M/Phs7jddlmZddlmZmZmZmZddlmZddl Z ddl Z ddl m Z ddl mZmZmZddlmZddlZddlZddlZddlmZmZddlmcmZdd lmZdd l m!Z!dd l"m#Z#dd l$m%Z%m&Z&dd l'm(Z(m)Z)ddl*m+Z+ddl,m-Z-m.Z.m/Z/m0Z0m1Z1ddl2m3Z3m4Z4m5Z5m6Z6ddl7m8Z8ddl9m:Z:ddl;mZ>m?Z?m@Z@mAZAddlBmCZCmDZDddgZEdZFdZGd:d;d ZHdd7ZYGd8d9ZZdS)?) annotations)Appender Substitutioncall_cached_functo_numpy)IterableN)SimpleNamespace)AnyLiteralcast)Sequence) gaussian_kdenorm)Summary)OLS) eval_measures)cache_readonlycache_writable) Docstringremove_parameters)SpecificationWarning) ArrayLike ArrayLike1D ArrayLike2D Float64ArrayNDArray) array_like bool_likeint_like string_like)arma2ma) tsa_model)PredictionResults)DeterministicProcessDeterministicTerm Seasonality TimeTrend)freq_to_periodlagmatARAutoRegaU statsmodels.tsa.AR has been deprecated in favor of statsmodels.tsa.AutoReg and statsmodels.tsa.SARIMAX. AutoReg adds the ability to specify exogenous variables, include time trends, and add seasonal dummies. The AutoReg API differs from AR since the model is treated as immutable, and so the entire specification including the lag length must be specified when creating the model. This change is too substantial to incorporate into the existing AR api. The function ar_select_order performs lag length selection for AutoReg models. AutoReg only estimates parameters using conditional MLE (OLS). Use SARIMAX to estimate ARX and related models using full MLE via the Kalman Filter. To silence this warning and continue using AR until it is removed, use: import warnings warnings.filterwarnings('ignore', 'statsmodels.tsa.ar_model.AR', FutureWarning) z Model has been fit using maxlag={0}, method={1}, ic={2}, trend={3}. These cannot be changed in subsequent calls to `fit`. Instead, use a new instance of AR. x np.ndarrayaxisintreturnfloat | np.ndarrayc4tj|dz|S)z= the maximum lag in the model. period : {None, int} 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 : 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'. deterministic : DeterministicProcess A deterministic process. If provided, trend and seasonal are ignored. A warning is raised if trend is not "n" or seasonal is not False. old_names : bool Flag indicating whether to use the v0.11 names or the v0.12+ names. .. deprecated:: 0.13.0 old_names is deprecated and will be removed after 0.14 is released. You must update any code reliant on the old variable names to use the new names. See Also -------- statsmodels.tsa.statespace.sarimax.SARIMAX Estimation of SARIMAX models using exact likelihood and the Kalman Filter. Notes ----- See the notebook `Autoregressions <../examples/notebooks/generated/autoregressions.html>`__ for an overview. Examples -------- >>> import statsmodels.api as sm >>> from statsmodels.tsa.ar_model import AutoReg >>> data = sm.datasets.sunspots.load_pandas().data['SUNACTIVITY'] >>> out = 'AIC: {0:0.3f}, HQIC: {1:0.3f}, BIC: {2:0.3f}' Start by fitting an unrestricted Seasonal AR model >>> res = AutoReg(data, lags = [1, 11, 12]).fit() >>> print(out.format(res.aic, res.hqic, res.bic)) AIC: 5.945, HQIC: 5.970, BIC: 6.007 An alternative used seasonal dummies >>> res = AutoReg(data, lags=1, seasonal=True, period=11).fit() >>> print(out.format(res.aic, res.hqic, res.bic)) AIC: 6.017, HQIC: 6.080, BIC: 6.175 Finally, both the seasonal AR structure and dummies can be included >>> res = AutoReg(data, lags=[1, 11, 12], seasonal=True, period=11).fit() >>> print(out.format(res.aic, res.hqic, res.bic)) AIC: 5.884, HQIC: 5.959, BIC: 6.071 r_ycFNnone) deterministic old_namesendogrlagsint | Sequence[int] | NonetrendLiteral['n', 'c', 't', 'ct']seasonalboolexogArrayLike2D | None hold_back int | NoneperiodmissingstrrEDeterministicProcess | NonerFc  Bt||dd|ttdt |ddd|_t |d|_t|dd |_ |j &|jrt|j |j |_ tj|jg} |rCt|j t sJ| t%|j t'|j jd r|j jj} n)t-j|j jjd } d|_| 3t| t6st9d | |_d|_nt7| | |_g|_d |_t | dd |_ | .|jdks|jrtCj"dtFd|j rtCj"dtHd|%|t|dd \|_&|_'|(|j)jd |_*|j+|j _,dS)N)rS)nrCtctrJF)optionsoptionalrLrRTr[indexrz,deterministic must be a DeterministicProcess)additional_termsrFrWzGWhen using deterministic, trend must be "n" and seasonal must be False.r3) stacklevelzoold_names will be removed after the 0.14 release. You should stop setting this parameter and use the new names.rP)-super__init__r r r _trendr _seasonalr_periodr@r: _index_freqr' from_string isinstancer/appendr&hasattr orig_endogr]r5arangerGshape_user_deterministicr$ TypeError_deterministics _exog_names_k_ar _old_nameswarningswarnr FutureWarning _check_lags_lags _hold_back_setup_regressorsrBnobs exog_namesxnames)selfrGrHrJrLrNrPrRrSrErFtermsr] __class__s r7razAutoReg.