ó áp7]c@ s0dZddlmZddlmZmZmZmZmZm Z m Z ddl m Z ddl mZddlZddlZddlmZddlmZdd lmZmZdd lmZmZmZdd lmZm Z dd l!m"Z"dd l#m$Z$m%Z%ddl&m'Z'ddl(m)Z)m*Z*m+Z+ddddddddddddddddd d!d"gZ,ej-ej.ej/ƒj0ƒZ1d#e2fd$„ƒYZ3dJdKe4d%„Z5dd&d'e4e4d(„Z7e4e8dd)dd*„Z9d+d,„Z:e4d-e4ddd)d.„Z;d-d/d0„Z<de8d1„Z=d-e8e4d2„Z>d-d3dd4„Z?e8e8d5„Z@e8d6„ZAd7„ZBd8e4d9„ZCdd:„ZDddd;„ZEd<„ZFe8e8d=„ZGd&d>dd?dd@„ZHddA„ZIdBdCdDd&dddE„ZJdF„ZKd&de4dG„ZLdH„ZMdI„ZNdS(Ls, Statistical tools for time series analysis iÿÿÿÿ(tdivision(t iteritemstrangetlranget string_typestlziptziptlong(tlstsq(t _next_regularN(t LinAlgError(tstats(tOLSt yule_walker(tInterpolationWarningtMissingDataErrortCollinearityWarning(t add_constanttBunch(tbds(t mackinnonpt mackinnoncrit(tARMA(tlagmatt lagmat2dst add_trendtacovftacftpacftpacf_ywtpacf_olstccovftccft periodogramtq_stattcointtarma_order_select_ictadfullertkpssRt pacf_burgtinnovations_algotinnovations_filtertlevinson_durbin_pacftlevinson_durbint ResultsStorecB seZd„ZRS(cC s|jS(N(t_str(tself((s8lib/python2.7/site-packages/statsmodels/tsa/stattools.pyt__str__$s(t__name__t __module__R/(((s8lib/python2.7/site-packages/statsmodels/tsa/stattools.pyR,#sc C sxi} |jƒ}xWt|||dƒD]>} |||dd…d| …f|Œ} | jƒ| | `stbiccs s$|]\}}|j|fVqdS(N(R6(R3R4R5((s8lib/python2.7/site-packages/statsmodels/tsa/stattools.pys bsst-statg»jg RQú?iÿÿÿÿs(Information Criterion %s not understood.( tlowerRtfittminRtnptabsttvaluest ValueError(tmodtendogtexogtstartlagtmaxlagtmethodtmodargstfitargst regresultstresultstlagt mod_instanceticbesttbestlagtstop((s8lib/python2.7/site-packages/statsmodels/tsa/stattools.pyt_autolag(s*1 ( % % !  tctAICc C sŒ|rt}nidd6dd6dd6dd6}|dksRt|ttfƒr_||}n|jƒ}|dkrŠtdƒ|‚ntj|ƒ}|j d}|dkr¾t |ƒnd}|dkr2ttj d tj |d d ƒƒƒ}t |d|d|ƒ}|dkrYtd ƒ‚qYn'||d|dkrYtd ƒ‚ntj|ƒ} t| dd…df|ddddƒ} | j d}|| dd!| dd…df<| | } |rßtƒ} n|r|dkr t| |dtƒ} n| } | j d| j dd}|sUtt| | |||ƒ\}}n3tt| | |||d|ƒ\}}}|| _||8}t| dd…df|ddddƒ} | j d}|| dd!| dd…df<| | } |}n |}d}|dkrSt| t| dd…d|d…f|ƒƒjƒ}n/t| | dd…d|d…fƒjƒ}|jd}t|d|ddƒ}tddd|d|ƒ}i|dd6|dd6|dd6}|rY|| _|| _|| _|| _|| _|| _d| _d| _ || _!d| _"|||| fS|sr|||||fS||||||fSdS(!s0 Augmented Dickey-Fuller unit root test The Augmented Dickey-Fuller test can be used to test for a unit root in a univariate process in the presence of serial correlation. Parameters ---------- x : array_like, 1d data series maxlag : int Maximum lag which is included in test, default 12*(nobs/100)^{1/4} regression : {'c','ct','ctt','nc'} Constant and trend order to include in regression * 'c' : constant only (default) * 'ct' : constant and trend * 'ctt' : constant, and linear and quadratic trend * 'nc' : no constant, no trend autolag : {'AIC', 'BIC', 't-stat', None} * if None, then maxlag lags are used * if 'AIC' (default) or 'BIC', then the number of lags is chosen to minimize the corresponding information criterion * 't-stat' based choice of maxlag. Starts with maxlag and drops a lag until the t-statistic on the last lag length is significant using a 5%-sized test store : bool If True, then a result instance is returned additionally to the adf statistic. Default is False regresults : bool, optional If True, the full regression results are returned. Default is False Returns ------- adf : float Test statistic pvalue : float MacKinnon's approximate p-value based on MacKinnon (1994, 2010) usedlag : int Number of lags used nobs : int Number of observations used for the ADF regression and calculation of the critical values critical values : dict Critical values for the test statistic at the 1 %, 5 %, and 10 % levels. Based on