_1stepmin_exogr dynamic_start dynamic_stepfcastsoffsetrjrlocrrNs` @rHpredictz ARDL.predictsz|7;6N6N D(E37 7 3hsG      4 IO !! $  :dFDI,?FFD  !z*di&95H  Jugt{DAAE  "  9%%{DKI ; Q  5t| 5II&*jEc$*ooI{ 5EE 0B0B0D0DEEEFF 844 Y  { x/ &  (."3i"?7!J!J /7Y3F///6/// { #  (9 1"1% )/!*>L(Mt&& #M4?U3J K K RV,,!">M>!2V!;~ ~(.q1}fl1o66 & &A#DJ// ' '3#g-'' +CC*US[1C#&!VaZ-  !v F1II$$VUC!Gg4EqIIIrJrNrQrrrrrformularr:Literal['none', 'raise'] ARDL | UECMc|j} d} d|vr,|d\}} | } tj|dz|}|jj}| |_|jj}| |_| ^|dd}|d| d} tj| |}|jj}| |_nd}||||||||||| | |  S) aM Construct an ARDL from a formula Parameters ---------- formula : str Formula with form dependent ~ independent | fixed. See Examples below. data : DataFrame DataFrame containing the variables in the formula. lags : {int, list[int]} The number of lags to include in the model if an integer or the list of lag indices to include. For example, [1, 4] will only include lags 1 and 4 while lags=4 will include lags 1, 2, 3, and 4. order : {int, sequence[int], dict} If int, uses lags 0, 1, ..., order for all exog variables. If sequence[int], uses the ``order`` for all variables. If a dict, applies the lags series by series. If ``exog`` is anything other than a DataFrame, the keys are the column index of exog (e.g., 0, 1, ...). If a DataFrame, keys are column names. causal : bool, optional Whether to include lag 0 of exog variables. If True, only includes lags 1, 2, ... trend : {'n', 'c', 't', 'ct'}, optional The trend to include in the model: * 'n' - No trend. * 'c' - Constant only. * 't' - Time trend only. * 'ct' - Constant and time trend. The default is 'c'. seasonal : bool, optional Flag indicating whether to include seasonal dummies in the model. If seasonal is True and trend includes 'c', then the first period is excluded from the seasonal terms. deterministic : DeterministicProcess, optional A deterministic process. If provided, trend and seasonal are ignored. A warning is raised if trend is not "n" and seasonal is not False. hold_back : {None, int}, optional Initial observations to exclude from the estimation sample. If None, then hold_back is equal to the maximum lag in the model. Set to a non-zero value to produce comparable models with different lag length. For example, to compare the fit of a model with lags=3 and lags=1, set hold_back=3 which ensures that both models are estimated using observations 3,...,nobs. hold_back must be >= the maximum lag in the model. period : {None, int}, optional The period of the data. Only used if seasonal is True. This parameter can be omitted if using a pandas object for endog that contains a recognized frequency. missing : {"none", "drop", "raise"}, optional 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'. Returns ------- ARDL The ARDL model instance Examples -------- A simple ARDL using the Danish data >>> from statsmodels.datasets.danish_data import load >>> from statsmodels.tsa.api import ARDL >>> data = load().data >>> mod = ARDL.from_formula("lrm ~ ibo", data, 2, 2) Fixed regressors can be specified using a | >>> mod = ARDL.from_formula("lrm ~ ibo | ide", data, 2, 2) N|z -1~rz ~ z - 1)rrrQrrrrr)indexsplitstripr from_formularr orig_endog)clsr`rrrOrrQrrrrrrf fixed_formulamodrgr endog_namers rHrizARDL.from_formulaXsz  '>>%,]]3%7%7 "G])//11Mw55x! #  $ s++A.4466J)AAmAAAM"=$77C),);EEKKEs    '    rJNrr)rrrrPrgrrOrhrrrrrQrRrrRrrrrrrrrrSr)rSr)rSrR)rSrrSri)rSr)rSr)rgrrOrirSr)rOrhrSri)rNT)rr=rrrrRrSr)rr=rrrrRrSr1rrrSr)r'rXr(rXr)rXrgrr*rrrr+rrSr,NNFNNNN)rrr'rEr(rErFrRrgrr*rrrr+rrrrN)r`r=rr:rrPrOrhrrrQrRrrRrrrrrrrrarSrb)rErKrL__doc__rpropertyrrQrrrr