__init__s dD'BBB ' ( w(=      #8Z884@@@ < DN &ty$2BCCDL*3*? *L*L)M  4dlC00 0 0 0 LLT\22 3 3 3 49' 1 1 8I(.EEIdio3A677E#(  $m-ABB P NOOO#0D '+D $ $#7$$$D ') #I{UKKK  $ K3  $.  M*$      ?  ME      '+&6&6 (9kDAAA' ' # DO    GM!$ ? r9r0list[int] | Nonec6t|j}|sdn|S)-The autoregressive lags included in the modelN)listrw)r}rHs r7ar_lagszAutoReg.ar_lags s"DJ)ttT)r9c|jS)z?The number of initial obs. excluded from the estimation sample.)rxr}s r7rPzAutoReg.hold_backs r9Literal['n', 'c', 'ct', 'ctt']c|jS)zThe trend used in the model.rbrs r7rJz AutoReg.trend {r9c|jS)z=Flag indicating that the model contains a seasonal component.rcrs r7rLzAutoReg.seasonal ~r9c"|jr|jndS)z-The deterministic used to construct the modelN)rmrors r7rEzAutoReg.deterministics(,'?It##TIr9c|jSz%The period of the seasonal component.rdrs r7rRzAutoReg.period# |r9r/c&|jjdS)zThe model degrees of freedom.)_xrlrs r7df_modelzAutoReg.df_model(sw}Qr9list[str] | Nonec|jS)z.Names of exogenous variables included in model)rprs r7r{zAutoReg.exog_names-s r9NonecdS)zInitialize the model (no-op).Nrs r7 initializezAutoReg.initialize2s r9tuple[list[int], int]cN| g}d|_net|trg}|D]>}t|d}t|tsJ||?t jt|}t j |dks.t j |j d|j dkrtdt j ||_d|D}nqt|d}t|tsJ||_|jdkrtdt jd|jdz}d|D}||j}||jkrtd|t |fS) NrrHrz1All values in lags must be positive and distinct.c,g|]}t|Srr/.0vs r7 z'AutoReg._check_lags..K///SVV///r9z#lags must be a non-negative scalar.c,g|]}t|Srrrs r7rz'AutoReg._check_lags..Srr9zNhold_back must be >= lags if lags is an int ormax(lags) if lags is array_like.)_maxlagrgrrr/rhr5arraysortedanyuniquerlr>maxrk)r}rHrPrwlagval _lags_arrs r7rvzAutoReg._check_lags6s <!EDLL h ' ' 0E " "sF++!#s+++++ S!!!!!#&--!8!8Iy1}%% 9Y''-a0IOA4FFF G6),,DL//Y///EE4((Cc3'' ' ' 'DL|a !FGGG !T\A%566I//Y///E   I t| # #3 c)nn$$r9c |j}|j}g}|jt|j|d\}}|fd|jDt|j|kr&|ddtj |jdz f}|j d|_ |j }|j drtjt||f}|jrg}d|jvr|dd|jvr|d|jr_|j}t+|t,sJd t/|D} d|jvr | dd} || nt1|j}||z}|j8tj||jf}||jj||d}||d}|j d |j dkr|j d} |j}|jd krd nt|j} |jr1t+|t,sJ|t-d|jvz } nd } t|j} |j d }t;d | d | d| d| d|d ||c|_|_||_ dS)Nsep)originalc g|] }d|z S)z.Lr)rr endog_namess r7rz-AutoReg._setup_regressors..es$ < < <#[::: % < < .vsDDD___DDDr9rrWz@The model specification cannot be estimated. The model contains z regressors (z trend, z seasonal, zS lags) but after adjustment for hold_back and creation of the lags, there are only z. data points available to estimate parameters.)!rrxrr)rGextendrwlenr5asarrayrlrqro in_samplec_rrrrbrhrcrdrgr/rangercolumnsrNr: param_namesr>rBrrp)r}maxlagrPr{r,yrEdeterministic_namesrRnamesregrJseasrHrzrs @r7ryzAutoReg._setup_regressors^s5O  & dj&59991 < < < < < < <    tz??V # #!!!RZ ++a//0AWQZ ,6688  q ! :h}--q01A B&(#$+%%'..{;;;$+%%'..w777>6!\F%fc22222DDeFmmDDDEdk)) %abb '..u555&*=+@&A&A#,z9J 9 al#A   di3 4 4 4 ijjM ijjM 71: " "'!*C\F++AAT[1A1AE~ !&#.....C4;$6 7 77tz??D71:D&)8=$(!  a%r9 nonrobustcov_typecov_kwdsdict[str, Any] | Noneuse_tAutoRegResultsWrapperc |jjddkrBtt|t jdt jdSt |j|j}||||}| }|j }|dkr3|s1|jjd}|jjd}|||z z } || z}t||j ||j |} t| S)a 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 ------- AutoRegResults Estimation results. See Also -------- 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)rr)rrrr)r) rrlrAutoRegResultsr5emptyrrBfit cov_paramsrparamsnormalized_cov_params) r}rrrols_modols_resrrzkscaleress r7rz AutoReg.fits| 7= q (tRXa[["(62B2BCC dgtw''++  ''))   { " "5 "7=#D a AD1H%E % J  N   )    %S)))r9rrr-ct|dd}|j|j|zz S)Nrr3)ndim)rrBsqueezerr}rs r7_residzAutoReg._resids@FH1555w  DGf$4#=#=#?#???r9floatc|j}||}||z}|dz tjdtjztj||z zdzz}|S)a Log-likelihood of model. Parameters ---------- params : ndarray The model parameters used to compute the log-likelihood. Returns ------- float The log-likelihood value. r3r)rzrr5logpi)r}rrzresidssrllfs r7loglikezAutoReg.loglikesby F##emqkRVAI..d 1C1CCaGH r9cJ||}|jj|zS)aP Score vector of model. The gradient of logL with respect to each parameter. Parameters ---------- params : ndarray The parameters to use when evaluating the Hessian. Returns ------- ndarray The score vector evaluated at the parameters. )rrT)r}rrs r7scorez AutoReg.scores$  F##wy5  r9cz||}||z|jz }|jj|jzd|z zS)a5 Fisher information matrix of model. Returns -1 * Hessian of the log-likelihood evaluated at params. Parameters ---------- params : ndarray The model parameters. Returns ------- ndarray The information matrix. r)rrzrr)r}rrsigma2s r7 informationzAutoReg.informations?  F##* DG#F 33r9c.