M/Phc~dZddlmZddlZddlZddlmZddlm Z ddl m Z ddl m Z ddlmcmZddlmZdd lmZdd lmZdd lmZmZdd lmZdd lmZGdde j Z!ee j"jGdde j"Z#Gdde j$Z%ej&e%e#dS)z8 ARIMA model class. Author: Chad Fulton License: BSD-3 )AppenderN)_is_using_pandas)sarimax)MEMORY_CONSERVE)diff) yule_walker)burg)hannan_rissanen) innovationsinnovations_mle)gls)SARIMAXSpecificationcXeZdZdZ d fd Zed Z d fd ZxZS)ARIMAai Autoregressive Integrated Moving Average (ARIMA) model, and extensions This model is the basic interface for ARIMA-type models, including those with exogenous regressors and those with seasonal components. The most general form of the model is SARIMAX(p, d, q)x(P, D, Q, s). It also allows all specialized cases, including - autoregressive models: AR(p) - moving average models: MA(q) - mixed autoregressive moving average models: ARMA(p, q) - integration models: ARIMA(p, d, q) - seasonal models: SARIMA(P, D, Q, s) - regression with errors that follow one of the above ARIMA-type models 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. 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. trend : str{'n','c','t','ct'} or iterable, optional Parameter controlling the deterministic trend. Can be specified as a string where 'c' indicates a constant term, 't' indicates a linear trend in time, and 'ct' includes both. Can also be specified as an iterable defining a polynomial, as in `numpy.poly1d`, where `[1,1,0,1]` would denote :math:`a + bt + ct^3`. Default is 'c' for models without integration, and no trend for models with integration. Note that all trend terms are included in the model as exogenous regressors, which differs from how trends are included in ``SARIMAX`` models. See the Notes section for a precise definition of the treatment of trend terms. enforce_stationarity : bool, optional Whether or not to require the autoregressive parameters to correspond to a stationarity process. enforce_invertibility : bool, optional Whether or not to require the moving average parameters to correspond to an invertible process. 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. trend_offset : int, optional The offset at which to start time trend values. Default is 1, so that if `trend='t'` the trend is equal to 1, 2, ..., nobs. Typically is only set when the model created by extending a previous dataset. 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'. Notes ----- This model incorporates both exogenous regressors and trend components through "regression with ARIMA errors". This differs from the specification estimated using ``SARIMAX`` which treats the trend components separately from any included exogenous regressors. The full specification of the model estimated here is: .. math:: Y_{t}-\delta_{0}-\delta_{1}t-\ldots-\delta_{k}t^{k}-X_{t}\beta & =\epsilon_{t} \\ \left(1-L\right)^{d}\left(1-L^{s}\right)^{D}\Phi\left(L\right) \Phi_{s}\left(L\right)\epsilon_{t} & =\Theta\left(L\right)\Theta_{s}\left(L\right)\eta_{t} where :math:`\eta_t \sim WN(0,\sigma^2)` is a white noise process, L is the lag operator, and :math:`G(L)` are lag polynomials corresponding to the autoregressive (:math:`\Phi`), seasonal autoregressive (:math:`\Phi_s`), moving average (:math:`\Theta`), and seasonal moving average components (:math:`\Theta_s`). `enforce_stationarity` and `enforce_invertibility` are specified in the constructor because they affect loglikelihood computations, and so should not be changed on the fly. This is why they are not instead included as arguments to the `fit` method. See the notebook `ARMA: Sunspots Data <../examples/notebooks/generated/tsa_arma_0.html>`__ and `ARMA: Artificial Data <../examples/notebooks/generated/tsa_arma_1.html>`__ for an overview. .. todo:: should concentrate_scale=True by default Examples -------- >>> mod = sm.tsa.arima.ARIMA(endog, order=(1, 0, 0)) >>> res = mod.fit() >>> print(res.summary()) NrrrrrrrTFnonecV|ddkp |ddk}||sd}n|d}t|||||dd|| | | | |  |_|jjjj}t |jjdk}|rBtj|jj}||d|dzkrtdd}|Ft|dr|j dd|jj df}n|dd|jj df}t||d|||||| | | |  ||_||_||j|jj d|_nd|_|jj|_|jj |_ gdfd |jD|_dS) Nrrcn) exogorderseasonal_ordertrendenforce_stationarityenforce_invertibilityconcentrate_scale