staticmethodrrfrrrrrDr^ classmethodri __classcell__rDs@rHr0r0sBBP$(03 H3%)59 $!4:H3H3H3H3H3H3H3H3T$$$X$X666X6X!!!X!GGGG\4GGGG $#' IIIII2$#' E'E'E'E'E'E'N17171717f86666v@D=A.226/337iJiJiJiJiJV ,-03 { 59 $!,2{ { { { { [{ { { { { rJr0r'r(rFrgr*rr+ceZdZdZiZ d/d0fd Zeeej jd d1d2dZ d3d4d Z d5d!Z d1d6d"Z e e# d7d8d,Zd9d:d.ZxZS);r1a4 Class to hold results from fitting an ARDL model. Parameters ---------- model : ARDL Reference to the model that is fit. params : ndarray The fitted parameters from the AR Model. cov_params : ndarray The estimated covariance matrix of the model parameters. normalized_cov_params : ndarray The array inv(dot(x.T,x)) where x contains the regressors in the model. scale : float, optional An estimate of the scale of the model. use_t : bool Whether use_t was set in fit N?Fmodelr0rr,rrFloat64Array | Nonerr8rrRcdt|||||i|_||_|j|_|jjd|_|j |_ |j |_ d|_ |j rt|j |_ |jj|_||_dS)Nrr)rr_cache_paramsr_nobsrr _n_totobsdf_model _df_modelr_ar_lags_max_lagrr~rrcov_params_default)rGr~rrrrrrDs rHrzARDLResults.__init__s  60%u      Z *1-   = / ..DM*.",rJr'rEr(rFrgrr*rr+c P|j|j|||||||S)Nrz)r~r^r)rGr'r(rFrgr*rr+s rHr^zARDLResults.predict s=z!! L"   rJr]stepsrXrSnp.ndarray | pd.Seriesc|jjjjd}t |t t jfr ||zdz }n|}|||d||S)aZ Out-of-sample forecasts Parameters ---------- steps : {int, str, datetime}, default 1 If an integer, the number of steps to forecast from the end of the sample. Can also be a date string to parse or a datetime type. However, if the dates index does not have a fixed frequency, steps must be an integer. exog : array_like, optional Exogenous values to use out-of-sample. Must have same number of columns as original exog data and at least `steps` rows fixed : array_like, optional Fixed values to use out-of-sample. Must have same number of columns as original fixed data and at least `steps` rows Returns ------- array_like Array of out of in-sample predictions and / or out-of-sample forecasts. See Also -------- ARDLResults.predict In- and out-of-sample predictions ARDLResults.get_prediction In- and out-of-sample predictions and confidence intervals rr]F)r'r(rFr*r+) r~rrjrr^rXr_r`r^)rGrrgrr'r(s rHforecastzARDLResults.forecast"smH *03 ec2:. / / %-!#CCC||S%$%   rJc|j|jng}t|}tj|jdz}d|d<|jjjd}|j|||z}t|D]\}}|| ||<|S)6Returns poly repr of an AR, (1 -phi1 L -phi2 L^2-...)Nr]r) rrcr_zerosrr~rrrrT)rGrk_ar ar_paramsr[rrrs rH _lag_reprzARDLResults._lag_reprOs#'=#<$--"7||HT]Q.//  ! .4Q7fv}45(( ( (FAs$QiZIcNNrJc z||||||||}tj||j} tj| tj|<|dn|}||jjdn|}|j||\} } } } | dkr]| } t| tj d| } |jtj | dzz| | d<t|tjrtj| |j } t#|| S) a! Predictions and prediction intervals 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. Unlike standard python slices, end is inclusive so that all the predictions [start, start+1, ..., end-1, end] are returned. dynamic : {bool, int, str, datetime, Timestamp}, optional Integer offset relative to `start` at which to begin dynamic prediction. 