p7]c @ sddlmZddlmZmZmZddlZddlmZm Z ddl m Z m Z ddl mZddlmZddlmZmZmZmZddljjjZddljjZdd lmZmZdd l m!Z!m"Z"dd l#m$Z$ddl%jj&Z'dd l(m)Z)d gZ*ddZ+dZ,ddZ-d ej.fdYZ/dej0fdYZ1de'j2fdYZ3e'j4e3e1e5dkrddl6j7Z8e8j9j:j;de<Z:e/e:j=Z>e>j?ddZ@e/e:j=ZAeAj?dddddddd d!d"ZBddlCZCddlDjEZFeFjGd#d$d%d&ZHeFjId'eHd(eJe:j=ZKeCjLd)eHjMd*eJe:j=d%d+ZNejOd$d$eJe:j=ZPeFjIePd%d&ZPddlMZMejQeeMjMjReKjSjTeUZVeCjWe:j=d,eVZ:e/e:d%d&ZXeXj?ddddZYejQd-d.d/d0d1d0d2d3d4d5g ZZej[eZZ\d6Z]ndS(7i(tdivision(t iteritemstrangetlmapN(tdottidentity(tinvtslogdet(tnorm(tOLS(tlagmatt add_trendt_ar_transparamst_ar_invtransparams(tcache_readonlytcache_writable(t approx_fprimet approx_hess(t KalmanFilter(tutiltARicC stj|dd|S(s<Helper function to calculate sum of squares along first axisitaxis(tnptsum(txR((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pytsumofsqscC s5|dks|r1||kr1td|ndS(NtcmlesEStart must be >= k_ar for conditional MLE or dynamic forecast. Got %d(t ValueError(tstarttk_artmethodtdynamic((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyt_check_ar_startsc C s|r|| nd}||ddd}tj||}|r^||||!||*n|| ||*tj|} xMt|D]?} |tj||| | |!} | | | <| || |s%  "cC sdS(N((R8((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyt initializeGscC sJ|j}|j}|j}t||||!j||||+|S(s Transforms params to induce stationarity/invertability. Reference --------- Jones(1980) (RR$tcopyR (R8R#tptkt newparams((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyt _transparamsJs    (cC sJ|j}|j}|j}t||||!j||||+|S(s9 Inverse of the Jones reparameterization (RR$R<R (R8t start_paramsR=R>R?((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyt_invtransparamsXs    (cC s|j}tj||||}tj|||d|} tj|df} ttt|dtj ||t| | jj d} | j ||dd} | } tj |} xt |D]}||t| | }tt| | | j}d|}ttt|| | j|}t|| t||} |t|| }tt|| |jt| | j} ||dkrt| | ||d|tT_mattR_mattalphatQ_0tPtZ_matR*tv_mattF_mattFinvtKtL((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyt_presample_fitbs& & $+c C st|dd}t|dd}|dkrb|dkrL| rLd}n|}|j|}n|dkr~|jd}ntt|j|||\}}}}d|kr||krtd|nt||||||||fS(NRtmleRiisEStart must be >= k_ar for conditional MLE or dynamic forecast. Got %s(tgetattrR5t_indexR3Rt_get_prediction_indexRR ( R8RRKRtindexRRt out_of_sampletprediction_index((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyR\s   * cC s|j|||\}}}}||dkr@tdn|j}|j}|j} |jj} |r|||d7}t| |||||Stj |d|} | dkrC|r|ddtj ||} nd} ||krC|j |||t |d|| | | | | ||c | 7*qCn||krS| Stj |j|} t||d}t||d}t t| ||d}| ||!| |)|rt| ||||}tj| |f} n| S(s Returns in-sample and out-of-sample prediction. Parameters ---------- params : array The fitted model parameters. start : int, str, or datetime Zero-indexed observation number at which to start forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. end : int, str, or datetime Zero-indexed observation number at which to end forecasting, ie., the first forecast is start. Can also be a date string to parse or a datetime type. dynamic : bool The `dynamic` keyword affects in-sample prediction. If dynamic is False, then the in-sample lagged values are used for prediction. If `dynamic` is True, then in-sample forecasts are used in place of lagged dependent variables. The first forecasted value is `start`. Returns ------- predicted values : array Notes ----- The linear Gaussian Kalman filter is used to return pre-sample fitted values. The exact initial Kalman Filter is used. See Durbin and Koopman in the references for more information. isend is before startRYi(R\RRR$RR(tsqueezeR,RR!RRXtminRtXtmaxtlentr_(R8R#RRKRR^t_RR$RR(RLR&t fittedvaluestpv_starttfv_starttfv_endtforecastvalues((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pytpredictsB#!      "    cC s|j}|j}|d}tjd||f}tj||fd|j}xtd|D]q}tj||| d ||d|ddf<||d|ddfctj|| |d 8R=tp1tparams0tVpinvR*((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyt_presample_varcovs   2= cC s}|j}|j}|j}t|jtj||}||}| dtjdtjtj||d|S(sQ Loglikelihood of AR(p) process using conditional sum of squares i( tnobstYRbRR`RRtlogtpi(R8R#RuRvRbtssrtsigma2((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyt _loglike_csss   " )cC s|j}|j}|j}|j}|j}|jrH|j|}n|| j}|rr|dg|}n dg}tj |dtj ||} || dddf} |j |} tj tj | j| | j} t||jtj ||} d|| | }||_t| d}d|tjdtjtj||| || |}|S( sO Loglikelihood of AR(p) process using exact maximum likelihood iiNg?ig@ig(RuRbR(RR$t transparamsR@R<RtasarrayRR5RtRREtitemRR`RzRRwRx(R8R#RuRbR(RR$typtctmuptdiffpRst diffpVpinvRyRztlogdettloglike((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyt _loglike_mles,       $'& <cC s-|jdkr|j|S|j|SdS(s The loglikelihood of an AR(p) process Parameters ---------- params : array The fitted parameters of the AR model Returns ------- llf : float The loglikelihood evaluated at `params` Notes ----- Contains constant term. If the model is fit by OLS then this returns the conditonal maximum likelihood. .. math:: \frac{\left(n-p\right)}{2}\left(\log\left(2\pi\right)+\log\left(\sigma^{2}\right)\right)-\frac{1}{\sigma^{2}}\sum_{i}\epsilon_{i}^{2} If it is fit by MLE then the (exact) unconditional maximum likelihood is returned. .. math:: -\frac{n}{2}log\left(2\pi\right)-\frac{n}{2}\log\left(\sigma^{2}\right)+\frac{1}{2}\left|V_{p}^{-1}\right|-\frac{1}{2\sigma^{2}}\left(y_{p}-\mu_{p}\right)^{\prime}V_{p}^{-1}\left(y_{p}-\mu_{p}\right)-\frac{1}{2\sigma^{2}}\sum_{t=p+1}^{n}\epsilon_{i}^{2} where :math:`\mu_{p}` is a (`p` x 1) vector with each element equal to the mean of the AR process and :math:`\sigma^{2}V_{p}` is the (`p` x `p`) variance-covariance matrix of the first `p` observations. RN(RR{R(R8R#((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyR9s! cC s|j}t||ddS(s Return the gradient of the loglikelihood at params. Parameters ---------- params : array-like The parameter values at which to evaluate the score function. Notes ----- Returns numerical gradient. tepsilong:0yE>(RR(R8R#R((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pytscore`s cC sdS(s% Not Implemented Yet N((R8R#((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyt informationpscC s|j}t||S(s4 Returns numerical hessian for now. (RR(R8R#R((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pythessianvs cC sd|j}t|d|dd}tj|}|rWt|dtd|dd}n||_|S(st Private method to build the RHS matrix for estimation. Columns are trend terms then lags. tmaxlagttrimtbothtprependttrendt has_constanttraise(R(R Rtget_trendorderR tTrueR$(R8RRR(RbR$((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyt_stackX}s ! RRYcC s|j}||}||_|j||}||_|j}td|}i} |dkrxrt||dD]]} ||| } t| jd| d|ddd|dd d d} t | || | tres((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pys sgjg RQ?ii#(R(RvRRbR$RcRRtfitRZRaRRtabsttvalues(R8RticRRR(RvRbR>tresultstlagt endog_tmpRtbestictbestlagtstop((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyt select_orders6       % Rtlbfgsi#ic K sX|j}|dkr+td|n||_||_||_t|j} |j}|dkrtt d| dd}n|}|dk r|j}|dkrtd |n|j ||||}n||_ ||dddf}|j ||}|j }tj|j|||_||_||_|dkrt||j}|j}| ||_|j|j|_nK|dkr|j}| |_|dkrt||jj}n9t|||krtdt|||fn|j|}|dkr|| jdd| jdd| jdd| jdtntt|jd|d|d|d| d| d| | }|j}|jr|j|}t |_qnt!j"j#|}t!j$||j%}t&|||}|dkrN| rN|j'|_'|j(|_(nt)|S(s Fit the unconditional maximum likelihood of an AR(p) process. Parameters ---------- maxlag : int If `ic` is None, then maxlag is the lag length used in fit. If `ic` is specified then maxlag is the highest lag order used to select the correct lag order. If maxlag is None, the default is round(12*(nobs/100.)**(1/4.)) method : str {'cmle', 'mle'}, optional cmle - Conditional maximum likelihood using OLS mle - Unconditional (exact) maximum likelihood. See `solver` and the Notes. ic : str {'aic','bic','hic','t-stat'} Criterion used for selecting the optimal lag length. aic - Akaike Information Criterion bic - Bayes Information Criterion t-stat - Based on last lag hqic - Hannan-Quinn Information Criterion If any of the information criteria are selected, the lag length which results in the lowest value is selected. If t-stat, the model starts with maxlag and drops a lag until the highest lag has a t-stat that is significant at the 95 % level. trend : str {'c','nc'} Whether to include a constant or not. 'c' - include constant. 