|| S)a The Hessian matrix of the model. Parameters ---------- params : ndarray The parameters to use when evaluating the Hessian. Returns ------- ndarray The hessian evaluated at the parameters. )rrs r7hessianzAutoReg.hessian/s  ((((r9 add_forecastsexog_oosrc\tj||jjdf}|j|}|jd}t ||ddd|f<|t|jz}|j 'tj |}|d||dd|df<|S)Nr)steps) r5zerosrrlro out_of_samplerrrwrNr)r}rrr,oos_exogn_deterministicloc exog_oos_as r7_setup_oos_forecastzAutoReg._setup_oos_forecast?s HmTW]1%56 7 7'55M5JJ".+!)(!3!3!!! o  DJ/ 9 H--J#N]N3AaaagJr9 predictionstartendpad pd.Seriesc~tjtj|tj|g}||z |z}t |jjtjtj fs || dS|j }||j j dkr}t|dd}|rVt |tjrtj|d||}n2tj|d||}ntj|}|||z |}|| d}tj||S)Nrr=)r=periodsr])r5hstackfullnanrgr:rjpdSeries DataFrame_indexrGrlgetattr PeriodIndex period_range date_range RangeIndex)r}rrrrn_valuesr]r=s r7_wrap_predictionzAutoReg._wrap_predictionMs.YRV 4 4jABB ;$$).BL0IJJ *xijj) )  !!$ $ $5&$//D +eR^44LOE!H4MMMEEM%(sKKKEE c**eckC'( + y51111r9dynamicnum_oosFloat64Array | Nonec$g}|j} d} || kr| |z } || z }t|| z d}|| z |jkrst|| z |dz| z } |j| } |6| } |||dz| dd|jd df<|| |dkr)||||tj |} |jjdt|j z }||j dn|j jdz}tj| jd}| d||z|d|<t|| jdD]o}t!|j D]3\}}||z }||kr ||}n|j||z}|| |||zf<4tj| ||dz|z||<p||||dz|z| S)z :param params: :param start: :param end: :param dynamic: :param num_oos: :param exog: :param exog_oos: :return: rrN)rxrrzslicercopyrlrhrr5vstackrrwrNrr enumeraterGrr)r}rrrrrrNrrrPadjis_locr,_reg det_col_idx forecastshjr fcast_locrs r7_dynamic_predictzAutoReg._dynamic_predictbsC*O  9  e#C  gmQ'' I $) + +59,cAg .ABBFAFFHH)-ecAgo)>!!!djm^%%%& JJqMMM Q;; JJt//BB C C Cy~~gmA&TZ8 DI-qq49?13EE HTZ]++ "8G8nv5 (7(w 1 .. @ @A#DJ// / /3G ''#I.CC*Y%67C+.Q a'((:d1q1u9o&>??IaLL$$YsQw7H#NNNr9c|||}|jdkr||zStj|}|jdn|jjd}|jjd|z t|jz }t|D]}}t|jD]A\} } || z } | dkr |j | n|| } tj | |||| zf<Btj |||dz|z||<~|S)Nrr) rrr5rrNrlrrrwrrrBr) r}rrrnew_xrnexog ar_offsetrrrrrs r7_static_oos_predictzAutoReg._static_oos_predicts(((;; <1  6> !HW%% Y&DIOA,>GM!$u,s4:> w A AA#DJ// : :3#g&)Aggdgcll9S>*,*S//aQ&'':eAAI&6&?@@IaLLr9c|j}|jjd}tjd|jjdf} t d||z } || z }||krrt||z |dz|z } |j| } |Jtj|} | } | ||dz| dd| jd df<| |z} |dkr| | ||dz| S| |||}tj | |f}| |||dz|z| S)a Path for static predictions Parameters ---------- params : ndarray The model parameters start : int Index of first observation end : int Index of last in-sample observation. Inclusive, so start:end+1 in slice notation. num_oos : int Number of out-of-sample observations, so that the returned size is num_oos + (end - start + 1). exog : {ndarray, DataFrame} Array containing replacement exog values exog_oos : {ndarray, DataFrame} Containing forecast exog values rrN) rxrGrlr5rrrrrrrr$r)r}rrrrrNrrPrzr,rrexog_arrrs r7_static_predictzAutoReg._static_predictsV:O z" Haq)* + +!Y&''   D==59,cAg .ABBFAD))FFHH+1%#'/+B!!!fl1o%'''(J a<<((E37CHH H00(KK Y =9:: $$Za'8I3OOOr93int | str | datetime.datetime | pd.Timestamp | Nonedtuple[np.ndarray, np.ndarray | pd.DataFrame | None, np.ndarray | pd.DataFrame | None, int, int, int]ct|d}t|tjsJt|tjr|}nt|ddd}t|tjr|}nt|ddd}|dn|}| |jdn|}|||\}}}} ||||||fS) NrrNr3T)rr[rr)rrgr5ndarrayrrr_get_prediction_index) r}rrNrrr_exog _exog_oosr_s r7_prepare_predictionzAutoReg._prepare_predictionsFH--&"*----- dBL ) ) DEEtV!dCCCE h - - P II"8Za$OOOI]!$dk"oo#!%!;!;E3!G!GsGQuiW<)r}rr dynamic_locr0s r7_parse_dynamiczAutoReg._parse_dynamics  c5", RYG  '!% 3 3G < < KA 5 KK __KKg,,K ??3 r9 bool | intc p||||||\}}}}}}|j||td|j|I|j|jjkr4d}t||j|jj|a|jd|jjdkr@d}t||jd|jjd|dkr|td|A||jdkr0d}t|||jdt |t r|r |jdkr|||||||S| ||}| |||||||S) a 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 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. Returns ------- predictions : {ndarray, Series} Array of out of in-sample predictions and / or out-of-sample forecasts. NzWexog and exog_oos cannot be used when the model does not contains exogenous regressors.z]The shape of exog {0} must match the shape of the exog variable used to create the model {1}.rz~The number of columns in exog_oos ({0}) must match the number of columns in the exog variable used to create the model ({1}).rzAexog_oos must be provided when producing out-of-sample forecasts.z}start and end indicate that {0} out-of-sample predictions must be computed. exog_oos has {1} rows but must have at least {0}.) r1rNr>rlformatrgrMrr'r:r) r}rrrrrNrrmsgs r7predictzAutoReg.predictsj7;6N6N D(E37 7 3hsG 9 $"2h6J: Y "DJ$)/$A$AB!DJ !H!HIII$N1%);;;. !JJx~a0$)/!2DEE{{x/ /%'HN14E*E*E2 !GX^A5F!G!GHHH w % % g $,!:K:K''sGT8 %%gu55$$ E3$   r9)rCFNNNrD)rGrrHrIrJrKrLrMrNrOrPrQrRrQrSrTrErUrFrMr0rr0rQr0rr0rM)r0rU)r0r/)r0r)r0r)rHrIrPrQr0r)rNF)rrTrrrrMr0r)rrr0r-)rrr0r)rr/rrr0r-) rr-rr/rr/rr/r0r)rrrr/rr/rr/rr/rNrrrr0r)rrrr/rrr0r-)rrrr/rr/rr/rNrrrr0r) rrrNrrrrr(rr(r0r)NNFNN)rrrr(rr(rr;rNrOrrOr0r)!