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. Datetime-like objects are not interpreted as offsets. They are instead used to find the index location of `dynamic` which is then used to to compute the offset. exog : array_like A replacement exogenous array. Must have the same shape as the exogenous data array used when the model was created. exog_oos : array_like An array containing out-of-sample values of the exogenous variable. Must has the same number of columns as the exog used when the model was created, and at least as many rows as the number of out-of-sample forecasts. fixed : array_like A replacement fixed array. Must have the same shape as the fixed data array used when the model was created. fixed_oos : array_like An array containing out-of-sample values of the fixed variables. Must have the same number of columns as the fixed used when the model was created, and at least as many rows as the number of out-of-sample forecasts. Returns ------- PredictionResults Prediction results with mean and prediction intervals rz) fill_valueNrr])rrkrf)r^r_ full_likesigma2r3isnanr~_index_get_prediction_indexrr+onescumsumr^rSeriesrfr-)rGr'r(rFrgr*rr+meanmean_var_oosrmas rHget_predictionzARDLResults.get_prediction[s4t||  <===#%6$ ]'*{dj##z77sCC 1c1 77((IBGAJJS999B"kBIb!e,<,<&?&?"@"@AF $-DJ4I0J0JJ :  %u$Etz-.. z * w   !    $ &)  !3s4:+;'<'<#=#="> ? 48 34 5 "X S0@%@$A B X() * X() * h*+ ,  yy  %     d%u=== rJ)Nr}F) r~r0rr,rr,rrrr8rrRrr)r'rEr(rErFrRrgrr*rrrr+r)r]NN)rrXrgrrrrSr)rSr,)r'rEr(rErFrRrgrr*rrrr+rrSr) NNFNNNNrTNN)r'rEr(rErFrRrgrr*rrrr+rrr8rrRrrrrrSrrrr8rSr)rErKrLrtrrrrr0r^rrrr_predict_paramsrrrxrys@rHr1r1s(F6:-------0X 4h??@@@D=A.226/337    A@ ..2/3 + + + + + Z    @D=A.226/337O1O1O1O1O1b\111@D=A.226/337(,*.1 1 1 1 211 f=========rJr1ceZdZiZejejjeZiZ ejejj e Z dS)rN rErKrL_attrswrap union_dictsr,TimeSeriesResultsWrapper _wrap_attrs_methods _wrap_methodsrNrJrHrr X F"$"*6KH$D$*8(MMMrJrc:eZdZdZfdZeddZxZS)r3zr Results from an ARDL order selection Contains the information criteria for all fitted model orders. c4d}t|||||dtjfd|Dt |_dx|jj_|j_|j |_tjfd|Dt |_ dx|j j_|j _|j |_ tjfd|Dt |_ d x|j j_|j _|j |_ dS) N))r)rrrc@|dt|ddfSr0)dict)ds rH_to_dictz4ARDLOrderSelectionResults.__init__.._to_dict9sQ4ae$ $rJc:i|]\}}|d|SrrNrZrtr[rs rHruz6ARDLOrderSelectionResults.__init__..=+ 7 7 741aQqT88A;; 7 7 7rJdtyperc:i|]\}}|d|Sr rNrs rHruz6ARDLOrderSelectionResults.__init__..CrrJrc:i|]\}}|d|S)rkrNrs rHruz6ARDLOrderSelectionResults.__init__..IrrJr) rrrritemsobject_aicrfrK sort_index_bic_hqic) rGr~icsrrr_icsrrDs @rHrz"ARDLOrderSelectionResults.__init__5sn# eXv>>> % % %I 7 7 7 7399;; 7 7 7v    165 ty~I((** I 7 7 7 7399;; 7 7 7v    165 ty~I((** Y 7 7 7 7399;; 7 7 7v    398  Z**,, rJrSric|jjS)z5The lags of exogenous variables in the selected model)_modelrrFs rHrz!ARDLOrderSelectionResults.dl_lagsNs{""rJrp)rErKrLrtrrurrxrys@rHr3r3.sb -----2###X#####rJr3rFrr) rrQicglobrrrrrrArrayLike1D | ArrayLike2DmaxlagrXmaxorderint | dict[Hashable, int]rrrrrLiteral['aic', 'bic']rrrrrrrrrac H,-t| dd}d}t|||||||| | | | |  }|j} |j}t j|d|dg}|| d}g}g}||d | d|tt|d j d d zg}|d D]}|d || d}|||tt|j d d z|||j }|j d r_tj |}tt|D]}||}||||zzz ||<||||zzz }d }|j d }i}|r|j|jng}d |D} |jD]\-}!| -fd|!Dz } t jd|D}tt|j d }"t|j d D];}t#|"|D](}#|| |#}$|||dd|#f|||$<)= the maximum lag in the model. period : {None, int}, optional The period of the data. Only used if seasonal is True. This parameter can be omitted if using a pandas object for endog that contains a recognized frequency. missing : {"none", "drop", "raise"}, optional Available options are 'none', 'drop', and 'raise'. If 'none', no NaN checking is done. If 'drop', any observations with NaNs are dropped. If 'raise', an error is raised. Default is 'none'. Returns ------- ARDLSelectionResults A results holder containing the selected model and the complete set of information criteria for all models fit. rT)rJc|jdr/||tj||ddzz }n|}|jd}d|z t |z}| tjdtjz|zdzzdz }t|||jdz||}ttj |}ttj |} ttj |} || | fS)Nr])rcondrr}rk)rrrr) rr_linalglstsqr)logpir rr1rrr) yrdfresidrrrrrrrs rH compute_icsz&ardl_select_order..compute_icss 71: BIOOAqO==a@@@EEE{1~tgenn,erva"%i&011A56:QWQZC   {44{44 0#66C~rJrrrNrr]rgc|dkr:d|D}dtd|DzStt}g}|D]U}||}|d||d.