ó áp7]c @s2dZddlmZddlmZddlZddlmZddl m Z m Z ddl j ZddlZddlmZmZddlmZdd lmZd d „Zd d ed d „Zdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZdefd„ƒYZd„Z defd„ƒYZ!defd„ƒYZ"dd„Z#ddd „Z$dddd!„Z&d"„Z'd#„Z(d$„Z)d%d&„Z*e+d'kr.d(gZ,d)e,kr¨ej-j.ƒZ/e0d*ƒdd+gZ1dd,gZ2e/j3e1e2d-dƒZ4e4e4j5ƒ8Z4e"e4ƒZ6d e6_7d e6_8e6j9d.d/ƒZ:e0e:j;ƒe"e4ƒZ<e<j9d.d0ƒZ=e0e=j;ƒe0e=j>j?e=j;ƒƒe0ej@e6jAd1d2ƒe=j;ƒƒe/j9e4d d ƒZBe0eBd ƒe0eBd ƒe0d3ƒe0d4ƒe0d+d,dgƒe0d5ƒe0e:j;ƒe0d6ƒe0e=j;ƒe0d7ƒe/jCZDe0eBd ejEejFeDeDƒeDjGd ƒƒe6jHe=j;ƒZIe0d8ƒe0ejFeDeDƒeDjGd eBd ƒe0d9ƒe0e=j>jJd:dd;…dd;…fƒe0d<ƒe0ejKjLej@e6jAd1d2ƒe=j;ƒƒdd;…dd;…f ƒe"e4d;ƒZMeMj9d.d0ƒZNe0eNj;ƒnd-ZOd(e,krŠe#eOdd=gddgd>d,ƒ\ZIZPejQƒejRd?ƒejSeIƒejRd@ƒejSePƒdAZTejUjVdBƒZTe0dCeTƒejUjTeTƒdDZWe$eOdeWgdd,gd>dEdFdƒ\ZIZPe*eIePƒe*eIdGePdGƒejUjTeTƒe&eOdeWgd d gd,d ggd>dEdFdƒ\ZXZYZZe*eXeO eYeO dHƒe*eXdGeO!eYdGeO!dHƒejUjTeTƒe&eOdeWgd d gddIggd>dEdFdƒ\Z[Z\ZZe*e[eO e\eO dJƒe*e[dGeO!e\dGeO!dJƒejUjTeTƒe&eOdeWgd d gddIgddIgddIggd>dEdFdƒ\Z]Z^Z_e*e]eO e^eO dKƒe*e]dGeO!e^dGeO!dKƒejUjTeTƒe&eOdeWgdd d gd ddIgd ddIgd ddIggd>dEdFdƒ\Z`ZaZbe*e`eO eaeO dKƒe*e`dGeO!eadGeO!dKƒejcdLƒZddedd dEdFddRedƒ\ZeZfZge*eedS efdS dKƒnejUjVdBƒZTe0dCeTƒejhdSƒjidTd;ƒZjejkejlejjGd d fƒejfƒZmedd gejndUdVd gdEdEd ggƒemƒ\ZoZpd-ZOd-ZqejUjTeTƒddWgZ1dd d gd dXdEggZ2e&eqeOe1e2d>dXdFdYƒ\Z`ZaZbe`eqeaeqebeqZ`ZaZbe*e`eO eaeO dKƒee`e`j5ƒƒZrd er_7d er_8ejndZdd[dEgƒer_serj9d\ejndZdd[dEgƒd]d-ƒZte0d^etj;ƒe*erjuerjPƒe0d_ƒe0e jvd`„dadId[gƒƒee`e`j5ƒƒZwd ew_7d er_8ejndZd[dgƒZxexew_sewj9d\exd]dbƒZye0dceyj;ƒee`e`j5ƒƒZwd ew_7d er_8ejndZd[dgƒZxexew_sewj9d\exd.d0d]dbƒZye0dceyj;ƒdde,kry ddelzm{Z{e{j|dfƒZ}e{j~dgdhƒZje0diejej€ejd;ƒƒdj ƒe"ej€ejd;ƒƒZMeMj9d\dkdd,gd]dlƒZe0ej;ƒe"ej€ejd;ƒƒZ‚e‚j9d\dkdd,gd]dld.d0ƒZƒe0eƒj;ƒne'dadId[ge`ƒZ„e0e„d ƒe&dSe1e2d>dmdFd2dRejldSƒƒ\Z…Z†Z‡ejUjˆdSƒZodadId[gZ;e'e;eoƒ\Z‰ZŠZ‹e‹ZŒd ZeŽe‹ƒZOdnejejeŒƒeƒejeod;eŒeƒeOejd;ej‘ƒZ’e0e‰e’ƒejUjTd ƒejcdoƒZ“xDe”d doƒD]3Z•ejUjˆƒZ–dIe“e•d d2e–e“e• aic, bic, ... -> test statistics, tvalue, fvalue, ... -> new to add: distribution (mean, cov) of non-linear transformation -> parameter restrictions or transformation with corrected covparams (?) -> sse, rss, rsquared ??? are they defined from this in general -> robust parameter cov ??? -> additional residual based tests, NW, ... likelihood ratio, lagrange multiplier tests ??? how much can be reused from linear model result classes where `errorsest = y - X*beta` ? for tsa: what's the division of labor between model, result instance and process examples: * arma: ls and mle look good * arimax: add exog, especially mean, trend, prefilter, e.g. (1-L) * arma_t: arma with t distributed errors (just a change in loglike) * garch: need loglike and (recursive) errorest * regime switching model without unobserved state, e.g. threshold roadmap for garch: * simple case * starting values: garch11 explicit formulas * arma-garch, assumed separable, blockdiagonal Hessian * empirical example: DJI, S&P500, MSFT, ??? * other standard garch: egarch, pgarch, * non-normal distributions * other methods: forecast, news impact curves (impulse response) * analytical gradient, Hessian for basic garch * cleaner simulation of garch * result statistics, AIC, ... * parameter constraints * try penalization for higher lags * other garch: regime-switching for pgarch (power garch) need transformation of etax given the parameters, but then misofilter should work general class aparch (see garch glossary) References ---------- see notes_references.txt Created on Feb 6, 2010 @author: "josef pktd" iÿÿÿÿ(tprint_function(tzipN(tassert_almost_equal(toptimizetsignal(tModeltLikelihoodModelResults(t miso_lfilter(ttsaicCstj|dd|ƒS(s<Helper function to calculate sum of squares along first axisitaxis(tnptsum(txR ((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pytsumofsq[sicCstj|ƒ}tj|ƒ}|dkr9|jƒ}n|jdkrX|j|}n t|ƒ}||}|rÃdtjdtj ƒtj|ƒ|d|}tj ||ƒ}||fSdtj tj|ƒ|ƒtj |d||ƒ|tjdtj ƒ}|SdS(Nigà¿i( R tasarrayt atleast_1dtNonetraveltndimtshapetlentlogtpiR (R tmutsigma2t returnllsR tnobstllstLL((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyt normloglike`s   3 OtLikelihoodModelcBs\eZdZd d„Zd„Zd„Zd„Zd„Zd„Z d ddd d „Z RS( s2 Likelihood model is a subclass of Model. cCs'tt|ƒj||ƒ|jƒdS(N(tsuperRt__init__t initialize(tselftendogtexog((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR scCsdS(s¸ Initialize (possibly re-initialize) a Model instance. For instance, the design matrix of a linear model may change and some things must be recomputed. N((R"((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR!ƒscCs t‚dS(s* Log-likelihood of model. N(tNotImplementedError(R"tparams((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pytloglikescCs t‚dS(sf Score vector of model. The gradient of logL with respect to each parameter. N(R%(R"R&((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pytscore“scCs t‚dS(sn Fisher information matrix of model Returns -Hessian of loglike evaluated at params. N(R%(R"R&((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyt information›scCs t‚dS(s1 The Hessian matrix of the model N(R%(R"R&((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pythessian£stnewtoni#g:Œ0âŽyE>c sØddddddg}|dkr>dgˆjjd}n||kr]td |ƒ‚n‡fd †}‡fd †}d}|jƒdkrld} tj|ƒ} tj| g} x—| |krPtjtj | d | d ƒ|kƒrPˆj | d ƒ} | d tj tj j | ƒˆj| d ƒƒ} | j| ƒ| d7} qºWtˆ| ƒ}| |_n_|dkrd}tj|||ddd|d|ƒ\}}}}}}}| }tˆ|ƒ}d}tt|jdƒ|||||||gƒƒˆ_n¼|dkrstj|||d|ddd|d|ƒ\}}}}}}tˆ|ƒ}| }nX|dkrËtj||ddd|d|ƒ\}}}}}tˆ|ƒ}| }n|ˆ_|S(sK Fit method for likelihood based models Parameters ---------- start_params : array-like, optional An optional method : str Method can be 'newton', 'bfgs', 'powell', 'cg', or 'ncg'. The default is newton. See scipy.optimze for more information. R+tbfgstpowelltcgtncgtfminiisUnknown fit method %scsˆj|ƒ S(N(R'(R&(R"(s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyt»tcsˆj|ƒ S(N(R((R&(R"(s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR1¼R2iÿÿÿÿiþÿÿÿt full_outputtmaxitertgtols8xopt, fopt, gopt, Hopt, func_calls, grad_calls, warnflags, tfhesstavextoltxtolN(RR$Rt ValueErrortlowerR tarraytinftalltabsR*tdottlinalgtinvR(tappendRt iterationRt fmin_bfgstdictRtsplitt optimresultstfmin_ncgR0t_results(R"t start_paramstmethodR4ttoltmethodstfR(thessRCtstartthistorytHt newparamstmlefittxopttfopttgopttHoptt func_callst grad_callstwarnflagtconvergetoptrestfcallstgcallsthcallstnitertfuncalls((R"s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pytfit©sT   "   $' '  $  N( t__name__t __module__t__doc__RR R!R'R(R)R*Rc(((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyRzs     