>hISrSSKrSSKJrJr SSKJr SSKJ r \Rr \Rr \Rr"SS\5r"SS \ 5rg) 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)ArmacL^\rSrSrSrU4SjrS SjrSrSrS Sjr Sr U=r $) TLinearModel2a'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. c>[S5 URRSUl[ US5(dSUlUR SLa4SUlSUlURRSS-UlSS/nOURRSS-Ul[R[R"URRSS-5-nUR US'X l[R"U5UlS/n[TU]95 URU5 UR!5 g) Nzrunning Tmodel initializefix_dfFdfscale)printexogshapek_varshasattrr fixed_paramsfixed_paramsmaskk_paramsnpnanzerosisnansuper initialize_set_extra_params_names_set_start_params)selfextra_params_namesfixdf __class__s pC:\Users\julio\OneDrive\Documentos\Trabajo\Ideas Frescas\venv\Lib\site-packages\statsmodels/miscmodels/tmodel.pyrTLinearModel.initialize>s  )*iiooa( tX&&DK ;;%  $D $(D ! IIOOA.2DM"& !IIOOA.2DMFFRXXdiiooa&81&<==E E"I % $&HHUOD !")   $$%78  cUbXlgSSKJn U"URUR5R 5nS[ R"UR5-nURUSUR&URSLaYU(a)[R"UR5nSU- S-nOSnXaS'[ R"UR 5US 'Xlg) Nr)OLSg?Fg@r) start_params#statsmodels.regression.linear_modelr)endogrfitronesrparamsrr rkurtosisresidsqrtr)r!r- use_kurtosisr)res_olskurtrs r%r TLinearModel._set_start_params]s  # ,  ?$**dii0446Grwwt}}55L)0L$++ &{{e# >>'--8DD1BB#%R #%777==#9 R , r'cDURU5RS5*$Nr nloglikeobssumr!r2s r%loglikeTLinearModel.loglikew!  (,,Q///r'cURbURU5nUSSnUSn[R"US5n[R"UR U5nUR nXe- U- n[US-S- 5[US- 5- nUS[U[-5-US-S- [SUS-U- -5---nU[U5-nU*$)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!r2betarrlocr/xlPxs r%r=TLinearModel.nloglikeobszs:    (&&v.Fcr{ BZvbz"ffTYY%  [% Aq!Ibe$44 s6"U(##r!tRiq!Q${0C&CCC ve}t r'cUc URn[R"X!SURRS5$)Nr )rrrFr)r!r2rs r%predictTLinearModel.predicts4 <99Dvvd#6DIIOOA$6788r')r rrrrr-)NF)N) __name__ __module__ __qualname____firstlineno____doc__rr r@r=rP__static_attributes__ __classcell__r$s@r%rr2s' !>-40+Z99r'rc@^\rSrSrSrSrSrSU4SjjrSrU=r $)TArmaagUnivariate Arma Model with t-distributed errors This inherit all methods except loglike from tsa.arma_mle.Arma This uses the standard t-distribution, the implied variance of the error is not equal to scale, but :: error_variance = df/(df-2)*scale**2 Notes ----- This might be replaced by a standardized t-distribution with scale**2 equal to variance cDURU5RS5*$r;r<r?s r%r@ TArma.loglikerBr'cURUSS5nUSn[R"US5n[RR X$- U5*[ U5-nU$)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,) geterrorsrrErt_logpdfrH)r!r2 errorsestrrllikes r%r=TArma.nloglikeobss\NN6#2;/ BZvbz"77??9?B77&-G r'c >UupxUb [U5Xx-S-:wa [S5eO3[R"S[R"Xx-5-SS/45n[ T U]"SUUX4US.UD6n U $)Nr z(start_param need sum(order) + 2 elementsg?r+r )orderr-methodmaxitertol)len ValueErrorr concatenater1rfit_mle) r!rgr-rhrirjkwdsnarnmaresr$s r%ro TArma.fit_mles  #< CIM1 !KLL2>>4 0B+BQF*KLLgo:E6B06-0:59:  r'rk)Nnmig:0yE>) rRrSrTrUrVr@r=rorWrXrYs@r%r[r[s& 0 *FJr'r[)rVnumpyrscipyrrstatsmodels.base.modelrstatsmodels.tsa.arma_mlerlogrHpirIgammalnrGrr[rkr'r%r}sR!H 9)   OO x9)x9v:D:r'