"g ddZddlmZddlmZddlmZddlmZddl m Z eddd d Z y ) z_ Yule-Walker method for estimating AR(p) model parameters. Author: Chad Fulton License: BSD-3 )deprecate_kwarg) linear_model)Bunch) SARIMAXParams)SARIMAXSpecificationunbiasedadjustedct||}|j}t|}|js t d|rdnd}t j ||||\|_}|dz|_td|i}||fS) a| Estimate AR parameters using Yule-Walker equations. 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. For some processes this option may result in a non-positive definite autocovariance matrix. Default is False. Returns ------- parameters : SARIMAXParams object Contains the parameter estimates from the final iteration. other_results : Bunch Includes one component, `spec`, which is the `SARIMAXSpecification` instance corresponding to the input arguments. Notes ----- The primary reference is [1]_, section 5.1.1. This procedure assumes that the series is stationary. For a description of the effect of the adjusted estimate of the autocovariance function, see 2.4.2 of [1]_. References ---------- .. [1] Brockwell, Peter J., and Richard A. Davis. 2016. Introduction to Time Series and Forecasting. Springer. )ar_order)speczYYule-Walker estimation unavailable for models with seasonal or non-consecutive AR orders.r mle)orderdemeanmethodr ) rendogris_ar_consecutive ValueErrorr yule_walker ar_paramssigma2r) rr rr r prsigma other_resultss i/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/tsa/arima/estimators/yule_walker.pyrrsT  9D JJE4 A  ! !CD D$ZF%11 XfV=AKaxAHM m N)rTF) __doc__statsmodels.compat.pandasrstatsmodels.regressionrstatsmodels.tools.toolsrstatsmodels.tsa.arima.paramsr#statsmodels.tsa.arima.specificationrrrrr$s6 6/)6DZ(<)<r