MacKinnon (2010) icbest : float The maximized information criterion if autolag is not None. resstore : ResultStore, optional A dummy class with results attached as attributes Notes ----- The null hypothesis of the Augmented Dickey-Fuller is that there is a unit root, with the alternative that there is no unit root. If the pvalue is above a critical size, then we cannot reject that there is a unit root. The p-values are obtained through regression surface approximation from MacKinnon 1994, but using the updated 2010 tables. If the p-value is close to significant, then the critical values should be used to judge whether to reject the null. The autolag option and maxlag for it are described in Greene. Examples -------- See example notebook References ---------- .. [*] W. Green. "Econometric Analysis," 5th ed., Pearson, 2003. .. [*] Hamilton, J.D. "Time Series Analysis". Princeton, 1994. .. [*] MacKinnon, J.G. 1994. "Approximate asymptotic distribution functions for unit-root and cointegration tests. `Journal of Business and Economic Statistics` 12, 167-76. .. [*] MacKinnon, J.G. 2010. "Critical Values for Cointegration Tests." Queen's University, Dept of Economics, Working Papers. Available at http://ideas.repec.org/p/qed/wpaper/1227.html tncRNitctitcttis#regression option %s not understoodg(@gY@g@s=sample size is too short to use selected regression componentsomaxlag must be less than (nobs/2 - 1 - ntrend) where n trend is the number of included deterministic regressorsNttrimtbothtoriginaltiniÿÿÿÿtprependRFt regressiontNtnobss1%s5%s10%s8The coefficient on the lagged level equals 1 - unit roots4The coefficient on the lagged level < 1 - stationarys$Augmented Dickey-Fuller Test Results(RNRPRQRRgÐ?(#tTruetNonet isinstancetintRR7R=R:tasarraytshapetlentceiltpowerR9tdiffRR,RRMR tautolag_resultsR8R<RRtresolsRBtusedlagtadfstatt critvaluesRZtH0tHARJR-(txRBRXtautolagtstoreRFt trenddictRZtntrendtxdifftxdalltxdshorttresstoretfullRHSRARJRKtalresRgRfRhtpvalueRi((s8lib/python2.7/site-packages/statsmodels/tsa/stattools.pyR%}sŠU "!     ) + "      + "   &/           tnonecC sË|dkr7ddl}d}|j|tƒt}ntjtj|ƒƒ}|jdkrtt d|jƒ‚n|j ƒ}|dkrŸt d |ƒ‚n|dkr´t}n t |ƒ}|r3|dkrát d ƒ‚ntj |ƒ} |dkr|jƒ}d || >> import statsmodels.api as sm >>> data = sm.datasets.macrodata.load_pandas() >>> rgdpg = data.data['realgdp'].pct_change().dropna() >>> acov = sm.tsa.acovf(rgdpg) >>> nobs = activity.shape[0] >>> theta, sigma2 = innovations_algo(acov[:4], nobs=nobs) See Also -------- innovations_filter References ---------- .. [*] Brockwell, P.J. and Davis, R.A., 2016. Introduction to time series and forecasting. Springer. is&acov must be 1-d or squeezable to 1-d.gs*rtol must be a non-negative float or None.snobs must be a positive integerigð?ii Niÿÿÿÿ(R:RƒR_R„R=R\R]tfloatR^R`tmaxtargwhereR¹R( R RZtrtolR~tmax_lagR5tthetaR¡R4tsubRæ((s8lib/python2.7/site-packages/statsmodels/tsa/stattools.pyR( s<.*%$##60#. $  c C s¡|}tjtj|ƒƒ}|jdkr<tdƒ‚n|jd}|j\}}||krstdƒ‚nt|tjtj fƒ}|rÁt |j ƒ|krÁd}t|ƒ‚qÁntj |ƒ}|d|d>> import statsmodels.api as sm >>> data = sm.datasets.macrodata.load_pandas() >>> rgdpg = data.data['realgdp'].pct_change().dropna() >>> acov = sm.tsa.acovf(rgdpg) >>> nobs = activity.shape[0] >>> theta, sigma2 = innovations_algo(acov[:4], nobs=nobs) >>> resid = innovations_filter(rgdpg, theta) See Also -------- innovations_algo References ---------- .. [*] Brockwell, P.J. and Davis, R.A., 2016. Introduction to time series and forecasting. Springer. is'endog must be 1-d or squeezable to 1-d.is2theta must be (nobs, q) where q is the moder ordersgIf endog is a Series or DataFrame, the index must correspond to the number of time series observations.Niÿÿÿÿtindex(R:RƒR_R„R=R`R]tpdt DataFrametSeriesRaRôR‹RR‰R‡( R?Ròt orig_endogRZtn_thetaR4t is_pandasRšR¼R¡that((s8lib/python2.7/site-packages/statsmodels/tsa/stattools.pyR)`s.