||d|dVt |}|r|dgkrd}nt|}|D]}|d|vr|d d||d< |D]"}||t||||<#|ftd|DzS)NrNci|] \}}||d S)NrrN)rZrtrs rHruz.perm_to_tuple..s888$!Q!-A---rJrc3$K|] \}}||fV dSrrrNrZrtr[s rH z;ardl_select_order..perm_to_tuple..s*==41aA======rJrr]c3$K|] \}}||fV dSrrrNrs rHrz;ardl_select_order..perm_to_tuple..s* > >DAq!Q > > > > > >rJ)rrrr}rr)rpermry_lagsr[rs rH perm_to_tuplez(ardl_select_order..perm_to_tuplesr 2::88$888A%==17799====== =    ) )Aq'C1v~ c!f%%%%#a&   Q(((( GG #A3FF6]]F ! !C1vQ3q6#5 #a&  ' 'Cv!qv#y5 > >AGGII > > >>>>>rJcg|]}d|fSrrrNrs rHr\z%ardl_select_order..s+++aq +++rJcg|]}|fSrNrN)rZrrts rHr\z%ardl_select_order..s'''aV'''rJcg|]}|SrNrN)rZas rHr\z%ardl_select_order..s///1Q///rJc>g|]\}}|ddd|fSrrrN)rZrr ios rHr\z%ardl_select_order.. s1 M M M41a111g1g: M M MrJrrk)rrrci|]\}}|| SrNrNrs rHruz%ardl_select_order..s66641a!Q666rJ)r%r0rrr_rrr}rrrrpinvrcrrrrr rTrrRr3).rrrgrrrrQrrrrrrrorig_hold_backrr#blocksalwaysselect iter_orders var_namesvarblockr pinv_alwaysrrr always_dfrrrr[ all_columnsrrr\rrflowestselected_orderrr~rrts. @@rHr2r2Ts pitDDDN$    #   DI \F _f_5vgG H HF IJJ F FK MM&/)**-...tE&/"7":Q">??@@AAAIf~vs#IJJ/ e4ek!nq&8 9 9::;;; A |A+innV,, s6{{## 7 7Aq AFkAo66F1II +/* *???2 QI C 4"&,":$,,++7+++K%%'' ( (DAq ''''Q''' 'DD O///// 0 05,,-- qwqz"" A AA$[!44 A A#mD$//&;q!AAAtG*i@@C A A ;' 4 4B M M M M9V;L;L M M MNNAqE+2a55t,C#BqrrF++ I I3lIJJSAXXTT3?@@@@JJa1 S1WW$GHHHH**C"{1a33CHHa + +B /E VF!!#huo <<F N66>!""#5666J  q  #    E %UC& I IIrJzZThe number of lags of the endogenous variable to include in the model. Must be at least 1.Gr)rKtypedesczIf int, uses lags 0, 1, ..., order for all exog variables. If a dict, applies the lags series by series. If ``exog`` is anything other than a DataFrame, the keys are the column index of exog (e.g., 0, 1, ...). If a DataFrame, keys are column names.z int, dictrz Construct an UECM from a formularReturnsrr5zEstimation results.zSee Also)zstatsmodels.tsa.ardl.ARDLNz/Autoregressive distributed lag model estimationc eZdZdZ dFdddddddddGfdZdHfd! ZdIfd# Zd$ZdJd&Ze e e d'dd(d)dKd0Z e dLdMd3Z dNdOd>Ze e ed2d dPddddddd@dQfdEZxZS)Rr4a Unconstrained Error Correlation Model(UECM) Parameters ---------- endog : array_like A 1-d endogenous response variable. The dependent variable. lags : {int, list[int]} The number of lags of the endogenous variable to include in the model. Must be at least 1. exog : array_like Exogenous variables to include in the model. Either a DataFrame or an 2-d array-like structure that can be converted to a NumPy array. order : {int, sequence[int], dict} If int, uses lags 0, 1, ..., order for all exog variables. If a dict, applies the lags series by series. If ``exog`` is anything other than a DataFrame, the keys are the column index of exog (e.g., 0, 1, ...). If a DataFrame, keys are column names. fixed : array_like Additional fixed regressors that are not lagged. causal : bool, optional Whether to include lag 0 of exog variables. If True, only includes lags 1, 2, ... trend : {'n', 'c', 't', 'ct'}, optional The trend to include in the model: * 'n' - No trend. * 'c' - Constant only. * 't' - Time trend only. * 'ct' - Constant and time trend. The default is 'c'. seasonal : bool, optional Flag indicating whether to include seasonal dummies in the model. If seasonal is True and trend includes 'c', then the first period is excluded