U Kv fã@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. csÌtdƒ|jjd|_t|dƒs&d|_|jdkrXd|_d|_|jjdd|_ddg}nP|jjdd|_t j t   |jjdd¡}|j|d<||_t   |¡|_dg}t t|ƒ ¡| |¡| ¡dS) Nzrunning Tmodel initializeéÚfix_dfFéÚdfÚscaleéþÿÿÿ)ÚprintÚexogÚshapeÚk_varsÚhasattrrÚ fixed_paramsZfixed_paramsmaskÚk_paramsÚnpÚnanÚzerosÚisnanÚsuperrÚ initializeZ_set_extra_params_namesÚ_set_start_params)ÚselfZextra_params_namesZfixdf©Ú __class__©úA/tmp/pip-unpacked-wheel-2v6byqio/statsmodels/miscmodels/tmodel.pyr>s$      zTLinearModel.initializeNFcCsœ|dk r||_nˆddlm}||j|jƒ ¡}dt |j¡}|j |d|j …<|j dkr’|rvt   |j¡}d|d}nd}||d<t |j¡|d <||_dS) Nr)ÚOLSgš™™™™™¹?Fg@éér éÿÿÿÿ)Ú start_paramsZ#statsmodels.regression.linear_modelr ÚendogrZfitrÚonesrÚparamsrrrZkurtosisZresidÚsqrtr )rr$Z use_kurtosisr Zres_olsZkurtr rrrr]s   zTLinearModel._set_start_paramscCs| |¡ d¡ S©Nr©Ú nloglikeobsÚsum©rr'rrrÚloglikewszTLinearModel.loglikec Cs¸|jdk r| |¡}|dd…}|d}t |d¡}t |j|¡}|j}|||}t|ddƒt|dƒ}|dt|t ƒ|ddtd|d|ƒ8}|t|ƒ8}| S)a… Loglikelihood of linear model with t distributed errors. Parameters ---------- params : ndarray The parameters of the model. The last 2 parameters are degrees of freedom and scale. Returns ------- loglike : ndarray The log likelihood of the model evaluated at `params` for each observation defined by self.endog and self.exog. Notes ----- .. math:: \ln L=\sum_{i=1}^{n}\left[-\lambda_{i}+y_{i}x_{i}^{\prime}\beta-\ln y_{i}!\right] The t distribution is the standard t distribution and not a standardized t distribution, which means that the scale parameter is not equal to the standard deviation. self.fixed_params and self.expandparams can be used to fix some parameters. (I doubt this has been tested in this model.) Nr r#rr g@gà?) rZ expandparamsrÚabsÚdotrr%Ú sps_gamlnÚnp_logÚnp_pi) rr'Úbetar r Úlocr%ÚxZlPxrrrr+zs    4 zTLinearModel.nloglikeobscCs*|dkr|j}t ||d|jjd…¡S)Nr)rrr0r)rr'rrrrÚpredict§szTLinearModel.predict)NF)N) Ú__name__Ú __module__Ú __qualname__Ú__doc__rrr.r+r7Ú __classcell__rrrrr2s   -rcs2eZdZdZdd„Zdd„Zd ‡fd d „ Z‡ZS) ÚTArmaa‹Univariate Arma Model with t-distributed errors This inherit all methods except loglike from tsa.arma_mle.Arma This uses the standard t-distribution, the implied variance of the error is not equal to scale, but :: error_variance = df/(df-2)*scale**2 Notes ----- This might be replaced by a standardized t-distribution with scale**2 equal to variance cCs| |¡ d¡ Sr)r*r-rrrr.¾sz TArma.loglikecCsH| |dd…¡}|d}t |d¡}tj |||¡ t|ƒ}|S)zÍ Loglikelihood for arma model for each observation, t-distribute Notes ----- The ancillary parameter is assumed to be the last element of the params vector Nr r#)Z geterrorsrr/rÚtZ_logpdfr2)rr'Z errorsestr r Zllikerrrr+Ãs zTArma.nloglikeobsNÚnméˆç:Œ0âŽyE>c  st|\}}|dk r.t|ƒ||dkrNtdƒ‚n t dt ||¡ddgf¡}tt|ƒjf|||||dœ|—Ž} | S)Nr z(start_param need sum(order) + 2 elementsgš™™™™™©?r"r)Úorderr$ÚmethodÚmaxiterÚtol)ÚlenÚ ValueErrorrZ concatenater&rr=Úfit_mle) rrBr$rCrDrEÚkwdsZnarZnmaÚresrrrrHØs  ýýz TArma.fit_mle)Nr?r@rA)r8r9r:r;r.r+rHr<rrrrr=­s ÿr=)r;ZnumpyrZscipyrrZstatsmodels.base.modelrZstatsmodels.tsa.arma_mlerÚlogr2Úpir3Zgammalnr1rr=rrrrÚs$  {