trend_offsetdatesfreqmissingvalidate_specificationa{In models with integration (`d > 0`) or seasonal integration (`D > 0`), trend terms of lower order than `d + D` cannot be (as they would be eliminated due to the differencing operation). For example, a constant cannot be included in an ARIMA(1, 1, 1) model, but including a linear trend, which would have the same effect as fitting a constant to the differenced data, is allowed.) rrrrrrr r!r"r#)measurement_errortime_varying_regressionmle_regressionsimple_differencinghamilton_representationcg|]}|v| Sr*).0keyunuseds [/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tsa/arima/model.py z"ARIMA.__init__..s#OOO3S=N=N3=N=N=N)r _spec_arima_modeldata orig_exoglen trend_termsnpmin ValueErrorrilock_trendsuper__init__r _input_exog exog_names_input_exog_namesk_exog _init_keys)selfendogrrrrrrrrr r!r"r# integrated has_trend lowest_trend input_exogr- __class__s @r.r=zARIMA.__init__s%1X\:^A%6%: ==EE ]E0 E.d$/ldG#9 ;;; &+5(4559  $6$"2">??LeAh):::: #$$$  d++ @!Yqqq$*:*B*C*C'CD !!!!T%5%=%>%>">?  4t5)!5"7/u44J  L L L &  %)_T5E5M5N5N%OD " "%)D " &- '/ ---POOO$/OOOr0c"dttfiS)Nfit) ARIMAResultsARIMAResultsWrapper)rCs r. _res_classeszARIMA._res_classess &9:;;r0c ||j|nd}ddg} |jr|| vrtd| d|d|i}g} |dkrgd} n |dkrd g} | D]/}||vrtd |d |d t ||||<0|i}|%|d vrtd|z||d<||d<||d<d}d}|jjdu}|s|dkr|rM|s|I|dkrC|jrt dt|jf|j|j |j d||d|\}}n|dkrtd|z| ddtj d,| | || d|}| s |j|_n|j}|jj }|jj }|jjrt#jd|zdt'||jj|jj|jj}|ddkr|dd|df}|ddkr|dd|d|df}|jr|j|d<|d krt1|f|ddd!|\}}n|d"krt3|f|ddd!|\}}ni|dkr!t5|f|d|ddd#|\}}nB|d$kr"t7|f|ddd%|\}}|d&}n|dkrt9|f||dd'|\}}||jr&|jjdkr|jstd(|j r&|jj!dkr|j"std)| r|j#}n| r+|j$j%}|j$&tN|j$j(s|j$j)s |j$j*r|j+}n|j,}||j#d*d*|| +}||_| r|j$&||S)-a^ Fit (estimate) the parameters of the model. Parameters ---------- start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. If None, the default is given by Model.start_params. transformed : bool, optional Whether or not `start_params` is already transformed. Default is True. includes_fixed : bool, optional If parameters were previously fixed with the `fix_params` method, this argument describes whether or not `start_params` also includes the fixed parameters, in addition to the free parameters. Default is False. method : str, optional The method used for estimating the parameters of the model. Valid options include 'statespace', 'innovations_mle', 'hannan_rissanen', 'burg', 'innovations', and 'yule_walker'. Not all options are available for every specification (for example 'yule_walker' can only be used with AR(p) models). method_kwargs : dict, optional Arguments to pass to the fit function for the parameter estimator described by the `method` argument. gls : bool, optional Whether or not to use generalized least squares (GLS) to estimate regression effects. The default is False if `method='statespace'` and is True otherwise. gls_kwargs : dict, optional Arguments to pass to the GLS estimation fit method. Only applicable if GLS estimation is used (see `gls` argument for details). cov_type : str, optional The `cov_type` keyword governs the method for calculating the covariance matrix of parameter estimates. Can be one of: - 'opg' for the outer product of gradient estimator - 'oim' for the observed information matrix estimator, calculated using the method of Harvey (1989) - 'approx' for the observed information matrix estimator, calculated using a numerical approximation of the Hessian matrix. - 'robust' for an approximate (quasi-maximum likelihood) covariance matrix that may be valid even in the presence of some misspecifications. Intermediate calculations use the 'oim' method. - 'robust_approx' is the same as 'robust' except that the intermediate calculations use the 'approx' method. - 'none' for no covariance matrix calculation. Default is 'opg' unless memory conservation is used to avoid computing the loglikelihood values for each observation, in which case the default is 'oim'. cov_kwds : dict or None, optional A dictionary of arguments affecting covariance matrix