p7]c @@sgddlmZddlmZmZmZddlmZddlZddl m Z ddl m Z m Z ddlmZddlmZmZmZmZdd lmZdd lmZddljjjZddljjZdd l m!Z!m"Z"dd l#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+dd l,m-Z-ddl.m/Z/ddl0m1Z1ddl2m3Z3m4Z4ddl5m6Z6dZ7dZ8dZ9dZ:dZ;dZ<dZ=dZ>dZ?e>idd6dd6dd 6e?d!6e<d"6Z@e>idd6dd6dd 6e?d!6e=d"6ZAd#ZBe>id$d6dd6eBd 6e?d!6e<d"6ZCe>id$d6dd6eBd 6e?d!6e=d"6ZDd%ZEd&ZFd'd(jGe>jHd(d)idd6eFd 6d*d!6d(eEd(e=d"6ZId'd(jGe>jHd(d)idd6eFd 6d*d!6d(eEd(d(jGe=jHd(d+ d,d(jGe=jHd(d+d"6ZJd-ZKd.ZLeMd/ZNeMdd0d1ZOd2ZPeQd3ZRd4ZSd5ZTd6ZUd7ZVdejWfd8YZXd$eXfd9YZYd:ejZfd;YZ[d<ej\fd=YZ]ej^e]e[d>e[fd?YZ_d@e]fdAYZ`ej^e`e_eadBkrcddlbjcZdddCl0meZeeedDdEgdDdFgdGdHZfeXefZgegjhdIdJdKdLdLfZiejjjkdMeedDdNdOgdLdFdPgdGdHZleXelZmemjhdIdJdKd)d)fZneXelZoeojhdIdJdKd)d)fdQdRZpedjqjrjsdSeQZteXetjuZvevjhdIdJdKdTdfZweedLdEdUdFgdVgdGdHZxeXexZyeyjhdKd+dLfdQdRdIdJdWezZ{eedDdEgdLdFdXdYgdGdHZ|eXe|Z}e}jhdKdLd+fdQdRdIdJZ~eedDdEdOdFdZgdLdUgdGdHZeXeZejhdKd[dLfdIdJdQdRZeedLd\gdDdEdOdFdZgdGdHZeXeZejhdKd[dLfdIdJdQdRZdd]lmZed^Zed_ZeYedLdLdLfjhZndS(`i(tabsolute_import(t string_typestrangetlong(tdatetimeN(toptimize(tttnorm(tlfilter(tdottlogtzerostpi(tinv(tcache_readonly(t yule_walkertOLS(tlagmatt add_trendt_ar_transparamst_ar_invtransparamst_ma_transparamst_ma_invtransparamst unintegratetunintegrate_levels(tutil(tAR(tarma2ma(tapprox_hess_cstapprox_fprime_cs(t KalmanFilters Notes ----- If exogenous variables are given, then the model that is fit is .. math:: \phi(L)(y_t - X_t\beta) = \theta(L)\epsilon_t where :math:`\phi` and :math:`\theta` are polynomials in the lag operator, :math:`L`. This is the regression model with ARMA errors, or ARMAX model. This specification is used, whether or not the model is fit using conditional sum of square or maximum-likelihood, using the `method` argument in :meth:`statsmodels.tsa.arima_model.%(Model)s.fit`. Therefore, for now, `css` and `mle` refer to estimation methods only. This may change for the case of the `css` model in future versions. spendog : array-like The endogenous variable. order : iterable The (p,q) order of the model for the number of AR parameters, differences, and MA parameters to use. exog : array-like, optional An optional array of exogenous variables. This should *not* include a constant or trend. You can specify this in the `fit` method.s-Autoregressive Moving Average ARMA(p,q) Models;Autoregressive Integrated Moving Average ARIMA(p,d,q) Modelsrendog : array-like The endogenous variable. order : iterable The (p,d,q) order of the model for the number of AR parameters, differences, and MA parameters to use. exog : array-like, optional An optional array of exogenous variables. This should *not* include a constant or trend. You can specify this in the `fit` method.sM Notes ----- Use the results predict method instead. s_ Notes ----- It is recommended to use dates with the time-series models, as the below will probably make clear. However, if ARIMA is used without dates and/or `start` and `end` are given as indices, then these indices are in terms of the *original*, undifferenced series. Ie., given some undifferenced observations:: 1970Q1, 1 1970Q2, 1.5 1970Q3, 1.25 1970Q4, 2.25 1971Q1, 1.2 1971Q2, 4.1 1970Q1 is observation 0 in the original series. However, if we fit an ARIMA(p,1,q) model then we lose this first observation through differencing. Therefore, the first observation we can forecast (if using exact MLE) is index 1. In the differenced series this is index 0, but we refer to it as 1 from the original series. s %(Model)s model in-sample and out-of-sample prediction Parameters ---------- %(params)s 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. However, if the dates index does not have a fixed frequency, end must be an integer index if you want out of sample prediction. exog : array-like, optional If the model is an ARMAX and out-of-sample forecasting is requested, exog must be