from the seasonal terms. deterministic : DeterministicProcess, optional A deterministic process. If provided, trend and seasonal are ignored. A warning is raised if trend is not "n" and seasonal is not False. hold_back : {None, int}, optional Initial observations to exclude from the estimation sample. If None, then hold_back is equal to the maximum lag in the model. Set to a non-zero value to produce comparable models with different lag length. For example, to compare the fit of a model with lags=3 and lags=1, set hold_back=3 which ensures that both models are estimated using observations 3,...,nobs. hold_back must be >= the maximum lag in the model. period : {None, int}, optional The period of the data. Only used if seasonal is True. This parameter can be omitted if using a pandas object for endog that contains a recognized frequency. missing : {"none", "drop", "raise"}, optional 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'. Notes ----- The full specification of an UECM is .. math :: \Delta Y_t = \delta_0 + \delta_1 t + \delta_2 t^2 + \sum_{i=1}^{s-1} \gamma_i I_{[(\mod(t,s) + 1) = i]} + \lambda_0 Y_{t-1} + \lambda_1 X_{1,t-1} + \ldots + \lambda_{k} X_{k,t-1} + \sum_{j=1}^{p-1} \phi_j \Delta Y_{t-j} + \sum_{l=1}^k \sum_{m=0}^{o_l-1} \beta_{l,m} \Delta X_{l, t-m} + Z_t \lambda + \epsilon_t where :math:`\delta_\bullet` capture trends, :math:`\gamma_\bullet` capture seasonal shifts, s is the period of the seasonality, p is the lag length of the endogenous variable, k is the number of exogenous variables :math:`X_{l}`, :math:`o_l` is included the lag length of :math:`X_{l}`, :math:`Z_t` are ``r`` included fixed regressors and :math:`\epsilon_t` is a white noise shock. If ``causal`` is ``True``, then the 0-th lag of the exogenous variables is not included and the sum starts at ``m=1``. See Also -------- statsmodels.tsa.ardl.ARDL Autoregressive distributed lag model estimation statsmodels.tsa.ar_model.AutoReg Autoregressive model estimation with optional exogenous regressors statsmodels.tsa.statespace.sarimax.SARIMAX Seasonal ARIMA model estimation with optional exogenous regressors statsmodels.tsa.arima.model.ARIMA ARIMA model estimation Examples -------- >>> from statsmodels.tsa.api import UECM >>> from statsmodels.datasets import danish_data >>> data = danish_data.load_pandas().data >>> lrm = data.lrm >>> exog = data[["lry", "ibo", "ide"]] A basic model where all variables have 3 lags included >>> UECM(data.lrm, 3, data[["lry", "ibo", "ide"]], 3) A dictionary can be used to pass custom lag orders >>> UECM(data.lrm, [1, 3], exog, {"lry": 1, "ibo": 3, "ide": 2}) Setting causal removes the 0-th lag from the exogenous variables >>> exog_lags = {"lry": 1, "ibo": 3, "ide": 2} >>> UECM(data.lrm, 3, exog, exog_lags, causal=True) When using NumPy arrays, the dictionary keys are the column index. >>> import numpy as np >>> lrma = np.asarray(lrm) >>> exoga = np.asarray(exog) >>> UECM(lrma, 3, exoga, {0: 1, 1: 3, 2: 2}) NrrFrrrrrrrgrrO _UECMOrderrrrrQrRrrrrrrrrSrct||||||||| | | |  t|_t|_dS)N)rrrrQrrrr)rrr5rUECMResultsWrapperr)rGrrrgrOrrrQrrrrrrDs rHrz UECM.__init__sb     '  * 2rJrPtuple[list[int], int]ct|ts|tdt||S)z(Check lags value conforms to requirementNzlags must be an integer or None)r^rrbr _check_lags)rGrrrDs rHr(zUECM._check_lagssD4,, ? =>> >ww""4333rJrhct|trA|D]+\}}t|ts|t d,n&t|ts|t dt |}|std|D]\}}|dgkrtd|S)z#Check order conforms to requirementNz.order values must be positive integers or NonezVorder must be None, a positive integer, or a dict containing positive integers or Nonez2Model must contain at least one exogenous variablerz7All included exog variables must have a lag length >= 1)r^rrrrbrrfra)rGrOrtr[rrrDs rHrfzUECM._check_orders eW % %    1!!Z00Q]#H  UJ// 5=7  $$U++ D    HCqczz M rJc||jj}t|tjr |jpd}n8t|tjr|jpd}nd}d|t|j j }| |d|jj }t|tj}g}|j D][\}}|T|r|d} nd|d} | | | dd} |ddD]} | d| | \|jrt!