Dj ddlZddlZddlmcmZddlZddlZddl m Z m Z ddl m Z ddlmZddlmZddlmZdd lmZdd lmZmZmZdd lmZdd lmZdd l m!Z!m"Z"m#Z#m$Z$ddl%m&Z&ddl'm(Z(m)Z)ddl*Z*ddgZ+dZ,dZ-dZ.dZ/GddeZ0y)N) gaussian_kdenorm) check_array)api) _validation) BaseARIMA)DTYPE)check_is_fittedif_delegate_has_method safe_indexing) statsmodels) matplotlib)if_has_delegate is_iterable check_endog check_exog)_get_plt)diff_invdiffARIMAARMAtoMAct|}t|}tj|}td|D]R}||kr||nd}tdt |dz|D]#}|||||z dz dk\r |||z dz ndzz }%|||<T|S)ar Convert ARMA coefficients to infinite MA coefficients. Compute coefficients of MA model equivalent to given ARMA model. MA coefficients are cut off at max_deg. The same function as ARMAtoMA() in stats library of R Parameters ---------- ar : array-like, shape=(n_orders,) The array of AR coefficients. ma : array-like, shape=(n_orders,) The array of MA coefficients. max_deg : int Coefficients are computed up to the order of max_deg. Returns ------- np.ndarray, shape=(max_deg,) Equivalent MA coefficients. Notes ----- Here is the derivation. Suppose ARMA model is defined as .. math:: x_t - ar_1*x_{t-1} - ar_2*x_{t-2} - ... - ar_p*x_{t-p}\\ = e_t + ma_1*e_{t-1} + ma_2*e_{t-2} + ... + ma_q*e_{t-q} namely .. math:: (1 - \sum_{i=1}^p[ar_i*B^i]) x_t = (1 + \sum_{i=1}^q[ma_i*B^i]) e_t where :math:`B` is a backward operator. Equivalent MA model is .. math:: x_t = (1 - \sum_{i=1}^p[ar_i*B^i])^{-1}\\ * (1 + \sum_{i=1}^q[ma_i*B^i]) e_t\\ = (1 + \sum_{i=1}[ema_i*B^i]) e_t where :math:``ema_i`` is a coefficient of equivalent MA model. The :math:``ema_i`` satisfies .. math:: (1 - \sum_{i=1}^p[ar_i*B^i]) * (1 + \sum_{i=1}[ema_i*B^i]) \\ = 1 + \sum_{i=1}^q[ma_i*B^i] thus .. math:: \sum_{i=1}[ema_i*B^i] = \sum_{i=1}^p[ar_i*B^i] \\ + \sum_{i=1}^p[ar_i*B^i] * \sum_{j=1}[ema_j*B^j] \\ + \Sum_{i=1}^q[ma_i*B^i] therefore .. math:: ema_i = ar_i (but 0 if i>p) \\ + \Sum_{j=1}^{min(i-1,p)}[ar_j*ema_{i-j}] + ma_i(but 0 if i>q) \\ = \sum_{j=1}{min(i,p)}[ar_j*ema_{i-j}(but 1 if j=i)] \\ + ma_i(but 0 if i>q) Examples -------- >>> ar = np.array([0.1]) >>> ma = np.empty(0) >>> ARMAtoMA(ar, ma, 3) array[0.1, 0.01, 0.001] rgr?)lennpemptyrangemin) armamax_degpqemaitempjs XC:\Crop_Prediction\Backend\crop-ai-system\venv\Lib\site-packages\pmdarima/arima/arima.pyrr's@ BA BA ((7 C 1g Ar!u3q#a!eQ-( HA BqEq1uqyA~SQ^3G GD HA  Jcn|j}|j}|r|dz }|d|z|||z dz z dz zzS)z2Compute the corrected Akaike Information Criterionrg@r)aicdf_model) model_resultsnobs add_constantr-r.s r*_aiccr2rsN   C%%H h$$/B*>"?""DE EEr+c|jdk(rtj||fStj|j|fddtjfS)zAppend to the endogenous array Parameters ---------- endog : np.ndarray, shape=(n_samples, [1]) The existing endogenous array new_y : np.ndarray, shape=(n_samples) The new endogenous array to append rN)ndimr concatenateravelnewaxis)endognew_ys r*_append_to_endogr:~sO  a >>5%. )>  u-.q"**}=>r+c d|jd|||d|}|j}|j|}|jdrL|jj } |jj } |jj} |jj} | dkDrC| dk(r| n t| | | } tj| | d|}t|d| }|d| zd}| dkDr:| dkDr5tj| | | z d|}t|| | }|d| z| zd}|j}tjtj dd g| }tj"| dz}d|d<d|d <tj|| }tj$|tj$||dd }|j&dd}||z }t)|||}|j*d}tj,tjd||z|z}|j.j0d|dz z g|j2}||tj4|zz |dddf<||tj4|zz|dddf<t7|dd d }t9|d d}||fS)aMCompute the prediction for a SARIMAX and get a conf interval Unfortunately, SARIMAX does not really provide a nice way to get the confidence intervals out of the box, so we have to perform the ``get_prediction`` code here and unpack the confidence intervals manually. Notes ----- For internal use only. )startendexogalphasimple_differencingrNrr rgFT)dtypecopypreserve_series)rDrC)get_predictionpredicted_meanconf_int specificationmodel orig_endog orig_k_difforig_k_seasonal_diffseasonal_periodsrrappendrpolynomial_reduced_ar np_polynomialpolypowarrayzerospolymulpolynomial_reduced_mar_params_variancecumsumdistppf dist_argssqrtrr) arima_resr<r=Xr@kwargsresultsfrIy_orgdDperiody_sdifff_tempar_poly poly_diffsdiff poly_sdiffr!r" n_predMinus1r&sigma2varr%y_preds r*$_seasonal_prediction_with_confidencerqs$'i&&    G Ae,H45** OO ' ' OO 0 011 q5 Ave4vq+AGYYwrs|Q/Ffa+FAx A q5VaZYYuq6z]^4a8Fffa0FA()A11!))"((B9*=qA !$ab "**5!4 jj"**Y "CDQRH H  , ,QR 0U{ r2|,++A.ii "cCi01F: GLL  R%!)^ @g.?.? @Q--AQ--A $UD IF8%t Fit on: [0, 1, 2, 3, 4] > Score on: [5, 6] > Append [5, 6] to end of self.arima_res_.data.endog values scoring : str or callable, optional (default='mse') If performing validation (i.e., if ``out_of_sample_size`` > 0), the metric to use for scoring the out-of-sample data: * If a string, must be a valid metric name importable from ``sklearn.metrics``. * If a callable, must adhere to the function signature:: def foo_loss(y_true, y_pred) Note that models are selected by *minimizing* loss. If using a maximizing metric (such as ``sklearn.metrics.r2_score``), it is the user's responsibility to wrap the function such that it returns a negative value for minimizing. scoring_args : dict, optional (default=None) A dictionary of key-word arguments to be passed to the ``scoring`` metric. trend : str or None, optional (default=None) The trend parameter. If ``with_intercept`` is True, ``trend`` will be used. If ``with_intercept`` is False, the trend will be set to a no- intercept value. If None and ``with_intercept``, 'c' will be used as a default. with_intercept : bool, optional (default=True) Whether to include an intercept term. Default is True. **sarimax_kwargs : keyword args, optional Optional arguments to pass to the SARIMAX constructor. Examples of potentially valuable kwargs: - time_varying_regression : boolean Whether or not coefficients on the exogenous regressors are allowed to vary over time. - enforce_stationarity : boolean Whether or not to transform the AR parameters to enforce stationarity in the auto-regressive component of the model. - enforce_invertibility : boolean Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. - simple_differencing : boolean Whether or not to use partially conditional maximum likelihood estimation for seasonal ARIMA models. If True, differencing is performed prior to estimation, which discards the first :math:`s D + d` initial rows but results in a smaller state-space formulation. If False, the full SARIMAX model is put in state-space form so that all datapoints can be used