'nc' - no constant. The below can be specified if method is 'mle' transparams : bool, optional Whether or not to transform the parameters to ensure stationarity. Uses the transformation suggested in Jones (1980). start_params : array-like, optional A first guess on the parameters. Default is cmle estimates. solver : str or None, optional Solver to be used if method is 'mle'. The default is 'lbfgs' (limited memory Broyden-Fletcher-Goldfarb-Shanno). Other choices are 'bfgs', 'newton' (Newton-Raphson), 'nm' (Nelder-Mead), 'cg' - (conjugate gradient), 'ncg' (non-conjugate gradient), and 'powell'. maxiter : int, optional The maximum number of function evaluations. Default is 35. tol : float The convergence tolerance. Default is 1e-08. full_output : bool, optional If True, all output from solver will be available in the Results object's mle_retvals attribute. Output is dependent on the solver. See Notes for more information. disp : bool, optional If True, convergence information is output. callback : function, optional Called after each iteration as callback(xk) where xk is the current parameter vector. kwargs See Notes for keyword arguments that can be passed to fit. References ---------- Jones, R.H. 1980 "Maximum likelihood fitting of ARMA models to time series with missing observations." `Technometrics`. 22.3. 389-95. See Also -------- statsmodels.base.model.LikelihoodModel.fit RtywRYsMethod %s not recognizedi gY@ig@taictbicthqicst-statsic option %s not understoodNs6Length of start params is %d. There are %d parameters.Rtpgtolg:0yE>tfactrtmt approx_gradRARRRRtcallback(RRRYg?(RRRst-stat(*tlowerRRRR|RdR(R5tinttroundRRRR$Rtmake_lag_namest endog_namest exog_namesRvRbR RR#RuRyRzRBt setdefaultRR3RR@tFalseRtlinalgtpinvRREt ARResultst mle_retvalst mle_settingstARResultsWrapper(R8RRRRR|RAtsolverRRRRtkwargsRuR(RRvRbR$tarfitR#tmlefitt pinv_exogtnormalized_cov_params((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyRsrF       !                      N(t__name__t __module__ttsbaset_tsa_doctbaset_missing_param_doct__doc__R5R4R;R@RBRXR\RRlRtR{RRRRRRRRR(((s7lib/python2.7/site-packages/statsmodels/tsa/ar_model.pyR7s.     # T  % '    8  RcB seZdZiZdddZedZedZe dZ e dZ e dZ e dZ e d Ze d Ze d Ze d Ze d ZddedZejjjdZdjed ede_RS(s Class to hold results from fitting an AR model. Parameters ---------- model : AR Model instance Reference to the model that is fit. params : array The fitted parameters from the AR Model. normalized_cov_params : array inv(dot(X.T,X)) where X is the lagged values. scale : float, optional An estimate of the scale of the model. Attributes ---------- aic : float Akaike Information Criterion using Lutkephol's definition. :math:`log(sigma) + 2*(1 + k_ar + k_trend)/nobs` bic : float Bayes Information Criterion :math:`\log(\sigma) + (1 + k_ar + k_trend)*\log(nobs)/nobs` bse : array The standard errors of the estimated parameters. If `method` is 'cmle', then the standard errors that are returned are the OLS standard errors of the coefficients. If the `method` is 'mle' then they are computed using the numerical Hessian. fittedvalues : array The in-sample predicted values of the fitted AR model. The `k_ar` initial values are computed via the Kalman Filter if the model is fit by `mle`. fpe : float Final prediction error using Lütkepohl's definition ((n_totobs+k_trend)/(n_totobs-k_ar-k_trend))*sigma hqic : float Hannan-Quinn Information Criterion. k_ar : float Lag length. Sometimes used as `p` in the docs. k_trend : float The number of trend terms included. 'nc'=0, 'c'=1. llf : float The loglikelihood of the model evaluated at `params`. See `AR.loglike` model : AR model instance A reference to the fitted AR model. nobs : float The number of available observations `nobs` - `k_ar` n_totobs : float The number of total observations in `endog`. Sometimes `n` in the docs. params : array The fitted parameters of the model. pvalues : array The p values associated with the standard errors. resid : array The residuals of the model. If the model is fit by 'mle' then the pre-sample residuals are calculated using fittedvalues from the Kalman Filter. roots : array The roots of the AR process are the solution to (1 - arparams[0]*z - arparams[1]*z**2 -...- arparams[p-1]*z**k_ar) = 0 Stability requires that the roots in modulus lie outside the unit circle. scale : float Same as sigma2 sigma2 : float The variance of the innovations (residuals). trendorder : int The polynomial order of the trend. 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