computation. **opg, oim, approx, robust, robust_approx** - 'approx_complex_step' : bool, optional - If True, numerical approximations are computed using complex-step methods. If False, numerical approximations are computed using finite difference methods. Default is True. - 'approx_centered' : bool, optional - If True, numerical approximations computed using finite difference methods use a centered approximation. Default is False. return_params : bool, optional Whether or not to return only the array of maximizing parameters. Default is False. low_memory : bool, optional If set to True, techniques are applied to substantially reduce memory usage. If used, some features of the results object will not be available (including smoothed results and in-sample prediction), although out-of-sample forecasting is possible. Default is False. Returns ------- ARIMAResults Examples -------- >>> mod = sm.tsa.arima.ARIMA(endog, order=(1, 0, 0)) >>> res = mod.fit() >>> print(res.summary()) N statespacer z2When parameters have been fixed, only the methods z can be used; got 'z'.)rrrr rz'Cannot override model level value for "z" when method="z".)rPr z_Estimation method "%s" does not use starting parameters, but `start_params` argument was given. start_params transformedincludes_fixedzIGLS estimation is not yet implemented for the case with fixed parameters.F)rrrinclude_constantarma_estimatorarma_estimator_kwargszkIf `exog` is given and GLS is disabled (`gls=False`), then the only valid method is 'statespace'. Got '%s'.dispr) return_params low_memorycov_typecov_kwdszsProvided `endog` series has been differenced to eliminate integration prior to parameter estimation by method "%s".) stacklevel)k_diffk_seasonal_diffseasonal_periodsr fixed_paramsr)ar_orderdemeanr )rcma_orderrdr )rerd)rrrdzNon-stationary autoregressive parameters found with `enforce_stationarity=True`. Consider setting it to False or using a different estimation method, such as method="statespace".zNon-invertible moving average parameters found with `enforce_invertibility=True`. Consider setting it to False or using a different estimation method, such as method="statespace".T)rRrSrZr[r*)-r1validate_estimator_has_fixed_paramsr9getattrrNotImplementedError estimate_glsrDrr setdefaultr<rKmlefit fit_details is_integratedwarningswarnr seasonal_diffr` _fixed_paramscopyrr r r r rmax_reduced_ar_order is_stationaryrmax_reduced_ma_order is_invertibleparamsssmconserve_memoryset_conserve_memoryrmemory_no_predictedmemory_no_gainmemory_no_smoothingfiltersmooth)rCrQrRrSmethod method_kwargsr gls_kwargsrZr[rXrYmethods_with_fixed_paramsrequired_kwargsnameprnhas_exogresrDrrr{funcrIs r.rKz ARIMA.fitst     / / 7 7 7 7 "F&23D$E!  ! f4M&M&ML,LLAGLLL   M \ ! !444OO ( ( (67O# 6 6D}$$ j9=vvv"GHHH")$"5"5M$    J  #>>> "+-3"4555-9M. )+6M- (.DE*+----$"2"7$($4$B%)%5%FHHH8a<<"1Xq%(3E!!$q((&4Q&7N1OH00AAAH0'DH4K'87';DD;Dd18d$,xAAA#.BH00AAA r0) NrrNTTFrNNrT) NTFNNNNNNFF) __name__ __module__ __qualname____doc__r=propertyrNrK __classcell__rIs@r.rrsjjV0948BF@DCG TPTPTPTPTPTPl<<X<GLBF8=MMMMMMMMMMr0rc`eZdZeejjjdfd ZxZS)rLNFc "|N|jjj}|jj}|jj|jj_|jj|j_t j|f|||d|}|||jj_||j_|S)N)rrefit fit_kwargs)modelr3r4r?r>r@r<append) rCrDrrrkwargsr4r?outrIs r.rzARIMAResults.appends   1I.J(, (>DJO %$(J$@DJ !eggnU>U(2>>6<>>  (1DJO %$.DJ ! r0)NFN) rrrrrSARIMAXResultsrrrrs@r.rLrLs]Xg$+34454r0rLceZdZiZejejjeZiZ ejejj e Z dS)rMN) rrr_attrswrap union_dictsrSARIMAXResultsWrapper _wrap_attrs_methods _wrap_methodsr*r0r.rMrMsV F"$"%16;;KH$D$%3X??MMMr0rM)'rstatsmodels.compat.pandasrrpnumpyr7statsmodels.tools.datarstatsmodels.tsa.statespacer(statsmodels.tsa.statespace.kalman_filterr statsmodels.tsa.statespace.toolsrstatsmodels.base.wrapperbasewrapperr,statsmodels.tsa.arima.estimators.yule_walkerr%statsmodels.tsa.arima.estimators.burgr 0statsmodels.tsa.arima.estimators.hannan_rissanenr ,statsmodels.tsa.arima.estimators.innovationsr r $statsmodels.tsa.arima.estimators.glsr rk#statsmodels.tsa.arima.specificationrSARIMAXrrrLrrMpopulate_wrapperr*r0r.rs /.....333333......DDDDDD111111'''''''''DDDDDD666666LLLLLL""""""""DDDDDDDDDDDDSSSSSGOSSSl ' ())7)*)6?????'7???)<88888r0