in estimation. Default is False. - measurement_error: boolean Whether or not to assume the endogenous observations endog were measured with error. Default is False. - mle_regression : boolean Whether or not to use estimate the regression coefficients for the exogenous variables as part of maximum likelihood estimation or through the Kalman filter (i.e. recursive least squares). If time_varying_regression is True, this must be set to False. Default is True. - hamilton_representation : boolean Whether or not to use the Hamilton representation of an ARMA process (if True) or the Harvey representation (if False). Default is False. - concentrate_scale : boolean Whether or not to concentrate the scale (variance of the error term) out of the likelihood. This reduces the number of parameters estimated by maximum likelihood by one, but standard errors will then not be available for the scale parameter. Attributes ---------- arima_res_ : ModelResultsWrapper The model results, per statsmodels endog_index_ : pd.Series or None If the fitted endog array is a ``pd.Series``, this value will be non-None and is used to validate args for in-sample predictions with non-integer start/end indices oob_ : float The MAE or MSE of the out-of-sample records, if ``out_of_sample_size`` is > 0, else np.nan oob_preds_ : np.ndarray or None The predictions for the out-of-sample records, if ``out_of_sample_size`` is > 0, else None Notes ----- * The model internally wraps the statsmodels `SARIMAX class `_ * After the model fit, many more methods will become available to the fitted model (i.e., :func:`pvalues`, :func:`params`, etc.). These are delegate methods which wrap the internal ARIMA results instance. See Also -------- :func:`pmdarima.arima.auto_arima` References ---------- .. [1] https://wikipedia.org/wiki/Autoregressive_integrated_moving_average c  Xtt| ||_||_||_||_||_||_||_ ||_ | |_ | |_ | |_ dD]>\} }| j| dsd| z}|r|dz }tj |t"@| |_y)N))dispT)callbackT) transparamsF)solverFzT'%s' is deprecated in the ARIMA constructor and will be removed in a future release.z Pass via **fit_kwargs instead)superr__init__orderseasonal_order start_paramsmethodmaxitersuppress_warningsout_of_sample_sizescoring scoring_argstrendwith_interceptpopwarningswarnDeprecationWarningsarimax_kwargs)selfrzr{r|r}r~rrrrrrrdeprecated_key still_in_usemsg __class__s r*ryzARIMA.__init__s$ eT#% ,(  !2"4 ( ,-# 7 (NL !!.$79;IJ;;C c#56 7-r+c fd}jrDtjd5tjd|\}_dddn|\}_t j jdu_jd_ tj_ S#1swY]xYw)z Internal fitc : j} j}| td| jrd} jsin j}t j j}tjjjd j||d|} jd j} j}| td jd|} jdd}|j d ||||d  }||fS) Nz$Expected non-None value for `method`c)r8r>rzr{rr|z%Expected non-None value for `maxiter`r~rtr)r|r}r~rtrF)r}r ValueErrorrr sm_compatcheck_seasonal_orderr{smtsa statespaceSARIMAXrzrr|r~fit) r}rrr{arimar|_maxiterrtfittedr_fit_argsrys r* _fit_wrapperz ARIMA._fit.._fit_wrappers7[[FJJE~ !GHH }!4!4--43F3F ..t/B/BC FF%%--"atzz-"! "E$<<8I8IJL||H !HII ||Ix8H<<*DUYY)    F&= r+FrecordignoreNr) rrcatch_warnings simplefilter arima_res_r bind_df_modelfit_with_exog_shapenobs_pmdarima __version__ pkg_version_)rrr_rrrs```` r*_fitz ARIMA._fits/ !d  ! !