__name__ __module__ __qualname____doc____annotations__rapropertyrrPrJrLrErRrr{rrvryrrrrrrrrrr$r'r1r:r? __classcell__rs@r7r+r+bs)]]~ /2#' $!C+6:C+C+C+C+C+C+C+C+J***X* XXXJJJXJX   X    X     &%&%&%&%P8&8&8&8&x$*. V*V*V*V*V*p@@@@(!!!!&4444())))    2222*<O<O<O<O|"4P4P4P4Pl====<0FJCG##''+f f f f f f f f f r9ceZdZdZdZdS)r*z The AR class has been removed and replaced with AutoReg See Also -------- AutoReg The replacement for AR that improved deterministic modeling c td)NzXAR has been removed from statsmodels and replaced with statsmodels.tsa.ar_model.AutoReg.NotImplementedErrorr}argskwargss r7raz AR.__init__s! 0   r9NrErFrGrHrarr9r7r*r*s-     r9ceZdZdZdZdS) ARResultszX Removed and replaced by AutoRegResults. See Also -------- AutoReg c td)NzNAR and ARResults have been removed and replaced by AutoReg And AutoRegResults.rOrQs r7razARResults.__init__s! *   r9NrTrr9r7rVrVs-     r9rVrrrrNrceZdZUdZiZded< d/fd Zd Zed Z ed Z ed Z ed Z edZ edZedZedZedZedZedZedZedZedZdZedZedZedZd0dZdZd1dZdZ e!e"e#j$jd  d2d!Z$ d2d"Z%d3d$Z&d%Z'e(e)& d4d)Z*d5d+Z+d6d,Z,d7d-Z-d7d.Z.xZ/S)8ra Class to hold results from fitting an AutoReg model. Parameters ---------- model : AutoReg 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, optional Whether use_t was set in fit summary_text : str, optional Additional text to append to results summary zdict[str, Any]_cacheN?Fc~t||||i|_||_|j|_|jjd|_|j |_ |j |_ ||_ |j t|j |_nd|_|jj|_||_||_dS)Nr)r`rar[_paramsrz_nobsrGrl _n_totobsr _df_modelr_ar_lags_use_tr_max_lagmodelrPrxcov_params_default _summary_text) r}rfrrrrr summary_textrs r7razAutoRegResults.__init__s (=uEEE  Z *1-   = $ ..DMMDM*.",)r9c "||_||_dS)aA Initialize (possibly re-initialize) a Results instance. Parameters ---------- model : Model The model instance. params : ndarray The model parameters. **kwargs Any additional keyword arguments required to initialize the model. N)r_rf)r}rfrrSs r7rzAutoRegResults.initializes  r9c|jS)r)rcrs r7rzAutoRegResults.ar_lagss }r9c|jS)zThe estimated parameters.)r_rs r7rzAutoRegResults.paramsrr9c|jS)z-The degrees of freedom consumed by the model.)rbrs r7rzAutoRegResults.df_modelrr9c |j|jz S)z2The remaining degrees of freedom in the residuals.)rzrbrs r7df_residzAutoRegResults.df_residsy4>))r9c|jS)zT The number of observations after adjusting for losses due to lags. )r`rs r7rzzAutoRegResults.nobss zr9c@d|jz t|jzS)Nr\)rzr8rrs r7rzAutoRegResults.sigma2sTY!4!444r9c|jSN)rrs r7rzAutoRegResults.scale s {r9crtjtj|S)a The standard errors of the estimated parameters. If `method` is 'cmle', then the standard errors that are returned are the OLS standard errors of the coefficients. If the `method` is 'mle' then they are computed using the numerical Hessian. )r5sqrtdiagrrs r7bsezAutoRegResults.bses(wrwt0011222r9cRtj|j|j|jdzS)z Akaike Information Criterion using Lutkepohl's definition. :math:`-2 llf + \ln(nobs) (1 + df_{model})` r)raicrrzrrs r7ryzAutoRegResults.aics$ 49dma6GHHHr9cRtj|j|j|jdzS)z Hannan-Quinn Information Criterion using Lutkepohl's definition. :math:`-2 llf + 2 \ln(\ln(nobs)) (1 + df_{model})` r)rhqicrrzrrs r7r{zAutoRegResults.hqic+s$!$(DIt}q7HIIIr9cD|j}|j}|j||z||z z zS)u Final prediction error using Lütkepohl's definition. :math:`((nobs+df_{model})/(nobs-df_{model})) \sigma^2` )rzrr)r}rzrs r7fpezAutoRegResults.fpe;s,y={th4(?CDDr9cRtj|j|j|jdzS)z Akaike Information Criterion with small sample correction :math:`2.0 * df_{model} * nobs / (nobs - df_{model} - 1.0)` r)raiccrrzrrs r7rzAutoRegResults.aiccGs$!$(DIt}q7HIIIr9cRtj|j|j|jdzS)zb Bayes Information Criterion :math:`-2 llf + \ln(nobs) (1 + df_{model})` r)rbicrrzrrs r7rzAutoRegResults.bicPs$ 49dma6GHHHr9cp|j}|j}||jd|jz S)z- The residuals of the model. N)rfrGrrx fittedvalues)r}rfrGs r7rzAutoRegResults.resid^s9   ##%%T_&&'$*;;;r9c@|j|jng}t|}tj|jdz}d|d<|j}|jj}| |jdnd}|j ||z |z ||z }t|D]\}} || || <|S)z6Returns poly repr of an AR, (1 -phi1 L -phi2 L^2-...)Nrr) rcrr5rrerbrfrNrlr_r) r}rk_ar ar_paramsrrNk_exogrrrs r7 _lag_reprzAutoRegResults._lag_reprgs#'=#<$--"7||HT]Q.//  ! >z"&"2Aho6F9JJK(( ( (FAs$QiZIcNNr9c|}|jddkrtjdStj|dzS)z The roots of the AR process. The roots are the solution to (1 - arparams[0]*z - arparams[1]*z**2 -...- arparams[p-1]*z**k_ar) = 0. Stability requires that the roots in modulus lie outside the unit circle. rrr+)rrlr5rroots)r}lag_reprs r7rzAutoRegResults.rootsusH>>## >!  ! !8A;; x!!R''r9cn|j}tj|j|jdtjzz S)z Returns the frequency of the AR roots. This is the solution, x, to z = abs(z)*exp(2j*np.pi*x) where z are the roots. r3)rr5arctan2imagrealr)r}zs r7arfreqzAutoRegResults.arfreqs, Jz!&!