|jnd} fdt#d | D} || ||||j|fS) rrzD..L1Nrrrcg|] }d| Sr rN)rZrr!s rHr\z2UECM._construct_variable_names..2s'GGGs6**S**GGGrJr])rrjr^rrrKrsqueezer}rrrrrrrrrr?r)rGry_baser&r exog_pandas dexog_namesrrx_namelag_baserr dendog_namesr!s @rHrzUECM._construct_variable_namess $ eRY ' ' Z&3FF r| , , ]]__)0SFFFft.677&~~~&&&I'  BL99   ))++ = =HC* #[[[FF)\\\Fv&&&!#2#;ss8==C&&';H';c';';<<<<$(J5TZAGGGGeAv6F6FGGG |$$${###t()))wrJrc& |jrt|jnd|_tj|jjtj}tj|jjd|dd<td|jdz }t||d\|_ |_ |j |_|jj}t!|t"j}tj|jjtj}|jjdd|dd<|g}|jD]h\}} | a|r|j|} n|} |jjdd| f|dd<||itj||_|r|} nDtj|jjtj} tj|d| dd<i} |jD]\}} | | dgkrdn | dd} | | |< || | |_|j|j|j |j|jd|_|j g} |jD]q\}} |d kr(| tj | 3| !D])}| tj |*r| d}tj| dd}d}|j!D]#} t|| t| nd}$t|j||_t|jd|_|tE|j|_#|j#|jkrtId ||j#d}|j%d|j%dkr,tId |j%dd |j%dd tj&||j#d|fS)rrr5r]Nrrr)rlevelsrrgrrgr rrr)'rrrr_rrrr3diffr/rrrrrrr^rrcopyrrrget_locrgrr_levelsrrrrr:rrXrrarr-)rGrdendogdlagrr/lvllvlsrrr]dexog adj_orderrsubvalrrrs rHrzUECM._construct_regressors8sQ +/*;s4:! diorv66WTY_1555qrr 1dlQ&'''-fdU'K'K'K$"&"6"@"@"B"BI'  BL99 l49?BF33)/#2#&ABB | ))++ ( (HC#+33C88CCC)."c2ABB CHHJJ'''t,,   3NN$$EEL88E 222E!""I  ))++ ! !HC;#!**$$3ss8C IcNN&&ui88 "4l_J[    + **,, 6 6HCf}} bjoo....!jjll66FMM"*V"4"455556 1IofQRRj)) ;%%'' O OCks3s888ANNKK4<55 4<++  !$,//DO ?T\ ) ) $/##$ 9Q<#)A, & &4SYq\44$'9Q<444  z!}}T_../44rJrTrrr=rrrr5c||||\}}}t|||||}t|S)Nrr)rr5r%rs rHrzUECM.fits[/3ii/8/ / + O &*oU   "#&&&rJardlr0cjd}i}|j}|D]k\}}t|}t|||t |j zkr#t |d|||<l|jd} nQt|j}t|j|kr#t |d|} ||j j | |j j ||j |j |j|j|j|j||j S)a| Construct a UECM from an ARDL model Parameters ---------- ardl : ARDL The ARDL model instance missing : {"none", "drop", "raise"}, default "none" How to treat missing observations. Returns ------- UECM The UECM model instance Notes ----- The lag requirements for a UECM are stricter than for an ARDL. Any variable that is included in the UECM must have a lag length of at least 1. Additionally, the included lags must be contiguous starting at 0 if non-causal or 1 if causal. zmUECM can only be created from ARDL models that include all {var_typ} lags up to the maximum lag in the model. exogenous)var_typN endogenous)rrrrrrQrr)rrrrcrXrQraformatrrrjrrrrrrr) rkrBrerr uecm_lagsrrrmax_valrs rH from_ardlzUECM.from_ardls:6 A  ,  % %HC#hhG73<  Gcdk/.B.B$BCC K!@!@AAA$IcNN < GG$,''G4<  G++ L!A!ABBBGs I  I  **]n;;,    rJrrr'rEr(rFrr*r+r,c J|durtd||||||\}}}}}} | dkrtdtj|jjdtj} |j|z| |jjd d<| ||dzS)rHFz#dynamic forecasts are not supportedrz)Out-of-sample forecasts are not supportedNr])NotImplementedErrorrQr_r2rrr3r) rGrr'r(rFrgr*rr+r)preds rHr^z UECM.predicts| %  %&KLL L6:6N6N D(E37 7 3hsG a<<%; wtz'*BF33$(Gf$4dgmA  !EC!GO$$rJrNr_r`rr:rac \t||||||||| | |  S)Nr_)rri) rkr`rrrOrrQrrrrrrDs rHrizUECM.from_formulasG"ww##     '$   rJro)rrrrrgrrOr#rrrrrQrRrrRrrrrrrrrrSr)rrPrrrSr&)rOrhrq)rr=rrrrRrSr5)r)rBr0rrrr)rrr'rEr(rErFrRrgrr*rrrr+rrSr,rs)r`r=rr:rrPrOrhrrrQrRrrRrrrrrrrrarSr4)rErKrLrtrr(rfrrrr=fit_docrrwrKr^from_formula_doc__str__replacerirxrys@rHr4r4Xswwz$(03 3%)59 $!4:33333333B4444444!!!FM5M5M5M5^Xcc'll$#' ' ' ' ' ' 'EK9 9 9 9 [9 |@D=A.226/337I%I%I%I%I%V X&&((00@@AA ,-03  59 $!,2       BA[     