((6 6%%h/'3~$T_ 6 6$0> C T__5 tmWWQZ %00 ' 6 6s %CC c t|td}|jd}t|tj r |j nd|_|t|ddt}|j}tj|j}t|d}||k\r tdd}d}|rO|| d}|d| }|A|jd} t|t!| |z | }t|t!d| |z }|j"||fi||Y|j%||} |j&sin |j&} ||| fi| |_| |_|j,||fi||St.j0|_d|_|S) aDFit an ARIMA to a vector, ``y``, of observations with an optional matrix of ``X`` variables. Parameters ---------- y : array-like or iterable, shape=(n_samples,) The time-series to which to fit the ``ARIMA`` estimator. This may either be a Pandas ``Series`` object (statsmodels can internally use the dates in the index), or a numpy array. This should be a one-dimensional array of floats, and should not contain any ``np.nan`` or ``np.inf`` values. X : array-like, shape=[n_obs, n_vars], optional (default=None) An optional 2-d array of exogenous variables. If provided, these variables are used as additional features in the regression operation. This should not include a constant or trend. Note that if an ``ARIMA`` is fit on exogenous features, it must be provided exogenous features for making predictions. **fit_args : dict or kwargs Any keyword arguments to pass to the statsmodels ARIMA fit. TrCrErNF)force_all_finiterDrCz7out-of-sample size must be less than number of samples!) n_periodsr_)rr r isinstancepdSeriesindex endog_index_rrvalget_scoring_metricrmaxrrslicerpredictroob_ oob_preds_updaternan) rrr_r n_samplescvr cv_samplescv_exogn_exogpredrs r*rz ARIMA.fits.  =GGAJ (2!RYY'?AGGT =1u5NA $ $((6QZ ?+, ,   B34J$B3A}'5"f+EF!!U1frk%:;  !Q#(#  !<<"<8D%)%6%62Dr<r=dynamiczUCannot produce in-sample confidence intervals for dynamic=True. Setting dynamic=FalseF)r^r<r=r_r@r) r rzrnumbersIntegralrrrrrrrq) rr_r<r=rreturn_conf_intr@r`rdresults_wrapperpredsrIs r*predict_in_samplezARIMA.predict_in_sample|sz l+ JJqM eW-- .519rparamsr) rrr_r~r` model_resrrrexog_dimX_primers r*rz ARIMA.updateusoB l+OO 1~A  =GGAJ    Q  =__++F ww FHwwqzV# /x8$:Q(" 3I;d6(!L JJ' (<(|jjdd|i|S)aReturns the confidence interval of the fitted parameters. Returns ------- alpha : float, optional (default=0.05) The significance level for the confidence interval. ie., the default alpha = .05 returns a 95% confidence interval. **kwargs : keyword args or dict Keyword arguments to pass to the confidence interval function. Could include 'cols' or 'method' r@rF)rrI)rr@r`s r*rIzARIMA.conf_int@s#(t''>e>v>>r+c.|jjS)zThe model degrees of freedom: ``k_exog`` + ``k_trend`` + ``k_ar`` + ``k_ma``. Returns ------- df_model : array-like The degrees of freedom in the model. )rr.rs r*r.zARIMA.df_modelPs'''r+c.|jjS)zGet the residual degrees of freedom: :code:`nobs - df_model` Returns ------- df_resid : array-like The residual degrees of freedom. )rdf_residrs r*r zARIMA.df_resid\s'''r+c.|jjS)zGet the fitted values from the model Returns ------- fittedvalues : array-like The predicted values for the original series )r fittedvaluesrs r*r zARIMA.fittedvaluesis+++r+c.