&))QY77r9cZ|j|j|jdS)z The in-sample predicted values of the fitted AR model. The `k_ar` initial values are computed via the Kalman Filter if the model is fit by `mle`. N)rfr?rrxrs r7rzAutoRegResults.fittedvaluess)z!!$+..t/@/@AAr9c0ddlm}t|dd}t|dd}||jn|}|jjd}|t |dzd }||j|d | }gd }|d krtdd |z }nStj tj d |d z|z dtj }| t}||d<tjd |d zd}tj|||S)at Ljung-Box test for residual serial correlation Parameters ---------- lags : int The maximum number of lags to use in the test. Jointly tests that all autocorrelations up to and including lag j are zero for j = 1, 2, ..., lags. If None, uses min(10, nobs // 5). model_df : int The model degree of freedom to use when adjusting computing the test statistic to account for parameter estimation. If None, uses the number of AR lags included in the model. Returns ------- output : DataFrame DataFrame containing three columns: the test statistic, the p-value of the test, and the degree of freedom used in the test. Notes ----- Null hypothesis is no serial correlation. The the test degree-of-freedom is 0 or negative once accounting for model_df, then the test statistic's p-value is missing. See Also -------- statsmodels.stats.diagnostic.acorr_ljungbox Ljung-Box test for serial correlation. r)acorr_ljungboxrHTr\rN F)rH boxpiercemodel_df)z Ljung-Boxz LB P-valueDFrdfLagnamerr])statsmodels.stats.diagnosticrrrrrlminrr5cliprkinfastyper/rr r) r}rHrrnobs_effective test_statscolsrr]s r7test_serial_correlationz&AutoRegResults.test_serial_correlations;D @?????ft444Hj4@@@$,$44==()!, <~*B//D#^ J    100 199QH %%BB1dQh//(:ArvFFB3B 4 a666|JEBBBBr9c^ddlm}gd}tj||j|S)a Test for normality of standardized residuals. Returns ------- Series Series containing four values, the test statistic and its p-value, the skewness and the kurtosis. Notes ----- Null hypothesis is normality. See Also -------- statsmodels.stats.stattools.jarque_bera The Jarque-Bera test of normality. r) jarque_bera)z Jarque-BeraP-valueSkewnessKurtosisr)statsmodels.stats.stattoolsrrrr)r}rr]s r7test_normalityzAutoRegResults.test_normalitysB( <;;;;;BBByTZ00>>>>r9cddlm}t|dd}|jjd}|t |dzd}g}t d |d zD]8}||j| }||d|d |g9tj d |d zd }gd }tj |||S)a ARCH-LM test of residual heteroskedasticity Parameters ---------- lags : int The maximum number of lags to use in the test. Jointly tests that all squared autocorrelations up to and including lag j are zero for j = 1, 2, ..., lags. If None, uses lag=12*(nobs/100)^{1/4}. Returns ------- Series Series containing the test statistic and its p-values. See Also -------- statsmodels.stats.diagnostic.het_arch ARCH-LM test. statsmodels.stats.diagnostic.acorr_lm LM test for autocorrelation. r)het_archrHTr\Nrrr)nlagsrr)zARCH-LMrrr) rrrrrlrrrhrr r) r}rHrroutrrr]rs r7test_heteroskedasticityz&AutoRegResults.test_heteroskedasticitys. :99999ft444)!, <~*B//DD1H%% . .C(4:S111C JJAA, - - - - a666+++|CU;;;;r9cddlm}|dg}t}|}|j|jdk}dt |jD}d}|j drZ||dgt|j zdd| }|j ||j ||}d }||jgt|jd d| }|j ||j ||} d t | jD}d}||dgt| j zd d| }|j ||S)a= Returns a summary containing standard model diagnostic tests Returns ------- Summary A summary instance with panels for serial correlation tests, normality tests and heteroskedasticity tests. See Also -------- test_serial_correlation Test models residuals for serial correlation. test_normality Test models residuals for deviations from normality. test_heteroskedasticity Test models residuals for conditional heteroskedasticity. r SimpleTabler]c&g|]\}}|dzg|zSrrrrrows r7rz5AutoRegResults.diagnostic_summary..-s&LLLFAs1q5'C-LLLr9)%10d%10.3frrrzTest of No Serial Correlationr)headerstitle header_align data_fmts)rrrrzTest of Normalityc&g|]\}}|dzg|zSrrrs r7rz5AutoRegResults.diagnostic_summary..Es3   $aQUGcM   r9z$Test of Conditional Homoskedasticity)statsmodels.iolib.tablerrrrrrvaluestolistrlrrtablesrhrr]r) r}rspacersmryscrrtabjbarch_lms r7diagnostic_summaryz!AutoRegResults.diagnostic_summarys& 877777bT""yy  ) ) + + VBEAI LLi 8H8H8J8J.K.KLLL8 8A; '+$rz"2"225 # C K  s # # # K  v & & &  " "< k YKNN%     3 6"""..00  (1'.2G2G2I2I(J(J   9 k Gd7?3338     3 r9rcL|j|j|||||S)NrX)rfr?r_)r}rrrrNrs r7r?zAutoRegResults.predictSs7z!! L "   r9ct||||||}tj||j}tj|tj|<|dn|}||jjdn|}|j||\}}} }| dkr]| } t| tj d| } |jtj | dzz|| d<t|tjrtj||j}t#||S) aY 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. Returns ------- PredictionResults Prediction results with mean and prediction intervals rXNrr+r)rHr3r)r?r5 full_likerrisnanrfrr-rr!onescumsumrgrrr]r#) r}rrrrNrmeanmean_varr0oosrmas r7get_predictionzAutoRegResults.get_prediction`s'V||S'x  <dk22#%6$ ]'*{dj##z77sCC 1c1 77((IBGAJJS999B"kBIb!e,<,<plotr5rconf_int get_lines get_xdata fill_betweenlegend)r} predictionsrrrrfigfigsizerrr0raxrcilowerupperrr,s