"g%dZddlZddlZddlmZddlmZddlm Z ddl m Z m Z ddl mZddlmZdd lmZdd lmZd d Z dd Zy)zs Innovations algorithm for MA(q) and SARIMA(p,d,q)x(P,D,Q,s) model parameters. Author: Chad Fulton License: BSD-3 N)minimize)Bunch)arma_innovations)acovfinnovations_algo)diff)SARIMAXSpecification) SARIMAXParams)hannan_rissanencdt||x}}|j}|r||jz }|js t dt |d}t ||jdz\}}td|jdzDcgc] }||d|f } }|} g} t|jdzD]^}t|}t|} |d k(r | || _ n#tj| |dz | |f| _ | j| `td |i} | | fScc}w) aq Estimate MA parameters using innovations algorithm. Parameters ---------- endog : array_like or SARIMAXSpecification Input time series array, assumed to be stationary. ma_order : int, optional Maximum moving average order. Default is 0. demean : bool, optional Whether to estimate and remove the mean from the process prior to fitting the moving average coefficients. Default is True. Returns ------- parameters : list of SARIMAXParams objects List elements correspond to estimates at different `ma_order`. For example, parameters[0] is an `SARIMAXParams` instance corresponding to `ma_order=0`. other_results : Bunch Includes one component, `spec`, containing the `SARIMAXSpecification` instance corresponding to the input arguments. Notes ----- The primary reference is [1]_, section 5.1.3. This procedure assumes that the series is stationary. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. )ma_orderzcInnovations estimation unavailable for models with seasonal or otherwise non-consecutive MA orders.T)fft)nobsNspecrr)r endogmeanis_ma_consecutive ValueErrorrrr ranger paramsnpr_appendr)rr demeanrmax_spec sample_acovfthetavi ma_paramssigma2outp other_resultss i/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/tsa/arima/estimators/innovations.py innovationsr(sOF+58DDD8 NNE  $  % %MN ND)L 83D3Dq3HIHE1',Q0A0AA0E'FG!q"1"uGIG F C 8$$q( )#Q/ t $ 6ayAHuuYq1u-vay89AH 1 M  %Hs D-ct||d|jjrBtjdt j j j|rjz t|t}tjjd\}} jdk(r|j|_ nt|d| } tjj jz} tjj"jz} t| j$| | d\} }|j&|_|j(|_| j&|_| j(|_| j.|_|j0s*dg|j2z|_dg|j4z|_|j6s6j8r*dg|j:z|_dg|j<z|_|j}nMt}||_ |j0s t?d j8r|j6s t?d fd }jA|}|i}d |vri|d <|d jCddtE||fi|}jG|jH_ tK|||d}|fS)a Estimate SARIMA parameters by MLE using innovations algorithm. Parameters ---------- endog : array_like Input time series array. order : tuple, optional The (p,d,q) order of the model for the number of AR parameters, differences, and MA parameters. Default is (0, 0, 0). 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). demean : bool, optional Whether to estimate and remove the mean from the process prior to fitting the SARIMA coefficients. Default is True. enforce_invertibility : bool, optional Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. Default is True. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The AR polynomial must be stationary. If `enforce_invertibility=True` the MA poylnomial must be invertible. If not provided, default starting parameters are computed using the Hannan-Rissanen method. minimize_kwargs : dict, optional Arguments to pass to scipy.optimize.minimize. Returns ------- parameters : SARIMAXParams object other_results : Bunch Includes four components: `spec`, containing the `SARIMAXSpecification` instance corresponding to the input arguments; `minimize_kwargs`, containing any keyword arguments passed to `minimize`; `start_params`, containing the untransformed starting parameters passed to `minimize`; and `minimize_results`, containing the output from `minimize`. Notes ----- The primary reference is [1]_, section 5.2. Note: we do not include `enforce_stationarity` as an argument, because this function requires stationarity. TODO: support concentrating out the scale (should be easy: use sigma2=1 and then compute sigma2=np.sum(u**2 / v) / len(u); would then need to redo llf computation in the Cython function). TODO: add support for fixed parameters TODO: add support for secondary optimization that does not enforce stationarity / invertibility, starting from first step's parameters References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. T)orderseasonal_orderenforce_stationarityenforce_invertibilityziProvided `endog` series has been differenced to eliminate integration prior to ARMA parameter estimation.)k_diffk_seasonal_diffseasonal_periodsrF)ar_orderr rr)r+r,r-zqGiven starting parameters imply a non-stationary AR process. Innovations algorithm requires a stationary process.z^Given starting parameters imply a non-invertible MA process with `enforce_invertibility=True`.cj|_tjjj dd j j ddj S)Nr) ar_paramsr"r#)constrain_paramsrr arma_loglikereduced_ar_polycoefreduced_ma_polyr#)rrr%rs r'objzinnovations_mle..objsg((0 -- a//44QR88'',,QR0CC Coptionsmaxiterd)rminimize_resultsminimize_kwargs start_params)&r r is_integratedwarningswarnr seasonal_diffr0rr r r1r rrarrayseasonal_ar_lagsseasonal_ma_lagsresidr3r"seasonal_ar_paramsseasonal_ma_paramsr# is_stationary k_ar_paramsk_seasonal_ar_params is_invertibler- k_ma_paramsk_seasonal_ma_paramsrunconstrain_params setdefaultrr4xr)rr*r+rr-r@r?sphr hr_results_r1r seasonal_hrseasonal_hr_resultsr9unconstrained_start_paramsr>r&r%rs` @@r'innovations_mler[Ys|  U>!9N PD JJE  % &U499%)%7%7&*&;&;= $4 A  %)26--OJ  A % BI%n%)&;=A xx 5 569N9NNHxx 5 569N9NNH/>  8h0 ,K, <$>3/BL%&C"*A*A$AB !yy  %  45 5  % %b.>.>NO OC"&!8!8!F'%' "I)))S9%?3"13 $$%5%7%78AH,*$ M m r:)rT))rrr)rrrrTTNN)__doc__rBnumpyrscipy.optimizerstatsmodels.tools.toolsrstatsmodels.tsa.innovationsrstatsmodels.tsa.stattoolsrr statsmodels.tsa.statespace.toolsr#statsmodels.tsa.arima.specificationr statsmodels.tsa.arima.paramsr 0statsmodels.tsa.arima.estimators.hannan_rissanenr r(r[r:r'rgsC #)8=1D6LAH