rJr4ceZdZUdZiZded< d+d,d Zed-d Zed-dZ ed-dZ ed-dZ d.d/dZ d.d0dZ ed-dZd1dZdZ d2d3d*ZdS)4r5a Class to hold results from fitting an UECM model. Parameters ---------- model : UECM Reference to the model that is fit. params : ndarray The fitted parameters from the AR Model. cov_params : ndarray The estimated covariance matrix of the model parameters. normalized_cov_params : ndarray The array inv(dot(x.T,x)) where x contains the regressors in the model. scale : float, optional An estimate of the scale of the model. rrrrr,rKr=rS"NDArray | pd.Series | pd.DataFramect|jjts|S|jjdjd}|jjdjd}|jjd||z}t|||zD],}||}|dr |dd||<-|j dkrtj |||Stj |||S) Nrr]r5r+rk)rrfrfrK) r^r~rrrrr%rendswithrmrrr)rGrrKndetnlvllblsrlbls rH_ci_wrapzUECMResults._ci_wrapSs$*/:66 Jz!/28;z!(+1!4z$_t _5tTD[)) # #Aq'C||E"" #crc(Q 8q==<T>>> >yDt4444rJrc|jjdjd}|jjdjd}tj|j|}||jd||z|z dS)z3Parameters of normalized cointegrating relationshiprr]r5N ci_params)r~rrr_r:rr^)rGrZr[r#s rHr`zUECMResults.ci_paramscspz!/28;z!(+1!4z$+&&t,}}T[4$;7$> LLLrJctjtj|}||dS)z8Standard Errors of normalized cointegrating relationshipci_bse)r_sqrtdiag ci_cov_paramsr^)rGbses rHrbzUECMResults.ci_bseks=gbgd00223344}}S(+++rJcj|jjdjd}tj5tjdt j|jt j|j z }t j ||<dddn #1swxYwY| |dS)z1T-values of normalized cointegrating relationshiprr]ignoreN ci_tvalues) r~rrrcatch_warnings simplefilterr_r:r`rbr3r^)rGrZtvaluess rHrizUECMResults.ci_tvaluesqsz!/28;  $ & & # #  !( + + +j002:dk3J3JJGFGDM # # # # # # # # # # # # # # #}}Wl333sABBBc$tj5tjdddtjt j|jz z}dddn #1swxYwY| |dS)z1P-values of normalized cointegrating relationshiprhrkr]N ci_pvalues) rrjrkrnormcdfr_absrir^)rGpvaluess rHrnzUECMResults.ci_pvalues{s $ & & H H  !( + + +1uz~~bfT_.E.EFFFGG H H H H H H H H H H H H H H H}}Wl333sAA11A58A5rrr8Float64Array | pd.DataFramect|d}|jr3tj|jd|dz z }n,tjd|dz z }|j}|j}|||zz |||zzg}t|tj stj |Stj|d}ddg|_|S)Nrr]rkr5rBrA)r$rrtdf_residppfror`rbr^rrr_rr=r)rGrqpseoutrs rH ci_conf_intzUECMResults.ci_conf_ints5'** : 0 &&**1uqy=99AA   UQY//A N [1r6z1q2v:&!RY'' (?3'' ' Ys # # #w'  rJrc|ffd }t}jjdjd}jjdjd}t jjd||z}t jj|}t jj j j ||}t|} d| _ |j| |S)NcRtj|Srr)r_r:r|)rrGs rH_ciz#UECMResults.ci_summary.._cis!:d..u5566 6rJrr]r5)rr%)rrfrlrrconf_intr~zCointegrating Vector)rr~rrr}r%r rr`rbrirnrrtablesr) rGrrrrZr[r%r~rtabs ` rH ci_summaryzUECMResults.ci_summarys 7 7 7 7 7 7yyz!/28;z!(+1!4$*/00D4KA  .:   > OO    T""*  3 rJc|jjd}|jjj}t |t j}|r|n |jj}tj ||jj g}|jj D]V\}}|O|r.| tj ||7| |dd|fWtj|}||jz}t |jjt s|S|jjjj} t j|| dS)Nr ci_residsrX)r~rrrr^rrrgr_r:rrrrrr`rrjrfr) rGrrg is_pandascolsrrci_xresidsrfs rHrzUECMResults.ci_residss' J  /z(tR\22  5ttdjo 1 tz/0*,2244 . .JC .KK 49 5 56666KKQQQV ---t$$&$*/:66 M *0yu;????rJc|jjdjd}|jjdjd}tt ||z}|}t j|}|t j||}|jd}t j|j d||z}||} t j ||f} t |D]'} | |kr d| z | | | f<||  | dzz | | |f<(| |z| j z}| |S)z6Covariance of normalized of cointegrating relationshiprr]r5rNrk) r~rrr}rrr_r:ix_rrTr^) rGrZr[r]covcov_aci_covmrr#rrs rHrezUECMResults.ci_cov_paramss2z!/28;z!(+1!45%%&&oo 3rvc3''( LODK((4$;7d| HaV  q 0 0ADyy$hAadG )tQw/AagJJVac!}}V$$$rJcdS)rNrNrFs rHrzUECMResults._lag_reprsrJrNT順caseLiteral[1, 2, 3, 4, 5]rrrrR asymptoticnsimrXseedHint | Sequence[int] | np.random.RandomState | np.random.Generator | Nonec |j}|dkrd} n |dvrd} nd} d|jD} t|jjt |j|jj| |j | } | |||} | } t| jj }|dkrtj|}nz|d krtj|dz}n\|d krtjd|dz}n=|d krtjd|d z}n|d krtjd |d z}tj|jd | jdf}t%|D] \}}d|||f< || z|jz}|| jz}|jtj|z|z|jd z }|}|r|dkrt.j}||f}||dz}||dz}t3j||dt.j}d|j_t3jt?|||dt?