r7_plot_predictionsz AutoRegResults._plot_predictionss KJJJJJJJ nS'**]'*{dj##z77sCC 1c1 __S ! !) S $ ** (y#' 3  Qj111  5$K007788BsdeeQh<SDEE1H5E5y::::E r",,..A OO3$%%     f  r9)predict_params皙?Tc l||||||} || |||||| S)a1 Plot in- and out-of-sample predictions Parameters ---------- %(predict_params)s alpha : {float, None} The tail probability not covered by the confidence interval. Must be in (0, 1). Confidence interval is constructed assuming normally distributed shocks. If None, figure will not show the confidence interval. in_sample : bool Flag indicating whether to include the in-sample period in the plot. fig : Figure An existing figure handle. If not provided, a new figure is created. figsize: tuple[float, float] Tuple containing the figure size values. Returns ------- Figure Figure handle containing the plot. rX)rr) r}rrrrNrrrrrrs r7 plot_predictzAutoRegResults.plot_predictsSJ))S'x*  %% UIsG   r9rcddlm}m}||||}|j}|d}t |jjdrD|jj8|jjj }||jj d}n3|jj } | tj |jj dz}|tj|jz } ||| |d|d|dd||d|d|d | tj|} |d }|| d d t-| } d} tj| d| d}||| |d||t1j|d|| ||d|d}ddlm}|| d||d|d}ddlm}|||||d|dd|S)aO Diagnostic plots for standardized residuals Parameters ---------- lags : int, optional Number of lags to include in the correlogram. Default is 10. fig : Figure, optional If given, subplots are created in this figure instead of in a new figure. Note that the 2x2 grid will be created in the provided figure using `fig.add_subplot()`. figsize : tuple, optional If a figure is created, this argument allows specifying a size. The tuple is (width, height). Notes ----- Produces a 2x2 plot grid with the following plots (ordered clockwise from top left): 1. Standardized residuals over time 2. Histogram plus estimated density of standardized residuals, along with a Normal(0,1) density plotted for reference. 3. Normal Q-Q plot, with Normal reference line. 4. Correlogram See Also -------- statsmodels.graphics.gofplots.qqplot statsmodels.graphics.tsaplots.plot_acf rrdatesNr+r)rzStandardized residualTHist)densityr)g\(\g\(\@rKDE)rzN(0,1)z Histogram plus estimated density)qqplots)linerz Normal Q-Q)plot_acf)rrH Correlogram) rrrrrrirfr:r _mpl_reprrPr5rkrlrurrhlinesset_xlim set_titlerhistrlinspacerpdfrstatsmodels.graphics.gofplotsrstatsmodels.graphics.tsaplotsr set_ylim)r}rHrrrrrrr,rP std_residstd_resid_nonmissingkdexlimrr s r7plot_diagnosticszAutoRegResults.plot_diagnosticss@ KJJJJJJJ nS'** __S ! ! 4:?G , , ;1L %//11A$*&(()AA ,IBIdj&6q&9:::ABGDK000  9 !QqT1R5 ,,, AaD!B%    ,--- )28E??);< __S ! ! $d&AAA9%%$ KQa ) ) 33q66''' 48A;;h/// D  7888__S ! !888888ysr**** \"""__S ! !::::::2D)))) ]### B r9c |j}|jjdz}d}|j}|jjK|jj}||dg}|d|ddzgz }n5t|tt|jj g}|jj}|jj rd|z}|j "t|j |j krd|z}|jj |d z }d |j d }t|jj} d | gfd ||zgfd|gfddd|dgfd|dgfg} dtt|jjgfdd|jzgfdd|jdzzgfdd|jzgfdd|jzgfdd|jzgfg} t+} | || | || ||ddd lm} |j rd!t5d|j dzD}|}|j}|j}t;j|}t;j|j |j!||f}| d"|Dgd#d$|%}| j"#||j$r.| j%| j%ng}| &||j$gz| S)&a Summarize the Model Parameters ---------- alpha : float, optional Significance level for the confidence intervals. Returns ------- smry : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary z Model ResultszConditional MLENz%m-%d-%Yz- r+zSeas. zRestr. z-X()zDep. Variable:zModel:zMethod:)zDate:N)zTime:NzSample:rr]rzNo. Observations:zLog Likelihoodz%#5.3fzS.D. of innovationsrAICBICHQIC)gleftgrightrF)rrrcg|]}d|zS)zAR.%drrs r7rz*AutoRegResults.summary..sHHHqw{HHHr9cbg|],}d|dzd|dzd|dzd|dzf-S)z%17.4frz%+17.4fjrr3r)rrs r7rz*AutoRegResults.summary..s\ !3q6)"SV+ 3q6) 3q6) r9)z Realz Imaginaryz Modulusz FrequencyRoots)rrstubs)'rfrrErxr:rstrftimerTrrjrLrrerNrrGrrryrr{radd_table_2colsadd_table_paramsrrrrrr5abs column_stackrrrrhrh extra_txt add_extra_txt)r}rrfrmethodrrsampleorderdep_nametop_left top_rightrrarstubsr(rr=modulusr: roots_tabler.s r7summaryzAutoRegResults.summarytsc& (+;;" 9? &IOEEl++J778F teBi00<<<= =FF%jj#c$)*>&?&?"@"@AF( :  %u$E < #DL(9(9DM(I(I%E :? & TME$DM$$$tz-.. z *   '  !    $ &)  !3s4:+;'<'<#=#="> ? 48 34 5 "X S0@%@$A B X() * X() * h*+ ,  yy  %     d%u=== 877777 = ,HHE!T]Q5F,G,GHHHGEJE;DfUmmG?EJ GT#JKKD%+ $ #K( K  { + + +   A*..