given. Note that you'll need to pass `k_ar` additional lags for any exogenous variables. E.g., if you fit an ARMAX(2, q) model and want to predict 5 steps, you need 7 observations to do this. dynamic : bool, optional 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`. %(extra_params)s Returns ------- %(returns)s %(extra_section)s s3predict : array The predicted values. tARMAtModelsCparams : array-like The fitted parameters of the model.tparamstt extra_paramstreturnst extra_sectionstyp : str {'linear', 'levels'} - 'linear' : Linear prediction in terms of the differenced endogenous variables. - 'levels' : Predict the levels of the original endogenous variables. tARIMAs Examples -------- >>> import statsmodels.api as sm >>> import matplotlib.pyplot as plt >>> import pandas as pd >>> >>> dta = sm.datasets.sunspots.load_pandas().data[['SUNACTIVITY']] >>> dta.index = pd.date_range(start='1700', end='2009', freq='A') >>> res = sm.tsa.ARMA(dta, (3, 0)).fit() >>> fig, ax = plt.subplots() >>> ax = dta.loc['1950':].plot(ax=ax) >>> fig = res.plot_predict('1990', '2012', dynamic=True, ax=ax, ... plot_insample=False) >>> plt.show() .. plot:: plots/arma_predict_plot.py salpha : float, optional The confidence intervals for the forecasts are (1 - alpha)% plot_insample : bool, optional Whether to plot the in-sample series. Default is True. ax : matplotlib.Axes, optional Existing axes to plot with.s. Plot forecasts s is?fig : matplotlib.Figure The plotted Figure instanceisO This is hard-coded to only allow plotting of the forecasts in levels. cC@s*x#t|D]}tj|}q W|S(N(Rtnptcumsum(txtnt_((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pytcumsum_nscC@sT|dkrtd|n1|s1d|krP||krPtd|ndS(NisCThe start index %d of the original series has been differenced awaytmlesEStart must be >= k_ar for conditional MLE or dynamic forecast. Got %d(t ValueError(tstarttk_artk_difftmethodtdynamic((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyt_check_arima_starts   cC@s|rtj|}|r'd| ks@||krX|dk rX||||!||*q|r~||||||!||*q|| ||*nd}|}|dkr|dkrtj| dkr|dkr| dddf} nOtj| dkr=t| |kr$tdn| dddf} nttj| ||dddd }|d| j}|tj d| ddd  f|jddddf}qs|d| j}tj |g| }n|dkrdtj| |}t||dddd }tj d| ddd  f|jddddf}ntj| }tj|| d}|r|r||||!||*n|r|| ||*n|||fS( sZ Returns endog, resid, mu of appropriate length for out of sample prediction. R-iiNs%1d exog given and len(exog) != k_exogtoriginaltinttrimtbothi( R'R tNonetndimtlenR.RR tsumtr_tarray(tendogtptqtk_trendtk_exogR/terrorst trendparamtexparamstarparamstmaparamststepsR2texogtresidtytXtmu((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyt_get_predict_out_of_samplesB+   !'E A R-c C@st|||f||dt\} } } }t|||||| || | | ||| |\}}}tj|}|dkr|r|dtj| || tj||| S|dtj| || Sn|rd}nd}xtt||dD]f}||tj| ||||!tj||| ||||!}|||<||||R?tfloat64RJRtfitR!R tsqueezeR;R9tinttroundRR0R.Rt column_stackR`RtalltabstrootsR=(RR]t start_ar_lagsR@RAR^t start_paramsR?RJt ols_paramsRuRtarmodt arcoefs_tmptp_tmpRKt endog_startt resid_startt lag_endogt lag_residRMtcoefstarcoefs((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyt_fit_start_params_hrs^#       "  '      ),: 6 c@s|dkr!j||}nfd}j||}jr]j|}ndgt|}tj||dtddddd d d |d d }|d}jrj|}n|S(Nscss-mlec@sj| S(N(t loglike_css(R!(R(s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyt(R"it approx_gradtmi tpgtolgHz>tfactrg@@tboundstiprintii(N(NN( Rt transparamst_invtransparamsR9R<Rt fmin_l_bfgs_bRRt _transparams(RR]R2RRtfuncRtmlefit((Rs:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyt_fit_start_params$s      cC@st||jdtfS(s Compute the score function at params. Notes ----- This is a numerical approximation. targs(RtlogliketFalse(RR!((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pytscore7scC@st||jdtfS(sx Compute the Hessian at params, Notes ----- This is a numerical approximation. R(RRR(RR!