|jjS)aGet the Hannan-Quinn Information Criterion: :code:`-2 * llf + 2 * (`df_model`) * log(log(nobs))` Like :func:`bic` if the model is fit using conditional sum of squares then the ``k_ar`` pre-sample observations are not counted in ``nobs``. Returns ------- hqic : float The HQIC References ---------- .. [1] https://en.wikipedia.org/wiki/Hannan-Quinn_information_criterion )rhqicrs r*r z ARIMA.hqicts$###r+c.|jjS)zGet the value of the moving average coefficients. Returns ------- maparams : array-like The MA coefficients. )rmaparamsrs r*rzARIMA.maparamsrr+c.|jjS)a]The roots of the MA coefficients are the solution to: :code:`(1 + maparams[0] * z + maparams[1] * z^2 + ... + maparams[ q-1] * z^q) = 0` Stability requires that the roots in modules lie outside the unit circle. Returns ------- maroots : array-like The MA roots. )rmarootsrs r*rz ARIMA.marootsrr+c|jS)zIf the model was built with ``out_of_sample_size`` > 0, a validation score will have been computed. Otherwise it will be np.nan. Returns ------- oob_ : float The "out-of-bag" score. )rrs r*oobz ARIMA.oobsyyr+c.|jjS)a\Get the parameters of the model. The order of variables is the trend coefficients and the :func:`k_exog` exogenous coefficients, then the :func:`k_ar` AR coefficients, and finally the :func:`k_ma` MA coefficients. Returns ------- params : array-like The parameters of the model. )rrrs r*rz ARIMA.paramss%%%r+c.|jjS)zGet the p-values associated with the t-values of the coefficients. Note that the coefficients are assumed to have a Student's T distribution. Returns ------- pvalues : array-like The p-values. )rpvaluesrs r*rz ARIMA.pvaluess&&&r+c.|jjS)aGet the model residuals. If the model is fit using 'mle', then the residuals are created via the Kalman Filter. If the model is fit using 'css' then the residuals are obtained via ``scipy.signal.lfilter`` adjusted such that the first :func:`k_ma` residuals are zero. These zero residuals are not returned. Returns ------- resid : array-like The model residuals. )rresidrs r*rz ARIMA.resids$$$r+c6|jjS)z Get a summary of the ARIMA model)rsummaryrs r*rz ARIMA.summarys&&((r+c Ntj|j}|j|j |j ||j |j|j|j|j|jd S)zGet the ARIMA model as a dictionary Return the dictionary representation of the ARIMA model Returns ------- res : dictionary The ARIMA model as a dictionary. ) rrrzr{rr-rrrr) rrr{rrrzrr-rrrr)rseasonals r*to_dictz ARIMA.to_dictsv11$2E2EF||~ZZ\ZZ&88:88:IIK88:88:kkm  r+crtddlm}|j||}|j}|j }t |drV|j}t |dr tj||j}|jj||df} n((g6//|| 70 1**Aw/JJq'"6"67**8812GEA AA&"))A,6E__S ! 4 !djj&< 12((*A #e*%A 5 !QqT1R5 , AaD!B%  ,- !288E?!34 __S !  $ $D 1  BGG   ))+  +,$ KKQa ) 3q6' 488A;h/ D  78__S !1(sr: \"__S !1%BT2 ]# B =  s (L,,L6) )rrrrNlbfgs2FrmseNNT)N)NNNFF皙?)rNFrW)NN)rW)rrNN)&__name__ __module__ __qualname____doc__ryrrrrrrrrrrr r-rrrrrrrIr.r r r rrrrrrrrrS __classcell__)rs@r*rrsrPh$--^JXPd   gT % CJ G@ ([zL)#*#*\".#.4L)(*(L)'*' L)#*#(L) #* #L) ?* ?L) (* (L) (* (L),*,L)$*$&L)(*(L)'*' L) &* &L) '* 'L) %* %L))*)\" # 0\"B#Br+)1pandasrnumpyrnumpy.polynomial.polynomial polynomialrRrr scipy.statsrrsklearn.utils.validationrrrrrrbaser compat.numpyr compat.sklearnr r rcompatrrrArrrrrutils.visualizationr utils.arrayrrr__all__rr2r:rqrrFr+r*rks33*0!  .-II*(   HV F > AHhIhr+