U Kv f:&@sddlZddlmZddlmZddlmZmZddl m Z ddl m Z dZ dd d Zdd d ZdddZdddZdddZdS)N) arima_process)prefix_dtype_map) _get_epsilonapprox_fprime_cs)find_best_blas_type)_arma_innovationszThe model's autoregressive parameters (ar_params) indicate that the process is non-stationary. The innovations algorithm cannot be used. FcCst|}|jdk}|r(|dddf}t|dkr8gn|}t|dkrNgn|}|j\}}tjd| f} tjd|f} |dkrt|||t|g\}} } t|} tj|| d}tj|| d}tj|| d}| | }t t |d} t t |d}t t |d}t j | | ||d|}| | | |\}}||||||\}}t|}t|dks|t|r|t|sttg}t|D]0}t||dd|f|||}||qt|j}|r||dddfd }|r|}||fS) ay Compute innovations using a given ARMA process. Parameters ---------- endog : ndarray The observed time-series process, may be univariate or multivariate. ar_params : ndarray, optional Autoregressive parameters. ma_params : ndarray, optional Moving average parameters. sigma2 : ndarray, optional The ARMA innovation variance. Default is 1. normalize : bool, optional Whether or not to normalize the returned innovations. Default is False. prefix : str, optional The BLAS prefix associated with the datatype. Default is to find the best datatype based on given input. This argument is typically only used internally. Returns ------- innovations : ndarray Innovations (one-step-ahead prediction errors) for the given `endog` series with predictions based on the given ARMA process. If `normalize=True`, then the returned innovations have been "whitened" by dividing through by the square root of the mean square error. innovations_mse : ndarray Mean square error for the innovations. rNdtypearma_transformed_acovf_fastarma_innovations_algo_fastarma_innovations_filter)sigma2nobsrg?)nparrayndim atleast_1dshaper_rrasfortranarrayitemgetattrrr arma_acovfanyisfiniteall ValueErrorNON_STATIONARY_ERRORrangeappendZvstackTZsqueeze)endog ar_params ma_paramsr normalizeprefixZsqueezedrZk_endogarmar _r r r rZacovfZacovf2thetavuiZu_ir.P/tmp/pip-unpacked-wheel-2v6byqio/statsmodels/tsa/innovations/arma_innovations.pyarma_innovationssz!          r0cCst|||||d}t|S)a Compute the log-likelihood of the given data assuming an ARMA process. Parameters ---------- endog : ndarray The observed time-series process. ar_params : ndarray, optional Autoregressive parameters. ma_params : ndarray, optional Moving average parameters. sigma2 : ndarray, optional The ARMA innovation variance. Default is 1. prefix : str, optional The BLAS prefix associated with the datatype. Default is to find the best datatype based on given input. This argument is typically only used internally. Returns ------- float The joint loglikelihood. )r#r$rr&)arma_loglikeobsrsum)r"r#r$rr&Zllf_obsr.r.r/ arma_loglikens r3cCst|}t|dkrgn|}t|dkr0gn|}|dkrZt|||t|g\}}}t|}tj||d}tj||d}tj||d}||}tt |d}|||||S)a Compute the log-likelihood for each observation assuming an ARMA process. Parameters ---------- endog : ndarray The observed time-series process. ar_params : ndarray, optional Autoregressive parameters. ma_params : ndarray, optional Moving average parameters. sigma2 : ndarray, optional The ARMA innovation variance. Default is 1. prefix : str, optional The BLAS prefix associated with the datatype. Default is to find the best datatype based on given input. This argument is typically only used internally. Returns ------- ndarray Array of loglikelihood values for each observation. Nr Zarma_loglikeobs_fast) rrrrrZascontiguousarrayrrrr)r"r#r$rr&r r)funcr.r.r/r1s   r1csn|dkr gn|}|dkrgn|}t|t|fdd}tj|||f}t|ddt|}t|||S)a Compute the score (gradient of the log-likelihood function). Parameters ---------- endog : ndarray The observed time-series process. ar_params : ndarray, optional Autoregressive coefficients, not including the zero lag. ma_params : ndarray, optional Moving average coefficients, not including the zero lag, where the sign convention assumes the coefficients are part of the lag polynomial on the right-hand-side of the ARMA definition (i.e. they have the same sign from the usual econometrics convention in which the coefficients are on the right-hand-side of the ARMA definition). sigma2 : ndarray, optional The ARMA innovation variance. Default is 1. prefix : str, optional The BLAS prefix associated with the datatype. Default is to find the best datatype based on given input. This argument is typically only used internally. Returns ------- ndarray Score, evaluated at the given parameters. Notes ----- This is a numerical approximation, calculated using first-order complex step differentiation on the `arma_loglike` method. Ncs.t|d||dSN)r3paramsr"pqr.r/r4szarma_score..func@lenrrrrr"r#r$rr&r4Zparams0epsilonr.r8r/ arma_scores"r@csn|dkr gn|}|dkrgn|}t|t|fdd}tj|||f}t|ddt|}t|||S)a Compute the score (gradient) per observation. Parameters ---------- endog : ndarray The observed time-series process. ar_params : ndarray, optional Autoregressive coefficients, not including the zero lag. ma_params : ndarray, optional Moving average coefficients, not including the zero lag, where the sign convention assumes the coefficients are part of the lag polynomial on the right-hand-side of the ARMA definition (i.e. they have the same sign from the usual econometrics convention in which the coefficients are on the right-hand-side of the ARMA definition). sigma2 : ndarray, optional The ARMA innovation variance. Default is 1. prefix : str, optional The BLAS prefix associated with the datatype. Default is to find the best datatype based on given input. This argument is typically only used internally. Returns ------- ndarray Score per observation, evaluated at the given parameters. Notes ----- This is a numerical approximation, calculated using first-order complex step differentiation on the `arma_loglike` method. Ncs.t|d||dSr5)r1r6r8r.r/r4szarma_scoreobs..funcr;r<r>r.r8r/ arma_scoreobss"rA)NNrFN)NNrN)NNrN)NNrN)NNrN)ZnumpyrZstatsmodels.tsarZ statsmodels.tsa.statespace.toolsrZstatsmodels.tools.numdiffrrZscipy.linalg.blasrrrr0r3r1r@rAr.r.r.r/s(     _  + 0