M/Ph%dZddlZddlZddlmZddlmZddlm Z ddl m Z m Z ddl mZddlmZdd lmZdd lmZdd Z ddZdS)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_rissanenTc t||x}}|j}|r||z }|jst dt |d}t ||jdz\ } fdtd|jdzD}|}g} t|jdzD]s} t| }t|} | d kr|| | _ n(tj || dz || f| _ | | ttd |i} | | fS) 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)nobsc(g|]}|d|fS)N).0ithetas l/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tsa/arima/estimators/innovations.py zinnovations..Ds%GGG!q"1"uGGGspecrr)r endogmeanis_ma_consecutive ValueErrorrrr ranger paramsnpr_appendr)rr demeanrmax_spec sample_acovfv ma_paramssigma2outrp other_resultsrs @r innovationsr-szF+58DDDDD8 NE % $  %NMNN ND)))L 83Dq3HIIIHE1GGGGuQ0AA0E'F'FGGGI F C 8$q( ) )#Q/// t $ $ $ 66ayAHHuYq1u-vay89AH 1 M  rrrrrrrrcZt||d|jjr6tjdt jjj|rz t|Qt}tj j d\}} jd kr |j |_ nt|d| } tjjjz} tjjjz} t| j| | d\} }|j|_|j|_| j|_| j|_| j|_|js d g|jz|_d g|jz|_|js'jr d g|jz|_d g|jz|_|j }nJt}||_ |jst?d jr|jst?d fd } |}|i}d|vri|d<|d!ddtE||fi|}#|j$_ 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_periodsrNF)ar_orderr r$r)r2r3r4zqGiven starting parameters imply a non-stationary AR process. 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