((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pythessianAscC@s|j|j}}|j|j}tj|}|dkrO|| ||*n|dkrt||||!j||||+n|dkrt|||j|||)n|S(s Transforms params to induce stationarity/invertability. Reference --------- Jones(1980) i( R0RaRCRBR't zeros_likeRtcopyR(RR!R0RaR^t newparams((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRKs  + %cC@s|j|j}}|j|j}|j}||||!}|||}|dkrtt|||||+n|dkrt|||||||+n|S(s9 Inverse of the Jones reparameterization i(R0RaRCRBRRR(RRR0RaR^RRtmacoefs((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRds   "c C@st|dd}t|dd}t|dd}|dkrtd|kr^| r^d}n|}|j|}ntt|j|||\}}}} d|kr|||krtd|nt||||||||| fS(NR2R-R0iR1sEStart must be >= k_ar for conditional MLE or dynamic forecast. Got %s(tgetattrR9t_indexR|Rt_get_prediction_indexR.R4( RR/RXR3tindexR2R0R1t out_of_sampletprediction_index((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRvs  * c C@stj|}|j|j}}|j|j}t|dd}d|krtj||\ }}}}}}} } } } } }tj ||||||| | | | | }t |t r |d}q n9|j j }|j|j}|dkr|t|j|| 8}n|j}|j}t|||f|j|jdt\}}}}tjd| ftjd|f}}tt||}xFt|D]8}t||d ddd ||d ||RgY@Ri RR2tmaxitert full_outputtdisptcallbackN(#R0RaRR?RJRCR;RuRtR.RwRBRlRgRRhtlowerR2R9R'RRRt setdefaultRRR|RRR!RRt ARMAResultst mle_retvalst mle_settingstARMAResultsWrapper(RRR_R2RtsolverRRRRRtkwargsR0RaR?RJRCRBR^RR!tnormalized_cov_paramstarmafit((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyR.sXN    0               cO@stddS(Ns.from_formula is not supported for ARMA models.(tNotImplementedError(tclstformulaRgtsubsett drop_colsRR((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyt from_formulasN(t__name__t __module__ttsbaset_tsa_doct _arma_modelt _arma_paramst _armax_notest__doc__R9R}RRRRRRRRRRt _arma_predictRRRRRRt classmethodR(((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRs0   k     37      c B@seZejied6ed6dd6eidd6d6ZdddddZ d Z ddddd Z dd Z dd d e ddddddd ZddddedZee_RS(RxR!R"R#R&R RyRzc C@sv|\}}} |dkr:t||| f||||Stt|j|} | j||||||| SdS(Ni(RR|R&t__new__R}( RR?R]RJRRR{R@tdRAtmod((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRs  cC@sdt|dd}t|dd}t|dd}|j|j|j|jf|j|||fS(NRRR{Rz(RR9R?RbR1RaRJ(RRRR{((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyt__getnewargs__s c C@s|\}}} |dkr*tdntt|j||| f||||||_t|j| ||_tj |jd||_t t |j|| |dk r|j ||_ n|dkrd|j|j_ndj||j|j_t |j} |jjd} |jjdk r[|jj| | |jjd 2 is not supportedR*isD.sD{0:d}.it row_labels(R.R|R&R}R1RR?t_first_unintegrateR'tdiffRwR;R9RJt endog_namesRgRetformatRRRt_cachet_index_generated( RR?R]RJRRR{R@RRAt orig_lengtht new_length((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyR}s* +   ! c C@st|dd}t|dd}t|dd}|dkrtd|kr^| r^d}n|}|j|}nGt|tttjfr||8}|dkrtd|qnt|tttjfr||8}nt t |j |||\}}}} d|j kr0| r0||8}nd|kr_|||kr_td|nt ||||||||| fS(NR2R-R0iR1sDThe start index %d of the original series has been differenced awaysEStart must be >= k_ar for conditional MLE or dynamic forecast. Got %s(RR9RRRRR'tintegerR.R|R&RR2R4( RR/RXR3RR2R0R1RR((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyR s.     *  Rmscss-mleRiiic  K@stt|j||||||||| | | } d} t|| jj| }|j|_| j|_| j |_ t |S(s Fits ARIMA(p,d,q) model by exact maximum likelihood via Kalman filter. Parameters ---------- start_params : array-like, optional Starting parameters for ARMA(p,q). If None, the default is given by ARMA._fit_start_params. See there for more information. transparams : bool, optional Whehter or not to transform the parameters to ensure stationarity. Uses the transformation suggested in Jones (1980). If False, no checking for stationarity or invertibility is done. method : str {'css-mle','mle','css'} This is the loglikelihood to maximize. If "css-mle", the conditional sum of squares likelihood is maximized and its values are used as starting values for the computation of the exact likelihood via the Kalman filter. If "mle", the exact likelihood is maximized via the Kalman Filter. If "css" the conditional sum of squares likelihood is maximized. All three methods use `start_params` as starting parameters. See above for more information. trend : str {'c','nc'} Whether to include a constant or not. 