U Kv f%@sdZddlZddlZddlmZddlmZddlm Z ddl m Z m Z ddl mZddlmZdd lmZdd lmZdd d ZdddZdS)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 st||d}}|j}|r&||}|js4tdt|dd}t||jdd\}fddtd|jdD}|}g} t|jdD]R} t| d}t |d } | d kr|| | _ nt j || d|| f| _ | | qtd |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)Zfft)Znobscsg|]}|d|fqS)N).0ithetar P/tmp/pip-unpacked-wheel-2v6byqio/statsmodels/tsa/arima/estimators/innovations.py Dszinnovations..specrr)rendogmeanZis_ma_consecutive ValueErrorrrr ranger paramsnpZr_appendr) rr demeanrZmax_specZ sample_acovfv ma_paramssigma2outrp other_resultsr rr innovationss.#      r$rrrrrrrcst||d|djjr>tdtjjjd|rNt d|dkrbt d}t j j dd\}} jd kr|j |_ nrt|d|d } tjj} tjj} t | j| | dd\} }|j|_|j|_| j|_| j|_| j|_|js.d g|j|_d g|j|_|jsZjrZd g|j|_d g|j|_|j }n8t d}||_ |jstd jr|jstd fd d} |}|dkri}d|kri|d<|d!ddt"||f|}#|j$_ t%|||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.)Zk_diffZk_seasonal_diffseasonal_periodsrNF)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`.cs<|_tjjjdd jjddjd S)Nr ) ar_paramsrr )constrain_paramsrrZ arma_loglikeZreduced_ar_polyZcoefZreduced_ma_polyr )rrr"rr robjs zinnovations_mle..objoptionsmaxiterd)rminimize_resultsminimize_kwargs start_params)&rrZ is_integratedwarningswarnrZ seasonal_diffr+rr r r,r rrarrayZseasonal_ar_lagsZseasonal_ma_lagsZresidr-rZseasonal_ar_paramsZseasonal_ma_paramsr Z is_stationaryZ k_ar_paramsZk_seasonal_ar_paramsZ is_invertibler*Z k_ma_paramsZk_seasonal_ma_paramsrZunconstrain_params setdefaultrr.xr)rr'r(rr*r6r5sphrZ hr_results_r,r Z seasonal_hrZseasonal_hr_resultsr0Zunconstrained_start_paramsr4r#r r/rinnovations_mleYs>             r?)rT)r%r&TTNN)__doc__r7ZnumpyrZscipy.optimizerZstatsmodels.tools.toolsrZstatsmodels.tsa.innovationsrZstatsmodels.tsa.stattoolsrrZ statsmodels.tsa.statespace.toolsrZ#statsmodels.tsa.arima.specificationrZstatsmodels.tsa.arima.paramsr Z0statsmodels.tsa.arima.estimators.hannan_rissanenr r$r?r r r rs"        D