t TSMLEModelcBsSeZdZd d„Zd„Zd„Zd„Zd„Zd dddd „Z RS( sp univariate time series model for estimation with maximum likelihood Note: This is not working yet cCs/tt|ƒj||ƒd|_d|_dS(Ni(RRgR tnartnma(R"R#R$((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR ós cCs t‚dS(N(R%(R"R&((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyt geterrorsûscCs t‚dS(s} Loglikelihood for timeseries model Notes ----- needs to be overwritten by subclass N(R%(R"R&((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR'þscCs&tj|jddƒ}||ƒdS(s- Score vector for Arma model tstepMaxg-Cëâ6?iÿÿÿÿ(tndttJacobianR'(R"R&tjac((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR( scCs&tj|jddƒ}||ƒdS(sE Hessian of arma model. Currently uses numdifftools Rkg-Cëâ6?iÿÿÿÿ(RlRmR((R"R&tHfun((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR*siˆR0g:Œ0âŽyE>c CsX|dkr't|dƒr'|j}ntt|ƒjd|d|d|d|ƒ}|S(shestimate model by minimizing negative loglikelihood does this need to be overwritten ? t _start_paramsRJR4RKRLN(RthasattrRpRRgRc(R"RJR4RKRLRT((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyRcs  N( RdReRfRR RjR'R(R*Rc(((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyRgìs   tGarch0cBs5eZdZdd„Zd„Zd„Zd„ZRS(s@Garch model, still experimentation stage: simplified structure, plain garch, no constraints still looking for the design of the base class serious bug: ar estimate looks ok, ma estimate awful -> check parameterization of lagpolys and constant looks ok after adding missing constant but still difference to garch11 function corrected initial condition -> only small differences left between the 3 versions ar estimate is close to true/DGP model note constant has different parameterization but design looks better cCsWtt|ƒj||ƒd|_d|_|d|_tj|jjƒƒ|_ dS(Nii( RRrR RhRit_etaxR Rtmeant_icetax(R"R#R$((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR :s    cCsdS(N((R"((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR!Esc Csj|\}}}|j|}|j}|jd}tj|||ƒ}tj|||d|ƒd} | S(sä Parameters ---------- params : tuple, (ar, ma) try to keep the params conversion in loglike copied from generate_gjrgarch needs to be extracted to separate function itzi(RsRuRRtlfiltictlfilter( R"R&tartmaRtetaxticetaxRRvth((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pytgethHs    c Cs |j|j}}tjdg|| fƒ}tjdg||||!fƒ}|d}|||f}|j|ƒ}||_||_tj|dƒ}d} t|ƒ} d} dtj tj |ƒ| ƒtj |j d|| ƒ| tj dtj ƒ} | S(sY Loglikelihood for timeseries model Notes ----- needs to be overwritten by subclass make more generic with using function _convertparams which could also include parameter transformation _convertparams_in, _convertparams_out allow for different distributions t, ged,... iiiÿÿÿÿgíµ ÷Æ°>gà¿i( RhRiR t concatenateR~tparams_convertedR}tmaximumRR RR#R( R"R&tptqRyRzRR}RR Rtllike((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR'gs#    ON(RdReRfRR R!R~R'(((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyRr's   tGarchXcBs>eZdZdd„Zd„Zd„Zd„Zd„ZRS(søGarch model, still experimentation stage: another version, this time with exog and miso_filter still looking for the design of the base class not done yet, just a design idea * use misofilter as in garch (gjr) * but take etax = exog this can include constant, asymetric effect (gjr) and other explanatory variables (e.g. high-low spread) todo: renames eta -> varprocess etax -> varprocessx icetax -> varprocessic (is actually ic of eta/sigma^2) cCsutt|ƒj||ƒd|_d|_tjtjtdfƒ|d|ƒ|_ tj |j j ƒƒ|_ dS(Nii( RRrR RhRiR t column_stacktonesRRsRRtRu(R"R#R$((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR ¨s   +cCsdS(N((R"((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR!·scCsdS(N((RyRzR((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pytconvert_mod2paramsºsc Cs{|\}}}|j|}|j}|j}t|||d|jƒd}|dk} | jƒrwtj|ƒ}n|S(sä Parameters ---------- params : tuple, (ar, ma) try to keep the params conversion in loglike copied from generate_gjrgarch needs to be extracted to separate function tuseici(RsRuRRtanyR R>( R"R&RyRzRR{R|RR}thneg((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR~½s      c Cs |j|j}}tjdg|| fƒ}tjdg||||!fƒ}|d}|||f}|j|ƒ}||_||_tj|dƒ}d} t|ƒ} d} dtj tj |ƒ| ƒtj |j d|| ƒ| tj dtj ƒ} | S(sY Loglikelihood for timeseries model Notes ----- needs to be overwritten by subclass make more generic with using function _convertparams which could also include parameter transformation _convertparams_in, _convertparams_out allow for different distributions t, ged,... iiiÿÿÿÿgíµ ÷Æ°>gà¿i( RhRiR RR~R€R}RRR RR#R( R"R&R‚RƒRyRzRR}RR RR„((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR'ås#    ON( RdReRfRR R!RˆR~R'(((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR…–s     (tGarchcBs5eZdZdd„Zd„Zd„Zd„ZRS(sOGarch model gjrgarch (t-garch) still experimentation stage, try with cCs/tt|ƒj||ƒd|_d|_dS(Ni(RRŒR RhRi(R"R#R$((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR s cCsdS(N((R"((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR!#sc Cs|\}}|j}|jd}tj|dfƒ}d|dd…df<|ddd…df|dd…dd…ftsqrt( R"R&RyRztetaRR{R}R‹terr((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyRj&s   0;  cCs¤|j|j}}tjdg|| fƒ}tj|ddfƒ}|d|d gà¿(ii(RhRiR RtzerosRjR€t errorsestR}R{RRRtR RR#R(R"R&R‚RƒRyRzRR’R}R{RR RtmuyR„((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR'Js&3;     ON(RdReRfRR R!RjR'(((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyRŒs    $c CsØ||}}tjdg|| fƒ}tj|ddfƒ}|d|dR;tTrueR R?RR( R"R&RtytylagR™t usepenaltyt oldparamst diffsumsqRR'((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR'²s$    % &V#c Cs„|j}|j}|j}t|tj||ƒƒ}d|dtj||tj||ƒdd…dfƒd||dd}d|||ddd|d}| d|||d|dd|tj||tj||ƒdd…dfƒd|d|||dd|||ddd|dd|d|}|jrhnt j |j ƒ} | |ƒS(s¾ Notes ----- Need to generalize for AR(p) and for a constant. Not correct yet. Returns numerical gradient. Depends on package numdifftools. iiþÿÿÿNiigà?( R#R$RR R R?R RR™RlRmR'( R"R&RžRŸRR¢tdsdrRtgradienttj((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR(Ñs   <&+ cCsdS(s% Not Implemented Yet N((R"R&((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR)ìscCstj|jƒ}||ƒS(sN Returns numerical hessian for now. Depends on numdifftools. (RltHessianR'(R"R&R}((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR*òsR,i#g:Œ0âŽyE>c s:|ˆ_|jƒ}‡fd†}|dkr^ttˆƒjd|d|d|d|ƒnØdg}|dkrˆtjd gƒ}n|d krÎtj ||d t d|ƒ}|d d!