'c' includes constant, 'nc' no constant. solver : str or None, optional Solver to be used. 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'. By default, the limited memory BFGS uses m=12 to approximate the Hessian, projected gradient tolerance of 1e-8 and factr = 1e2. You can change these by using kwargs. maxiter : int, optional The maximum number of function evaluations. Default is 500. 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 : int, optional If True, convergence information is printed. For the default l_bfgs_b solver, disp controls the frequency of the output during the iterations. disp < 0 means no output in this case. callback : function, optional Called after each iteration as callback(xk) where xk is the current parameter vector. start_ar_lags : int, optional Parameter for fitting start_params. When fitting start_params, residuals are obtained from an AR fit, then an ARMA(p,q) model is fit via OLS using these residuals. If start_ar_lags is None, fit an AR process according to best BIC. If start_ar_lags is not None, fits an AR process with a lag length equal to start_ar_lags. See ARMA._fit_start_params_hr for more information. kwargs See Notes for keyword arguments that can be passed to fit. Returns ------- `statsmodels.tsa.arima.ARIMAResults` class See Also -------- statsmodels.base.model.LikelihoodModel.fit : for more information on using the solvers. ARIMAResults : results class returned by fit Notes ----- If fit by 'mle', it is assumed for the Kalman Filter that the initial unknown state is zero, and that the initial variance is P = dot(inv(identity(m**2)-kron(T,T)),dot(R,R.T).ravel('F')).reshape(r, r, order = 'F') N( R|R&RR9t ARIMAResultst_resultsR!R1RRtARIMAResultsWrapper(RRR_R2RRRRRRRRRRt arima_fit((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyR,sN      tlinearcC@st|ttfrX|j|\}}}t|trH|j}n||j7}n|dkr| s||j|jkr|dk rt t |j |||||S|j }d|_ t t |j |||||} ||_ | Sn|dkr|j j} |sbt t |j |||||} |j|||\}}} }|j} d|jkrb|| d7}|| d7}| r| | | ||d!}| dkr|tj| |d|d!7}nt| | | }tj|t| | || f}q_| | ||d!}| dkr_|tj| |d|d!7}q_q|j}| r | | | t||jd||d!}| dkr|tj| |d|d!7}nt| | | }tj|t| | || f}q| | t||||d!}| dkr|tj| |d|d!7}qn<||j|jks|dkra|j}|j }|j}|j}|j}t|||f||dt\}}}}d|_ t t |j |||||} |s?|j|||\}}}}||7}n||_ | |dtj| St t |j |||||} | |dtj| S|Std|dS( NRitlevelsR-iiRPstyp %s not understood(RRRt_get_index_label_loctsliceR/R1R0R9R|R&RRaRgR?RR2R'RRR=RR`RCRBRQRRR(R.(RR!R/RXRJttypR3R+RARR?RRRtfvR R0R@RCRBR1RERFRGRH((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRs          !  %   ( & %  " ("          N(RRRRt _arima_modelt _arima_paramsRRR9RRR}RRRRRRt_arima_predict(((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyR&s    ! "  Z  eRcB@seZdZiZdddZedZedZedZ edZ edZ edZ ed Z ed Zd Zed Zed ZedZedZedZedZdddedZee_dZdZddddZddZddddZdddededdZe e_RS(s; Class to hold results from fitting an ARMA model. Parameters ---------- model : ARMA instance The fitted model instance params : array Fitted parameters normalized_cov_params : array, optional The normalized variance covariance matrix scale : float, optional Optional argument to scale the variance covariance matrix. Attributes ---------- aic : float Akaike Information Criterion :math:`-2*llf+2* df_model` where `df_model` includes all AR parameters, MA parameters, constant terms parameters on constant terms and the variance. arparams : array The parameters associated with the AR coefficients in the model. arroots : array The roots of the AR coefficients 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. bic : float Bayes Information Criterion -2*llf + log(nobs)*df_model Where if the model is fit using conditional sum of squares, the number of observations `nobs` does not include the `p` pre-sample observations. bse : array The standard errors of the