M/PhbdZddlZddlmZmZddlmZddlm Z ej Z ej Z ejZGddeZGdd e ZdS) 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>eZdZdZfdZd dZdZdZd dZxZ 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. cvtd|jjd|_t |dsd|_|jdur-d|_d|_|jjddz|_ddg}n{|jjddz|_tj tj |jjddzz}|j|d<||_tj ||_dg}t|||dS) Nzrunning Tmodel initializefix_dfFdfscale)printexogshapek_varshasattrr fixed_paramsfixed_paramsmaskk_paramsnpnanzerosisnansuper initialize_set_extra_params_names_set_start_params)selfextra_params_namesfixdf __class__s ]/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/miscmodels/tmodel.pyrzTLinearModel.initialize>s% )***ioa( tX&& DK ;%   $D $(D ! IOA.2DM"&  !IOA.2DMFRXdioa&81&<===E E"I %D $&HUOOD !")   $$%7888      NFc| ||_dSddlm}||j|j}dt j|jz}|j |d|j <|j durG|r"tj |j}d|z dz}nd}||d<t j|j|d <||_dS) Nr)OLSg?Fg@r) start_params#statsmodels.regression.linear_modelr'endogrfitronesrparamsrr rkurtosisresidsqrtr)r r+ use_kurtosisr'res_olskurtr s r$rzTLinearModel._set_start_params]s  # ,D    ? ? ? ? ? ?c$*di004466Grwt}555L)0L$+ &{e## >'-88DD1BBB#% R #%77=#9#9 R ,D   r%cT||d SNr nloglikeobssumr r0s r$loglikezTLinearModel.loglikew'  ((,,Q////r%c|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..Fcrc{ BZvbz""fTY%%  S[% Aq!!Ibe$4$44 s6"U(###r!tRiq!Q${0C0C&CCC ve}}t r%cn||j}tj||d|jjdS)Nr )rrrBr)r r0rs r$predictzTLinearModel.predicts4 <9DvdF#6DIOA$6#67888r%)NF)N) __name__ __module__ __qualname____doc__rrr=r:rK __classcell__r#s@r$rr2s  !!!!!>----4000+++Z99999999r%rc4eZdZdZdZdZ d fd 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 cT||d Sr8r9r<s r$r=z TArma.logliker>r%c||dd}|d}tj|d}tj||z | t |z}|S)z Loglikelihood for arma model for each observation, t-distribute Notes ----- The ancillary parameter is assumed to be the last element of the params vector Nrr*) geterrorsrrArt_logpdfrD)r r0 errorsestr rllikes r$r:zTArma.nloglikeobssgNN6#2#;// BZvbz""7??9U?B777&--G r%Nnm:0yE>c |\}}|)t|||zdzkrtdn0tjdtj||zzddgf}t jd|||||d|} | S)Nr z(start_param need sum(order) + 2 elementsg?r)r )orderr+methodmaxitertol)len ValueErrorr concatenater/rfit_mle) r r_r+r`rarbkwdsnarnmaresr#s r$rgz TArma.fit_mlesS  #<  C#IM11 !KLLL2>4c 0B0B+BQF*KLLLeggo:E6B06-0::59::  r%)Nr[r\r])rLrMrNrOr=r:rgrPrQs@r$rSrSso 000 *FJr%rS)rOnumpyrscipyrrstatsmodels.base.modelrstatsmodels.tsa.arma_mlerlogrDpirEgammalnrCrrSrcr%r$rss!!H 999999))))))   O x9x9x9x9x9)x9x9x9v:::::D:::::r%