\ˆ_ ˆ_ n|dkrtj ||d t d|ƒ}|d ˆ_ n|dkr6tj||ƒ}|dˆ_ ndS(sÚ Fit the unconditional maximum likelihood of an AR(p) process. Parameters ---------- start_params : array-like, optional A first guess on the parameters. Defaults is a vector of zeros. method : str, optional Unconstrained solvers: Default is 'bfgs', 'newton' (newton-raphson), 'ncg' (Note that previous 3 are not recommended at the moment.) and 'powell' Constrained solvers: 'bfgs-b', 'tnc' See notes. maxiter : int, optional The maximum number of function evaluations. Default is 35. tol = float The convergence tolerance. Default is 1e-08. penalty : bool Whether or not to use a penalty function. Default is False, though this is ignored at the moment and the penalty is always used if appropriate. See notes. Notes ----- The unconstrained solvers use a quadratic penalty (regardless if penalty kwd is True or False) in order to ensure that the solution stays within (-1,1). The constrained solvers default to using a bound of (-.999,.999). csˆj|ƒ S(N(R'(R&(R"(s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR1"R2R+R,R/RJRKR4RLg+‡ÙÎ÷ï¿g+‡ÙÎ÷ï?isbfgs-bt approx_gradtboundsittncR-N(R+R,R/(g+‡ÙÎ÷ï¿g+‡ÙÎ÷ï?(R™R:RR—RcRR R;Rt fmin_l_bfgs_bRR&tllftfmin_tnct fmin_powell( R"RJRKR4RLR™tminfuncR¨tretval((R"s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyRcús(!        N( RdReRfRR R!R'R(R)R*RœRc(((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR—žs      tArmacBs\eZdZd d„Zd„Zd„Zd„Zd„Zd„Z d ddd d „Z RS( sˆ univariate Autoregressive Moving Average model Note: This is not working yet, or does it this can subclass TSMLEModel cCs/tt|ƒj||ƒd|_d|_dS(Ni(RR°R RhRi(R"R#R$((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR Es cCsdS(N((R"((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR!MscCsn|j|j}}tjdg|| fƒ}tjdg||||!fƒ}tj|||jƒ}|S(Ni(RhRiR RRRxR#(R"R&R‚RƒtrhoytrhoeR’((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyRjPs #cCs†|j|ƒ}tj|dddƒ}d}t|ƒ}d|tj|ƒtj|d||ƒ|tjdtjƒ}|S(sª Loglikelihood for arma model Notes ----- The ancillary parameter is assumed to be the last element of the params vector iÿÿÿÿigíµ ÷Æ°>igà¿(RjR RRRR R(R"R&R’RR RR„((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR'Xs DcCs&tj|jddƒ}||ƒdS(s- Score vector for Arma model Rkg-Cëâ6?iÿÿÿÿ(RlRmR'(R"R&Rn((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR(uscCs&tj|jddƒ}||ƒdS(sE Hessian of arma model. Currently uses numdifftools Rkg-Cëâ6?iÿÿÿÿ(RlRmR((R"R&Ro((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR*€siˆR0g:Œ0âŽyE>c Cso|dkr>tjdtj|j|jƒdgfƒ}ntt|ƒjd|d|d|d|ƒ}|S(Ngš™™™™™©?iRJR4RKRL( RR RR‡RhRiRR°Rc(R"RJR4RKRLRT((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyRc‰s  2N( RdReRfRR R!RjR'R(R*Rc(((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pyR°=s     gð?cCskddlm}||||dƒ}||d}tj|ƒ}tj|ƒtjj|ƒ}||fS(srsimulate garch like process but not squared errors in arma used for initial trial but produces nice graph iÿÿÿÿ(tarma_generate_samplegš™™™™™¹?i(tstatsmodels.tsa.arima_processR³R texpRŽtrandomtrandn(RRyRzRR³R}R((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pytgenerate_kindofgarchs gš™™™™™¹?cCsL|tjj|ƒ}tj|||dƒ}tj|ƒ|}||fS(svsimulate standard garch scale : float scale/standard deviation of innovation process in GARCH process i(R R¶R·RRxRŽ(RRyRzRtscaleRR}R((s<lib/python2.7/site-packages/statsmodels/sandbox/tsa/garch.pytgenerate_garch¨sc CsÜ|dkr%|tjj|ƒ}n|}tj|dfƒ}||dd…df<|ddd…df|dd…dd…fJsn   r;oj ŸS 6  7 3            %        1 ) * H *      0 00B6 6 +?    - "       &! 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