'YHhbdZddlZddlmZmZddlmZddlm Z ejZ ejZ ejZGddeZGdd e Zy) aLinear 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 N)specialstats)GenericLikelihoodModel)Armac>eZdZdZfdZddZdZdZddZxZ S) 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. ctd|jjd|_t |dsd|_|j dur4d|_d|_|jjddz|_ddg}n|jjddz|_tjtj|jjddzz}|j |d<||_tj||_dg}t|9|j||j!y) Nzrunning Tmodel initializefix_dfFdfscale)printexogshapek_varshasattrr fixed_paramsfixed_paramsmaskk_paramsnpnanzerosisnansuper initialize_set_extra_params_names_set_start_params)selfextra_params_namesfixdf __class__s V/var/www/html/planif/env/lib/python3.12/site-packages/statsmodels/miscmodels/tmodel.pyrzTLinearModel.initialize>s  )*iiooa( tX&DK ;;%  $D $(D ! IIOOA.2DM"& !IIOOA.2DMFFRXXdiiooa&81&<==E E"I %D $&HHUOD !")   $$%78  c|||_yddlm}||j|jj }dt j|jz}|j|d|j|jdurS|r(tj|j}d|z dz}nd}||d<t j|j |d <||_y) Nr)OLSg?Fg@r) start_params#statsmodels.regression.linear_modelr'endogrfitronesrparamsrr rkurtosisresidsqrtr)r r+ use_kurtosisr'res_olskurtr s r$rzTLinearModel._set_start_params]s  # ,D  ?$**dii0446Grwwt}}55L)0L$++ &{{e# >>'--8DD1BB#% R #%777==#9 R ,D r%cD|j|jd SNr nloglikeobssumr r0s r$loglikezTLinearModel.loglikew!  (,,Q///r%c|j|j|}|dd}|d}tj|d}tj|j |}|j }||z |z }t|dzdz t|dz z }|dt|tzz|dzdz td|dz|z zzzz}|t|z}| 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.) Nrr*r r g@g?) r expandparamsrabsdotrr- sps_gamlnnp_lognp_pi) r r0betar rlocr-xlPxs r$r:zTLinearModel.nloglikeobszs:    (&&v.Fcr{ BZvbz"ffTYY%  S[% Aq!Ibe$44 s6"U(##r!tRiq!Q${0C&CCC ve}t r%c~| |j}tj||d|jjdS)Nr )rrrBr)r r0rs r$predictzTLinearModel.predicts6 <99DvvdF#6DIIOOA$6788r%)NF)N) __name__ __module__ __qualname____doc__rrr=r:rK __classcell__r#s@r$rr2s" !>-40+Z9r%rc4eZdZdZdZdZ dfd ZxZS)TArmaaUnivariate 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 cD|j|jd Sr8r9r<s r$r=z TArma.logliker>r%c|j|dd}|d}tj|d}tjj ||z | t |z}|S)z Loglikelihood for arma model for each observation, t-distribute Notes ----- The ancillary parameter is assumed to be the last element of the params vector Nrr*) geterrorsrrArt_logpdfrD)r r0 errorsestr rllikes r$r:zTArma.nloglikeobss^NN6#2;/ BZvbz"77??9U?B77&-G r%c |\}}|t|||zdzk7r=tdtjdtj||zzddgf}t |d|||||d|} | S)Nr z(start_param need sum(order) + 2 elementsg?r)r )orderr+methodmaxitertol)len ValueErrorr concatenater/rfit_mle) r r\r+r]r^r_kwdsnarnmaresr#s r$rdz TArma.fit_mlesS  #< C#IM1 !KLL>>4c 0B+BQF*KLLgo:E6B06-0:59:  r%)Nnmig:0yE>)rLrMrNrOr=r:rdrPrQs@r$rSrSs& 0 *FJr%rS)rOnumpyrscipyrrstatsmodels.base.modelrstatsmodels.tsa.arma_mlerlogrDpirEgammalnrCrrSr`r%r$rqsR!H 9)   OO x9)x9v:D:r%