o þ0Gfbã@sjdZddlZddlmZmZddlmZddlm Z ej Z ej Z ejZGdd„deƒZGdd „d e ƒZdS) aÞLinear Model with Student-t distributed errors Because the t distribution has fatter tails than the normal distribution, it can be used to model observations with heavier tails and observations that have some outliers. For the latter case, the t-distribution provides more robust estimators for mean or mean parameters (what about var?). References ---------- Kenneth L. Lange, Roderick J. A. Little, Jeremy M. G. Taylor (1989) Robust Statistical Modeling Using the t Distribution Journal of the American Statistical Association Vol. 84, No. 408 (Dec., 1989), pp. 881-896 Published by: American Statistical Association Stable URL: http://www.jstor.org/stable/2290063 not read yet Created on 2010-09-24 Author: josef-pktd License: BSD TODO ---- * add starting values based on OLS * bugs: store_params does not seem to be defined, I think this was a module global for debugging - commented out * parameter restriction: check whether version with some fixed parameters works éN)ÚspecialÚstats)ÚGenericLikelihoodModel)ÚArmacsDeZdZdZ‡fdd„Zddd„Zdd „Zd d „Zdd d „Z‡Z S)Ú TLinearModela?Maximum Likelihood Estimation of Linear Model with t-distributed errors This is an example for generic MLE. Except for defining the negative log-likelihood method, all methods and results are generic. Gradients and Hessian and all resulting statistics are based on numerical differentiation. csÈtdƒ|jjd|_t|dƒsd|_|jdur,d|_d|_|jjdd|_ddg}n(|jjdd|_t j t   |jjdd¡}|j|d<||_t   |¡|_dg}t ƒ ¡| |¡| ¡dS) Nzrunning Tmodel initializeéÚfix_dfFéÚdfÚscaleéþÿÿÿ)ÚprintÚexogÚshapeÚk_varsÚhasattrrÚ fixed_paramsZfixed_paramsmaskÚk_paramsÚnpÚnanZzerosZisnanÚsuperÚ initializeZ_set_extra_params_namesÚ_set_start_params)ÚselfZextra_params_namesZfixdf©Ú __class__©ú=lib/python3.10/site-packages/statsmodels/miscmodels/tmodel.pyr>s$        zTLinearModel.initializeNFcCsž|dur ||_dSddlm}||j|jƒ ¡}dt |j¡}|j |d|j …<|j durJ|rc  sp|\}}|durt|ƒ||dkrtdƒ‚nt dt ||¡ddgf¡}tƒjd|||||dœ|¤Ž} | S)Nr z(start_param need sum(order) + 2 elementsgš™™™™™©?r r)Úorderr"ÚmethodÚmaxiterÚtolr)ÚlenÚ ValueErrorrZ concatenater$rÚfit_mle) rr@r"rArBrCÚkwdsZnarZnmaÚresrrrrFØsÿ  ýýz TArma.fit_mle)Nr=r>r?)r6r7r8r9r,r)rFr:rrrrr;­sÿr;)r9ZnumpyrZscipyrrZstatsmodels.base.modelrZstatsmodels.tsa.arma_mlerÚlogr1Zpir2Zgammalnr0rr;rrrrÚs$  {