parameters. These are computed using the numerical Hessian. df_model : array The model degrees of freedom = `k_exog` + `k_trend` + `k_ar` + `k_ma` df_resid : array The residual degrees of freedom = `nobs` - `df_model` fittedvalues : array The predicted values of the model. hqic : float Hannan-Quinn Information Criterion -2*llf + 2*(`df_model`)*log(log(nobs)) Like `bic` if the model is fit using conditional sum of squares then the `k_ar` pre-sample observations are not counted in `nobs`. k_ar : int The number of AR coefficients in the model. k_exog : int The number of exogenous variables included in the model. Does not include the constant. k_ma : int The number of MA coefficients. k_trend : int This is 0 for no constant or 1 if a constant is included. llf : float The value of the log-likelihood function evaluated at `params`. maparams : array The value of the moving average coefficients. maroots : array The roots of the MA coefficients are the solution to (1 + maparams[0]*z + maparams[1]*z**2 + ... + maparams[q-1]*z**q) = 0 Stability requires that the roots in modules lie outside the unit circle. model : ARMA instance A reference to the model that was fit. nobs : float The number of observations used to fit the model. If the model is fit using exact maximum likelihood this is equal to the total number of observations, `n_totobs`. If the model is fit using conditional maximum likelihood this is equal to `n_totobs` - `k_ar`. n_totobs : float The total number of observations for `endog`. This includes all observations, even pre-sample values if the model is fit using `css`. params : array The parameters of the model. The order of variables is the trend coefficients and the `k_exog` exognous coefficients, then the `k_ar` AR coefficients, and finally the `k_ma` MA coefficients. pvalues : array The p-values associated with the t-values of the coefficients. Note that the coefficients are assumed to have a Student's T distribution. resid : array The model residuals. If the model is fit using 'mle' then the residuals are created via the Kalman Filter. If the model is fit using 'css' then the residuals are obtained via `scipy.signal.lfilter` adjusted such that the first `k_ma` residuals are zero. These zero residuals are not returned. scale : float This is currently set to 1.0 and not used by the model or its results. sigma2 : float The variance of the residuals. If the model is fit by 'css', sigma2 = ssr/nobs, where ssr is the sum of squared residuals. If the model is fit by 'mle', then sigma2 = 1/nobs * sum(v**2 / F) where v is the one-step forecast error and F is the forecast error variance. See `nobs` for the difference in definitions depending on the fit. g?c C@stt|j|||||j|_|j}||_|j}||_|j}||_|j}||_t|j |_ |j } | |_ |||| } | d|_ | |_ |j| |_i|_dS(Ni(R|RR}RRuRCRBR0R;R?tn_totobsRat _ic_df_modeltdf_modeltdf_residR( RRxR!RtscaleRuRCRBR0RaR((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyR}Ys&             cC@s"tjtjd|j fdS(Nii(R'RR=RG(R((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pytarrootsnscC@s!tjtjd|jfdS(Nii(R'RR=RH(R((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pytmarootsrscC@s'|j}tj|j|jdtS(s Returns the frequency of the AR roots. This is the solution, x, to z = abs(z)*exp(2j*np.pi*x) where z are the roots. i(RR'tarctan2timagtrealR (Rtz((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pytarfreqvs cC@s'|j}tj|j|jdtS(s Returns the frequency of the MA roots. This is the solution, x, to z = abs(z)*exp(2j*np.pi*x) where z are the roots. i(RR'RRRR (RR((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pytmafreqs cC@s%|j|j}|j|||j!S(N(RCRBR!R0(RR^((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRGscC@s(|j|j}|j}|j||S(N(RCRBR0R!(RR^R0((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRHs cC@s|jj|jS(N(RxRR!