"g ldZddlmZddlZddlmZddlmZddl m Z ddl m Z edd d d Z y) zg Durbin-Levinson recursions for estimating AR(p) model parameters. Author: Chad Fulton License: BSD-3 )deprecate_kwargN)Bunch) SARIMAXParams)SARIMAXSpecification)acovfunbiasedadjustedc Rt||x}}|j}|js tdt ||d||j }|j dk(r dg}|dg}n4t j|j |j f} t j|j dz} |d|dz | d<|d| d<| dd| dd zz z| d<td|j D]q} | | dz d| f} || dzt j| || dd z | | z | | | f<| | | | f| ddd zz | | d| f<| | d| | | fd zz z| | dz<sdgt|j D cgc]} | | d| dzfc} z}| }g} t|j dzD][} t| }t| }| dk(r || |_ n t j|| || f|_ | j|]td |i}| |fScc} w) a} Estimate AR parameters at multiple orders using Durbin-Levinson recursions. Parameters ---------- endog : array_like or SARIMAXSpecification Input time series array, assumed to be stationary. ar_order : int, optional Autoregressive order. Default is 0. demean : bool, optional Whether to estimate and remove the mean from the process prior to fitting the autoregressive coefficients. Default is True. adjusted : bool, optional Whether to use the "adjusted" autocovariance estimator, which uses n - h degrees of freedom rather than n. This option can result in a non-positive definite autocovariance matrix. Default is False. Returns ------- parameters : list of SARIMAXParams objects List elements correspond to estimates at different `ar_order`. For example, parameters[0] is an `SARIMAXParams` instance corresponding to `ar_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 2.5.1. 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. )ar_orderzgDurbin-Levinson estimation unavailable for models with seasonal or otherwise non-consecutive AR orders.T)r fftdemeannlagrN)rr)specr)rendogis_ar_consecutive ValueErrorrr npzerosrangedotrparamsr_appendr)rr r r rmax_specgamma ar_paramssigma2Phivitmpoutp other_resultss m/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/tsa/arima/estimators/durbin_levinson.pydurbin_levinsonr)sP+58DDD8 NNE  % %$% % %(V(( *EAF (hh))8+<+<=> HHX&&* +!HuQx'D Qx!tq3t9a<'(!q(++, 1Aac2A2g,Cq1usE!Ab&M(BBadJC1IAqD C"I 55C2A2Jtq3q!t9a</0Aa!eH  1 FeHr3s; 6)6D+Z(Y)Yr2