|||dd}n*| j jd }tC||||||\}}tE|||ddS)ad Cointegration bounds test of Pesaran, Shin, and Smith Parameters ---------- case : {1, 2, 3, 4, 5} One of the cases covered in the PSS test. cov_type : str The covariance estimator to use. The asymptotic distribution of the PSS test has only been established in the homoskedastic case, which is the default. The most common choices are listed below. Supports all covariance estimators that are available in ``OLS.fit``. * 'nonrobust' - The class OLS covariance estimator that assumes homoskedasticity. * 'HC0', 'HC1', 'HC2', 'HC3' - Variants of White's (or Eiker-Huber-White) covariance estimator. `HC0` is the standard implementation. The other make corrections to improve the finite sample performance of the heteroskedasticity robust covariance estimator. * 'HAC' - Heteroskedasticity-autocorrelation robust covariance estimation. Supports cov_kwds. - `maxlags` integer (required) : number of lags to use. - `kernel` callable or str (optional) : kernel currently available kernels are ['bartlett', 'uniform'], default is Bartlett. - `use_correction` bool (optional) : If true, use small sample correction. cov_kwds : dict, optional A dictionary of keyword arguments to pass to the covariance estimator. `nonrobust` and `HC#` do not support cov_kwds. use_t : bool, optional A flag indicating that small-sample corrections should be applied to the covariance estimator. asymptotic : bool Flag indicating whether to use asymptotic critical values which were computed by simulation (True, default) or to simulate a sample-size specific set of critical values. Tables are only available for up to 10 components in the cointegrating relationship, so if more variables are included then simulation is always used. The simulation computed the test statistic under and assumption that the residuals are homoskedastic. nsim : int Number of simulations to run when computing exact critical values. Only used if ``asymptotic`` is ``True``. seed : {None, int, sequence[int], RandomState, Generator}, optional Seed to use when simulating critical values. Must be provided if reproducible critical value and p-values are required when ``asymptotic`` is ``False``. Returns ------- BoundsTestResult Named tuple containing ``stat``, ``crit_vals``, ``p_values``, ``null` and ``alternative``. The statistic is the F-type test statistic favored in PSS. Notes ----- The PSS bounds test has 5 cases which test the coefficients on the level terms in the model .. math:: \Delta Y_{t}=\delta_{0} + \delta_{1}t + Z_{t-1}\beta + \sum_{j=0}^{P}\Delta X_{t-j}\Gamma + \epsilon_{t} where :math:`Z_{t-1}` contains both :math:`Y_{t-1}` and :math:`X_{t-1}`. The cases determine which deterministic terms are included in the model and which are tested as part of the test. Cases: 1. No deterministic terms 2. Constant included in both the model and the test 3. Constant included in the model but not in the test 4. Constant and trend included in the model, only trend included in the test 5. Constant and trend included in the model, neither included in the test The test statistic is a Wald-type quadratic form test that all of the coefficients in :math:`\beta` are 0 along with any included deterministic terms, which depends on the case. The statistic returned is an F-type test statistic which is the standard quadratic form test statistic divided by the number of restrictions. References ---------- .. [*] Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds testing approaches to the analysis of level relationships. 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