(R((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRscC@s_|j}|jj|}t|dkrBtjd|dStjtjt| S(Nigi(R!RxRR;R'tsqrttdiagR (RR!thess((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pytbses  cC@s&|j}|jj|}t| S(N(R!RxRR (RR!R ((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyt cov_paramss cC@sd|jd|jS(Nii(RR(R((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pytaicscC@s(|j}d|jtj||jS(Ni(RuRR'R R(RRu((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRs cC@s5|j}d|jdtjtj||jS(Nii(RuRR'R R(RRu((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pythqics cC@s|j}|jj}|j}|j}|dk ra|jdkra|dkra||}qan|jdkr|dkr||}n||j}|S(NRi(RxR?RR0RJR9R2RK(RRxR?R0RJR ((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRYs      cC@s|jj|jS(N(RxRR!(R((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRKscC@s)|j}tjtj|j|dS(Ni(RRtsfR'Rttvalues(RR((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pytpvaluess cC@s|jj|j||||S(N(RxRR!(RR/RXRJR3((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRscC@sc|j}ttjd|j ftjd|jfd|}tj|tj|d}|S(Nitlagsi(RRR'R=RGRHRR((RRIRtma_reptfcasterr((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyt_forecast_errors   cC@s>tjd|d}tj||||||f}|S(Nig@(RtppfR'tc_(RRTR*talphatconsttconf_int((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyt_forecast_conf_intsig?c C@s|dk r2tj|}|jdkrR|jdkrR|dddf}nL|jdkrt||jkrtdn|dddf}n|jd|krtdn|j|jdkrtdn|jdkrJtj |j j |j d|j df|f}qJn|jrJtdnt |j||j|j|j|j |j|j j|d|j j }|j|}|j|||}|||fS( s Out-of-sample forecasts Parameters ---------- steps : int The number of out of sample forecasts from the end of the sample. exog : array If the model is an ARMAX, you must provide out of sample values for the exogenous variables. This should not include the constant. alpha : float The confidence intervals for the forecasts are (1 - alpha) % Returns ------- forecast : array Array of out of sample forecasts stderr : array Array of the standard error of the forecasts. conf_int : array 2d array of the confidence interval for the forecast iNs%1d exog given and len(exog) != k_exogisnew exog needed for each stepsIexog must contain the same number of variables as in the estimated model.sSForecast values for exog are required when the model contains exogenous regressors.R2(R9R'RRCR:R;R.RR0RRxRJRBRWR!RKRaR?R2R+R1(RRIRJR.RTR*R0((s:lib/python2.7/site-packages/statsmodels/tsa/arima_model.pyRTs2 ,   c C@sDddlm}|j}|jjd}|j}t|dd}d|krY|}n ||j}|jj d-k r|jj }||j dg} | d|dj dg7} n&t |d t t |jj} |j|j} } |st | | f} nt | || f} d.d |jj| gfd |gfd/d0d| dgfd| dgfg} dt t |jjgfdd|jgfdd|jdgfdd|jgfdd|jgfdd|jgfg}|}|j|d| d|d||j|d|dtddlm}| r| rgtd| dD]}d |^qm}gtd| dD]}d!|^q}||}tj|j|jf}tj|j |j!f}n| r7gtd| dD]}d!|^q}|}|j}|j!}nQ| rgtd| dD]}d |^qQ}|}|j}|j }ng}t |r@tj"|}tj#|j$|j%||f}|g|D]8}d"|dd#|dd"|d$d"|d%f^qd&d'd(d)d*gdd+d,|}|j&j'|n|S(1sSummarize the Model Parameters ---------- alpha : float, optional Significance level for the confidence intervals. Returns ------- smry : Summary instance This holds the summary table and text, which can be printed or converted to various output formats. See Also -------- statsmodels.iolib.summary.Summary i(tSummarys Model ResultsR1R-s%m-%d-%Ys- is - sDep. Variable:sModel:sMethod:sDate:sTime:sSample:R"isNo. Observations:sLog Likelihoods%#5.3fsS.D. of innovationsg?tAICtBICtHQICtglefttgrightttitleR.tuse_t(t SimpleTablesAR.%dsMA.%ds%17.4fs%+17.4fjiitheaderss Reals Imaginarys Moduluss FrequencytRootststubsN(sDep. 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This should not include the constant. alpha : float The confidence intervals for the forecasts are (1 - alpha) % Returns ------- forecast : array Array of out of sample forecasts stderr : array Array of the standard error of the forecasts. conf_int : array 2d array of the confidence interval for the forecast Notes ----- Prediction is done in the levels of the original endogenous variable. 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