*D"I   yD,>+?? @ @ @ r9c x|j} |j}|bt|tjtjfr|j}ntj|j d}| |}t||j |j |j||j|j|d }n>#t"$r1} d} | f| jz| _| | jd} ~ wwxYw|jdu|jdukr%|jt-dt-d|jI|jj d|jj dkr#t-d |jj dd |r|in|}|jd i|Sd } t1||j|j|j|j| } t;| S)a' Apply the fitted parameters to new data unrelated to the original data Creates a new result object using the current fitted parameters, applied to a completely new dataset that is assumed to be unrelated to the model's original data. The new results can then be used for analysis or forecasting. Parameters ---------- endog : array_like New observations from the modeled time-series process. exog : array_like, optional New observations of exogenous regressors, if applicable. refit : bool, optional Whether to re-fit the parameters, using the new dataset. Default is False (so parameters from the current results object are used to create the new results object). fit_kwargs : dict, optional Keyword arguments to pass to `fit` (if `refit=True`). Returns ------- AutoRegResults Updated results object containing results for the new dataset. See Also -------- AutoRegResults.append statsmodels.tsa.statespace.mlemodel.MLEResults.apply Notes ----- The `endog` argument to this method should consist of new observations that are not necessarily related to the original model's `endog` dataset. Care is needed when using deterministic processes with cyclical components such as seasonal dummies or Fourier series. These deterministic components will align to the first observation in the data and so it is essential that any new data have the same initial period. Examples -------- >>> import pandas as pd >>> from statsmodels.tsa.ar_model import AutoReg >>> index = pd.period_range(start='2000', periods=3, freq='Y') >>> original_observations = pd.Series([1.2, 1.5, 1.8], index=index) >>> mod = AutoReg(original_observations, lags=1, trend="n") >>> res = mod.fit() >>> print(res.params) y.L1 1.219512 dtype: float64 >>> print(res.fittedvalues) 2001 1.463415 2002 1.829268 Freq: A-DEC, dtype: float64 >>> print(res.forecast(1)) 2003 2.195122 Freq: A-DEC, dtype: float64 >>> new_index = pd.period_range(start='1980', periods=3, freq='Y') >>> new_observations = pd.Series([1.4, 0.3, 1.2], index=new_index) >>> new_res = res.apply(new_observations) >>> print(new_res.params) y.L1 1.219512 dtype: float64 >>> print(new_res.fittedvalues) 1981 1.707317 1982 0.365854 Freq: A-DEC, dtype: float64 >>> print(new_res.forecast(1)) 1983 1.463415 Freq: A-DEC, dtype: float64 NrF)rHrJrLrNrPrRrErFzAn exception occured during the creation of the cloned AutoReg instance when applying the existing model specification to the new data. The original traceback appears below.zFexog must be provided when the original model contained exog variableszHexog must be None when the original model did not contain exog variablesrzSThe number of exog variables passed must match the original number of exog values (rznParameters and standard errors were estimated using a different dataset and were then applied to this dataset.)rrir)rfrErgrrrr]r5rkrlapplyr+rrJrLrPrR ExceptionrRwith_traceback __traceback__rNr>rrrrgrrr) r}rGrNrefit fit_kwargsexistingrEr]modexcerrorsmry_txtrs r7r;zAutoRegResults.applys+Z: 8$2M(ebi%>??6!KEEIek!n55E - 3 3E : : %n!*",+   CC 8 8 8!  x#(*CH$$S%677 7 8 H (-4"7 8 8}( %!  M % #A&#(.*;;;D*2-*=a*@DDD   ))1zJ37((Z(( ( =   K  #  &*!    %S)))sBB&& C!0,CC!cZd fd }j}|jdu}||dukr|rd}nd}t|t|jjt jt jfr||jj|d}n&||j tj |dd}t|jj t jt jfr||jj |d }n(|&||jtj |dd} |||| S) a. Append observations to the ones used to fit the model Creates a new result object using the current fitted parameters where additional observations are appended to the data used to fit the model. The new results can then be used for analysis or forecasting. Parameters ---------- endog : array_like New observations from the modeled time-series process. exog : array_like, optional New observations of exogenous regressors, if applicable. refit : bool, optional Whether to re-fit the parameters, using the new dataset. Default is False (so parameters from the current results object are used to create the new results object). fit_kwargs : dict, optional Keyword arguments to pass to `fit` (if `refit=True`). Returns ------- AutoRegResults Updated results object containing results for the new dataset. See Also -------- AutoRegResults.apply statsmodels.tsa.statespace.mlemodel.MLEResults.append Notes ----- The endog and exog arguments to this method must be formatted in the same way (e.g. Pandas Series versus Numpy array) as were the endog and exog arrays passed to the original model. The endog argument to this method should consist of new observations that occurred directly after the last element of endog. For any other kind of dataset, see the apply method. Examples -------- >>> import pandas as pd >>> from statsmodels.tsa.ar_model import AutoReg >>> index = pd.period_range(start='2000', periods=3, freq='Y') >>> original_observations = pd.Series([1.2, 1.4, 1.8], index=index) >>> mod = AutoReg(original_observations, lags=1, trend="n") >>> res = mod.fit() >>> print(res.params) y.L1 1.235294 dtype: float64 >>> print(res.fittedvalues) 2001 1.482353 2002 1.729412 Freq: A-DEC, dtype: float64 >>> print(res.forecast(1)) 2003 2.223529 Freq: A-DEC, dtype: float64 >>> new_index = pd.period_range(start='2003', periods=3, freq='Y') >>> new_observations = pd.Series([2.1, 2.4, 2.7], index=new_index) >>> updated_res = res.append(new_observations) >>> print(updated_res.params) y.L1 1.235294 dtype: float64 >>> print(updated_res.fittedvalues) dtype: float64 2001 1.482353 2002 1.729412 2003 2.223529 2004 2.594118 2005 2.964706 Freq: A-DEC, dtype: float64 >>> print(updated_res.forecast(1)) 2006 3.335294 Freq: A-DEC, dtype: float64 Tcddlm}t|}t||st |d|d|jd|st j||gSt|}|t|zdz } j ||\}}}} || ||tj ||gdS) Nr) _check_indexz must have the same type as the z& used to originally create the model (z).r)rr4) #statsmodels.tsa.statespace.mlemodelrHtypergrnrEr5 concatenaterrfr-rconcat) orignewr use_pandasrHtyprrr0 append_ixr}s r7_checkz%AutoRegResults.append.._checks H H H H H Ht**Cc3'' EETEE47LEEE 3~tSk222IIE#c(("Q&C!%!A!A%!M!M Aq!Y LCt 4 4 4 49dC[q111 1r9Nz>Original model does not contain exog data but exog data passedz5Original model has exog data but not exog data passedrGF)rOrN)r?r@)T)rfrNr>rgr:rjrrrrGr5r orig_exogr;) r}rGrNr?r@rRrAno_exogerrs ` r7rhzAutoRegResults.appendis]` 2 2 2 2 2 2":-4' tt| $ $ N NS// ! hm.BL0I J J F8=3UGDDEEF 5 1 17uE hm- 2>> from statsmodels.tsa.ar_model import ar_select_order >>> data = sm.datasets.sunspots.load_pandas().data['SUNACTIVITY'] Determine the optimal lag structure >>> mod = ar_select_order(data, maxlag=13) >>> mod.ar_lags array([1, 2, 3, 4, 5, 6, 7, 8, 9]) Determine the optimal lag structure with seasonal terms >>> mod = ar_select_order(data, maxlag=13, seasonal=True, period=12) >>> mod.ar_lags array([1, 2, 3, 4, 5, 6, 7, 8, 9]) Globally determine the optimal lag structure >>> mod = ar_select_order(data, maxlag=13, glob=True) >>> mod.ar_lags array([1, 2, 9]) r_Nrr)dtypecz|j}|j}d|z t|jz}| t jdtjz|zdzzdz }t||||}ttj |}ttj |}ttj |}|||fS)Nr\r3r)rzrrr) rzrr8rr5rrr rrryrr{)rrzrrrryrr{s r7 compute_icsz$ar_select_order..compute_icsMsx<tgci000erva"%i&011A56:S   ~1377~1377 3S99C~r9ctjdtjjddf}t j|tjd}tjd|dd}|S)z0Fake mod and results to handle no regressor caser)rzrGrN)rrzrr k_constant)r rlr5rrr)rBrrrers r7 ic_no_dataz#ar_select_order..ic_no_data\s128QWQZO+D+D   k#rx{{++!'!*#a   {3r9FTc3K|]}|VdSrsr)rrs r7 z"ar_select_order..ps"44q444444r9r3r+ r`rY)ryrr{c |dSNrr)r,key_locs r7z!ar_select_order..sAaDMr9key)r+rNrlrBrr5rrMrrrhrrtuplerkint32viewuint8 unpackbitsreshapewhererAROrderSelectionResults)rGricglobrJrLrNrPrRrSrFfull_modr"r,base_colselicsrhrrrHbitsmasksmaskselected_modelrBrernrs @@@r7ar_select_orderrsx     H'/m&?HM  " "QE ; DAqwqzE!F*H '!'!*D ) ) )CJLC           1,1Hx&( ()vz"" 1 1A+/C8a<' (6#;;  Azz||,---a111c6##''))C44E!QUOO44444D *11dD JJkk#../ 0 0 0 0 1yF"(333AAAtG<yy""}T""**2r22q  A+/1q51A;3F0F+G44R4,DAEAQK'' ( (QQQZ  1 1D04C8f,, -6#;;  Azz||,---a111c6##''))C$*Q.//D *11dD JJkk#../ 0 0 0 01--b1G 1111 2 2 2CVAYN      C #3UHf E EEr9ceZdZdZdd ZeddZeddZeddZeddZ eddZ eddZ eddZ eddZ dS) ryzp Results from an AR order selection Contains the information criteria for all fitted model orders. rfr+r>list[tuple[int | tuple[int, ...], tuple[float, float, float]]]rJrrLrMrRrQc||_||_||_||_||_t |d}d|D|_t |d}d|D|_t |d}d|D|_dS)Nc|ddS)Nrrrrs r7roz2AROrderSelectionResults.__init__..!Qr9rpc&i|]\}}||dSrrrrqrs r7 z4AROrderSelectionResults.__init__.."555XS#S#a&555r9c|ddSrmrrs r7roz2AROrderSelectionResults.__init__..rr9c&i|]\}}||dSrrrs r7rz4AROrderSelectionResults.__init__..rr9c|ddS)Nrr3rrs r7roz2AROrderSelectionResults.__init__..s1ar9c&i|]\}}||dS)r3rrs r7rz4AROrderSelectionResults.__init__..s"777hc3c3q6777r9) _model_icsrbrcrdr_aic_bic_hqic) r}rfrrJrLrRryrr{s r7raz AROrderSelectionResults.__init__s   ! S//00055555 S//00055555 c0011177$777 r9r0c|jS)z:The model selected using the chosen information criterion.)rrs r7rfzAROrderSelectionResults.modelrr9c|jS)z4Flag indicating if a seasonal component is included.rrs r7rLz AROrderSelectionResults.seasonalrr9c|jS)z*The trend included in the model selection.rrs r7rJzAROrderSelectionResults.trendrr9c|jSrrrs r7rRzAROrderSelectionResults.periodrr9"dict[int | tuple[int, ...], float]c|jS)z The Akaike information criterion for the models fit. Returns ------- dict[tuple, float] )rrs r7ryzAROrderSelectionResults.aic yr9c|jS)z The Bayesian (Schwarz) information criteria for the models fit. Returns ------- dict[tuple, float] )rrs r7rzAROrderSelectionResults.bicrr9c|jS)z The Hannan-Quinn information criteria for the models fit. 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