$   4,!cC s²ddlm}tj|ƒ}|jdd|t|ƒkrwtdjt|jdt|ƒdƒdƒƒ‚ni}x.td|dƒD]}i}|r¶dGHd|fGHn|}t ||d d d dƒ} |r4t | d d …d|d…fd t ƒ} t | d d …dd …fd t ƒ} n t dƒ‚t | d d …df| ƒjƒ} t | d d …df| ƒjƒ} | j| j| j|| j}|râd||jj||| jƒ| j|fGHn||jj||| jƒ| j|f|d<| j| j| j| j}|rXd||jj||ƒ|fGHn||jj||ƒ|f|d>> from statsmodels.tsa.arima_process import arma_generate_sample >>> import statsmodels.api as sm >>> import numpy as np >>> arparams = np.array([.75, -.25]) >>> maparams = np.array([.65, .35]) >>> arparams = np.r_[1, -arparams] >>> maparam = np.r_[1, maparams] >>> nobs = 250 >>> np.random.seed(2014) >>> y = arma_generate_sample(arparams, maparams, nobs) >>> res = sm.tsa.arma_order_select_ic(y, ic=['aic', 'bic'], trend='nc') >>> res.aic_min_order >>> res.bic_min_order Notes ----- This method can be used to tentatively identify the order of an ARMA process, provided that the time series is stationary and invertible. This function computes the full exact MLE estimate of each model and can be, therefore a little slow. An implementation using approximate estimates will be provided in the future. In the meantime, consider passing {method : 'css'} to fit_kw. iÿÿÿÿ(Röiis.Need a list or a tuple for ic if not a string.RPNtcolumnsRôt _min_order(tpandasRöRR]RtlistttupleR=R:R¹RaR\R_R%R4t enumeratetgetattrtdictRRtwhereR9tupdateR(RÚtmax_artmax_maticR R5R6Rötar_rangetma_rangeRGty_arrtartmaR>R¡tcriteriatrestdfstmin_resRtmins((s8lib/python2.7/site-packages/statsmodels/tsa/stattools.pyR$Âs<9 &  $ (+!2 cC stjtj|ƒƒS(sJ Returns True if 'data' contains missing entries, otherwise False (R:R†R‰(tdata((s8lib/python2.7/site-packages/statsmodels/tsa/stattools.pyR…$scC sddlm}t|ƒ}tj|ƒ}|jƒ}||jkratdj|j ƒƒ‚n|dkr°t |t tj d|dƒƒƒj ƒj}dddd g}nF|d krá||jƒ}d d d dg}ntdj|ƒƒ‚|d(krd}d} || tƒn|dkrittjdtj|dd)ƒƒƒ}t||dƒ}n*|dkr‡t||ƒ}n t|ƒ}||krºtdj||ƒƒ‚nddddg} tj|jƒdƒ|d} t|||ƒ} | | } tj| || ƒ}|| dkr>|dtƒn || dkr^|dtƒni|dd6|dd 6|dd!6|d"d#6}|rýtƒ}||_||_|d krÃd$nd%}d&j|ƒ|_d'j|ƒ|_ | |||fS| |||fSd(S(*sŠ Kwiatkowski-Phillips-Schmidt-Shin test for stationarity. Computes the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test for the null hypothesis that x is level or trend stationary. Parameters ---------- x : array_like, 1d Data series regression : str{'c', 'ct'} Indicates the null hypothesis for the KPSS test * 'c' : The data is stationary around a constant (default) * 'ct' : The data is stationary around a trend lags : {None, str, int}, optional Indicates the number of lags to be used. If None (default), lags is calculated using the legacy method. If 'auto', lags is calculated using the data-dependent method of Hobijn et al. (1998). See also Andrews (1991), Newey & West (1994), and Schwert (1989). If set to 'legacy', uses int(12 * (n / 100)**(1 / 4)) , as outlined in Schwert (1989). store : bool If True, then a result instance is returned additionally to the KPSS statistic (default is False). Returns ------- kpss_stat : float The KPSS test statistic p_value : float The p-value of the test. The p-value is interpolated from Table 1 in Kwiatkowski et al. (1992), and a boundary point is returned if the test statistic is outside the table of critical values, that is, if the p-value is outside the interval (0.01, 0.1). lags : int The truncation lag