ó áp7]c@sbdZddlmZddlZddlmZmZddlm Z de fd„ƒYZ dS(s‘ Created on Sun Oct 10 14:57:50 2010 Author: josef-pktd, Skipper Seabold License: BSD TODO: check everywhere initialization of signal.lfilter iÿÿÿÿ(trangeN(tsignaltoptimize(tGenericLikelihoodModeltArmacBs¿eZdZdd„Zd„Zd„Zd„Zd„Zdddd„Z ddd d d d „Z ddd „Z dddd„Z ddddd„Z ddd„Zedd„ƒZRS(sü univariate Autoregressive Moving Average model, conditional on initial values The ARMA model is estimated either with conditional Least Squares or with conditional Maximum Likelihood. The implementation is using scipy.filter.lfilter which makes it faster than the Kalman Filter Implementation. The Kalman Filter Implementation however uses the exact Maximum Likelihood and will be more accurate, statistically more efficent in small samples. In large samples conditional LS, conditional MLE and exact MLE should be very close to each other, they are equivalent asymptotically. Notes ----- this can subclass TSMLEModel TODO: - CondLS return raw estimation results - needs checking that there is no wrong state retained, when running fit several times with different options - still needs consistent order options. - Currently assumes that the mean is zero, no mean or effect of exogenous variables are included in the estimation. cCs/tt|ƒj||ƒd|_d|_dS(Ni(tsuperRt__init__tnartnma(tselftendogtexog((s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pyR0s cCsdS(N((R ((s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pyt initialize8sc Cs¼|j|j}}tjdg|| fƒ}tjdg||||!fƒ}dt||ƒ}tj|ƒ}|||d*tj|ƒ}|||d*tj|||jƒ} | S(Ni( RRtnpt concatenatetmaxtzerosRtlfilterR ( R tparamstptqtartmatmaxlagtarmaxtmamaxt errorsest((s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pyt geterrors;s#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¿(RR tmaximumtlentlogtsumtpi(R RRtsigma2taxistnobstllike((s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pytloglikeMs DcCsr|j|ƒ}tj|dddƒ}d}t|ƒ}dtj|ƒ|d|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?(RR RRRR (R RRR!R"R#R$((s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pyt nloglikeobsks 0itlsc sët|dƒs(tdt|ƒƒ‚n|\}}|ˆ_|ˆ_ˆjjƒ}|d krdtj |ƒ}dtj |ƒ} tj || f}n|j ƒ}|dkrt dddt ƒ} | j|ƒtjˆj|| \} } } }}nv|dkrng‡fd †}t d d dt ƒ} | j|ƒtj||| \} }}} }}}d\} }| ˆ_tjd g| | fƒˆ_tjd g| |||!fƒˆ_ˆj| ƒˆ_| | | ||fS(sp Estimate lag coefficients of an ARIMA process. Parameters ---------- order : sequence p,d,q where p is the number of AR lags, d is the number of differences to induce stationarity, and q is the number of MA lags to estimate. method : str {"ls", "ssm"} Method of estimation. LS is conditional least squares. SSM is state-space model and the Kalman filter is used to maximize the exact likelihood. rhoy0, rhoe0 : array_like (optional) starting values for estimation Returns ------- (rh, cov_x, infodict, mesg, ier) : output of scipy.optimize.leastsq rh : estimate of lag parameters, concatenated [rhoy, rhoe] cov_x : unscaled (!) covariance matrix of coefficient estimates t__iter__s8order must be an iterable sequence. Got type %s insteadgà?R'tftolg»½×Ùß|Û=t full_outputtssmcstjˆj|ƒdƒS(Ni(R RR(trho(R (s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pytättmaxiteriiN(NN(thasattrt ValueErrorttypeRRR tsqueezetNoneR tonestr_tlowertdicttTruetupdateRtleastsqRt fmin_bfgsRRtar_esttma_estterror_estimate(R tordert start_paramstmethodtoptkwdsRRtxtarcoefs0tmacoefs0t optim_kwdstrhtcov_xtinfodicttmesgtierterrfnsumtfopttgoptt_((R s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pytfitœs8       *  *   &tnmiˆg:Œ0âŽyE>c Ksÿ|\}}\} } |||_|_|dkratjdtj||ƒdgfƒ}ntt|ƒjd|d|d|d||} | j } | |_ tjdg| | fƒ|_ tjdg| | | | !fƒ|_ |j | ƒ|_ | S(sYEstimate an ARMA model with given order using Conditional Maximum Likelihood Parameters ---------- order : tuple, 2 elements specifies the number of lags(nar, nma) to include, not including lag 0 start_params : array_like, 1d, (nar+nma+1,) start parameters for the optimization, the length needs to be equal to the number of ar plus ma coefficients plus 1 for the residual variance method : str optimization method, as described in LikelihoodModel maxiter : int maximum number of iteration in the optimization tol : float tolerance (?) for the optimization Returns ------- mlefit : instance of (GenericLikelihood ?)Result class contains estimation results and additional statistics gš™™™™™©?iRAR/RBttolN(RRR4R RR5RRRQRR=R>RR?( R R@RARBR/RStkwdsRRRRtmlefitRH((s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pytfit_mleôs ,   &cCs|j|jS(sQpast predicted values of time series just added, not checked yet (R R?(R RR((s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pyt predicteds i cCsbtj|jtj|ƒf}|dkr7|j}n|dkrO|j}ntj|||ƒS(sonperiod ahead forecast at the end of the data period forecast is based on the error estimates N( R R6R?RR4R=R>RR(R RRtnperiodteta((s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pytforecast)s     icCsò|dkrt‚n|j|j}}d}|j}|j} |j|||!ddd…} |j|||||!ddd…} g} xRt||ƒD]A} | jt| | | || !ƒt| || || !ƒƒq Wt j | ƒS(sîrolling h-period ahead forecast without reestimation, 1 period ahead only in construction: uses loop to go over data and not sure how to get (finite) forecast polynomial for h-step Notes ----- just the idea: To improve performance with expanding arrays, specify total period by endog and the conditional forecast period by step_ahead This should be used by/with results which should contain predicted error or noise. Could be either a recursive loop or lfilter with a h-step ahead forecast filter, but then I need to calculate that one. ??? further extension: allow reestimation option question: return h-step ahead or range(h)-step ahead ? iiNiÿÿÿÿ( tNotImplementedErrorRRR?R RRtappendRR tasarray(R t step_aheadtstarttendR RRtkterrorstyt arcoefs_revt macoefs_revRWti((s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pyt forecast25s    !)?c Cs’ddlm}|j|j}}d}|j|||!}|j|||||!}||||ƒ|d} |j} tj| | ƒ} | S(s1another try for h-step ahead forecasting i(tarma2mai(t arima_processRhRRRR?R tconvolve( R R^R_RhRRRaRRtmarepRbt forecasts((s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pyt forecast3\s cCs)|tjj|ƒ}tj|||ƒS(N(R trandomtrandnRR(tclsRRtnsampletstdRY((s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pytgenerate_samplemsN(ii(ii(t__name__t __module__t__doc__R4RR RR%R&RQRVRWRZRgRmt classmethodRs(((s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pyRs     1X' '( Rvtstatsmodels.compat.pythonRtnumpyR tscipyRRtstatsmodels.base.modelRR(((s7lib/python2.7/site-packages/statsmodels/tsa/arma_mle.pyt s