parameter crit : dict The critical values at 10%, 5%, 2.5% and 1%. Based on Kwiatkowski et al. (1992). resstore : (optional) instance of ResultStore An instance of a dummy class with results attached as attributes Notes ----- To estimate sigma^2 the Newey-West estimator is used. If lags is None, the truncation lag parameter is set to int(12 * (n / 100) ** (1 / 4)), as outlined in Schwert (1989). The p-values are interpolated from Table 1 of Kwiatkowski et al. (1992). If the computed statistic is outside the table of critical values, then a warning message is generated. Missing values are not handled. References ---------- Andrews, D.W.K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59: 817-858. Hobijn, B., Frances, B.H., & Ooms, M. (2004). Generalizations of the KPSS-test for stationarity. Statistica Neerlandica, 52: 483-502. Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54: 159-178. Newey, W.K., & West, K.D. (1994). Automatic lag selection in covariance matrix estimation. Review of Economic Studies, 61: 631-653. Schwert, G. W. (1989). Tests for unit roots: A Monte Carlo investigation. Journal of Business and Economic Statistics, 7 (2): 147-159. iÿÿÿÿ(R€sx of shape {0} not understoodRQigX9´Èv¾?gã¥›Ä °Â?gºI +‡Æ?gÙÎ÷Sã¥Ë?RNgh‘í|?5Ö?goƒÀÊ¡Ý?g‘í|?5^â?gÙÎ÷Sã¥ç?shypothesis '{0}' not understoodtlegacysUThe behavior of using lags=None will change in the next release. Currently lags=None is the same as lags='legacy', and so a sample-size lag length is used. After the next release, the default will change to be the same as lags='auto' which uses an automatic lag length selection method. To silence this warning, either use 'auto' or 'legacy'g(@gY@g@tautos/lags ({}) must be < number of observations ({})gš™™™™™¹?gš™™™™™©?gš™™™™™™?g{®Gáz„?is-p-value is smaller than the indicated p-valueis-p-value is greater than the indicated p-values10%s5%s2.5%is1%tlevelR sThe series is {0} stationarys The series is not {0} stationaryNgÐ?(!RR€RaR:R_R7tsizeR=RR`R RRR8R#RŠR\RR^RbRcR9t _kpss_autolagR‰R§t_sigma_est_kpsstinterpRR,tlagsRZRjRk(RlRXRWRnR€RZthypotresidsR-Rštpvalstetats_hatt kpss_stattp_valuet crit_dicttrstoretstationary_type((s8lib/python2.7/site-packages/statsmodels/tsa/stattools.pyR&+sZI   .   )    ! 2   cC sutj|dƒ}xWtd|dƒD]B}tj||||| ƒ}|d|d||d7}q'W||S(s{ Computes equation 10, p. 164 of Kwiatkowski et al. (1992). This is the consistent estimator for the variance. iigð?(R:R‰RRŒ(RYRZRWR\R¡t resids_prod((s8lib/python2.7/site-packages/statsmodels/tsa/stattools.pyRUÀs "c C sðttj|d ƒƒ}tj|dƒ|}d}x_td|dƒD]J}tj||||| ƒ}||d}||7}|||7}qIW||}d }dtj|||ƒ} tj|t| tj||ƒƒgƒ} | S( sè Computes the number of lags for covariance matrix estimation in KPSS test using method of Hobijn et al (1998). See also Andrews (1991), Newey & West (1994), and Schwert (1989). Assumes Bartlett / Newey-West kernel. g@g"@iiigð?g@gÿ²{ò°Pò?gÇqÇqÌ?gUUUUUUÕ?(R^R:RcR‰RRŒtamin( RYRZtcovlagsts0ts1R¡RbR\tpwrt gamma_hattautolags((s8lib/python2.7/site-packages/statsmodels/tsa/stattools.pyRTÌs  +(((Ot__doc__t __future__Rtstatsmodels.compat.pythonRRRRRRRtstatsmodels.compat.numpyRtstatsmodels.compat.scipyR tnumpyR:R:Rõt numpy.linalgR RR t#statsmodels.regression.linear_modelR R tstatsmodels.tools.sm_exceptionsRRRtstatsmodels.tools.toolsRRtstatsmodels.tsa._bdsRtstatsmodels.tsa.adfvaluesRRtstatsmodels.tsa.arima_modelRtstatsmodels.tsa.tsatoolsRRRt__all__R®tfinfotdoubletepsR"tobjectR,R‚RMR\R%R[RR"RRR'RRRR R!R+R*R(R)RR#R4R$R…R&RURT(((s8lib/python2.7/site-packages/statsmodels/tsa/stattools.pytsd4   T »„  X"?MU#  B 4S ?ˆ  €  a •