ó áp7]c@s®dZddlmZddlZddlmZdd„Zdd„Zdd„Z dd „Z d d d „Z ddd„Z ddde d„Zd„Zdd„ZdS(sx Statistical tests to be used in conjunction with the models Notes ----- These functions haven't been formally tested. iÿÿÿÿ(tstatsN(t ValueWarningicCs[tj|ƒ}tj|dd|ƒ}tj|dd|ƒtj|dd|ƒ}|S(s? Calculates the Durbin-Watson statistic Parameters ---------- resids : array-like Returns ------- dw : float, array-like The Durbin-Watson statistic. Notes ----- The null hypothesis of the test is that there is no serial correlation. The Durbin-Watson test statistics is defined as: .. math:: \sum_{t=2}^T((e_t - e_{t-1})^2)/\sum_{t=1}^Te_t^2 The test statistic is approximately equal to 2*(1-r) where ``r`` is the sample autocorrelation of the residuals. Thus, for r == 0, indicating no serial correlation, the test statistic equals 2. This statistic will always be between 0 and 4. The closer to 0 the statistic, the more evidence for positive serial correlation. The closer to 4, the more evidence for negative serial correlation. itaxisi(tnptasarraytdifftsum(tresidsRt diff_residstdw((s:lib/python2.7/site-packages/statsmodels/stats/stattools.pyt durbin_watsons0cCsrtj|ƒ}|j|}|dkr_ddlm}|dt|ƒtƒtjtjfStj |d|ƒS(sÇ Omnibus test for normality Parameters ---------- resid : array-like axis : int, optional Default is 0 Returns ------- Chi^2 score, two-tail probability iiÿÿÿÿ(twarnsPomni_normtest is not valid with less than 8 observations; %i samples were given.R( RRtshapetwarningsR tintRtnanRt normaltest(RRtnR ((s:lib/python2.7/site-packages/statsmodels/stats/stattools.pyt omni_normtest2s  cCs•tj|ƒ}tj|d|ƒ}dtj|d|ƒ}|j|}|d|ddd|dd}tjj|dƒ}||||fS(sU Calculates the Jarque-Bera test for normality Parameters ---------- data : array-like Data to test for normality axis : int, optional Axis to use if data has more than 1 dimension. Default is 0 Returns ------- JB : float or array The Jarque-Bera test statistic JBpv : float or array The pvalue of the test statistic skew : float or array Estimated skewness of the data kurtosis : float or array Estimated kurtosis of the data Notes ----- Each output returned has 1 dimension fewer than data The Jarque-Bera test statistic tests the null that the data is normally distributed against an alternative that the data follow some other distribution. The test statistic is based on two moments of the data, the skewness, and the kurtosis, and has an asymptotic :math:`\chi^2_2` distribution. The test statistic is defined .. math:: JB = n(S^2/6+(K-3)^2/24) where n is the number of data points, S is the sample skewness, and K is the sample kurtosis of the data. Rig@iig@(RRRtskewtkurtosisR tchi2tsf(RRRRRtjbtjb_pv((s:lib/python2.7/site-packages/statsmodels/stats/stattools.pyt jarque_beraMs( &cCsd|d kr!|jƒ}d}ntj||ƒ}tj|dddgd|ƒ\}}}|j|ƒ}|jf}|d k r²t|jƒ}|j |dƒt |ƒ}ntj ||ƒ}tj ||ƒ}tj||d|ƒ} t j |d|ƒ} ||d|||} ||tjt||ƒd|ƒ} ||| } | | | | fS( sª Calculates the four skewness measures in Kim & White Parameters ---------- y : array-like axis : int or None, optional Axis along which the skewness measures are computed. If `None`, the entire array is used. Returns ------- sk1 : ndarray The standard skewness estimator. sk2 : ndarray Skewness estimator based on quartiles. sk3 : ndarray Skewness estimator based on mean-median difference, standardized by absolute deviation. sk4 : ndarray Skewness estimator based on mean-median difference, standardized by standard deviation. Notes ----- The robust skewness measures are defined .. math:: SK_{2}=\frac{\left(q_{.75}-q_{.5}\right) -\left(q_{.5}-q_{.25}\right)}{q_{.75}-q_{.25}} .. math:: SK_{3}=\frac{\mu-\hat{q}_{0.5}} {\hat{E}\left[\left|y-\hat{\mu}\right|\right]} .. math:: SK_{4}=\frac{\mu-\hat{q}_{0.5}}{\hat{\sigma}} .. [*] Tae-Hwan Kim and Halbert White, "On more robust estimation of skewness and kurtosis," Finance Research Letters, vol. 1, pp. 56-73, March 2004. ig9@gI@gÀR@Riig@N(tNonetravelRtsortt percentiletmeantsizetlistR tinsertttupletreshapeRRtabs(tyRtq1tq2tq3tmuR tmu_btq2_btsigmatsk1tsk2tsk3tsk4((s:lib/python2.7/site-packages/statsmodels/stats/stattools.pytrobust_skewness‚s&0   *  'g@gI@c Cs¬|d||d|f}tj||ƒ\}}}}tj|||kƒ}tj|||kƒ} tj|||kƒ} tj|||kƒ} | || | S(sW KR3 estimator from Kim & White Parameters ---------- y : array-like, 1-d alpha : float, optional Lower cut-off for measuring expectation in tail. beta : float, optional Lower cut-off for measuring expectation in center. Returns ------- kr3 : float Robust kurtosis estimator based on standardized lower- and upper-tail expected values Notes ----- .. [*] Tae-Hwan Kim and Halbert White, "On more robust estimation of skewness and kurtosis," Finance Research Letters, vol. 1, pp. 56-73, March 2004. gY@(RRR( R%talphatbetatperct lower_alphat upper_alphat lower_betat upper_betatl_alphatu_alphatl_betatu_beta((s:lib/python2.7/site-packages/statsmodels/stats/stattools.pyt_kr3Îsg@g9@cCs(|\}}|\}}tjdƒ}tjj}tjj}|tjdƒdƒ\} } } } } }d |d <|| | | | | |d <|tj|d |d fƒƒ\}}d ||ƒ|d ||ƒ||d <|tj|d |d fƒƒ\}}d|d||d <|S(si Calculates the expected value of the robust kurtosis measures in Kim and White assuming the data are normally distributed. Parameters ---------- ab: iterable, optional Contains 100*(alpha, beta) in the kr3 measure where alpha is the tail quantile cut-off for measuring the extreme tail and beta is the central quantile cutoff for the standardization of the measure db: iterable, optional Contains 100*(delta, gamma) in the kr4 measure where delta is the tail quantile for measuring extreme values and gamma is the central quantile used in the the standardization of the measure Returns ------- ekr: array, 4-element Contains the expected values of the 4 robust kurtosis measures Notes ----- See `robust_kurtosis` for definitions of the robust kurtosis measures igð?g@g@g@g@g@iiiigY@igÀ(gð?g@g@g@g@g@(RtzerosRtnormtppftpdftarray(tabtdgR2R3tdeltatgammatexpected_valueR@RAR&R'R(tq5tq6tq7tq_alphatq_betatq_deltatq_gamma((s:lib/python2.7/site-packages/statsmodels/stats/stattools.pytexpected_robust_kurtosisñs    + )*)c Cs™|dks0|jƒjdkrE|jdkrE|jƒ}d}n|\}}|\}}dddddd|d ||d |f } tj|| d |ƒ\ } } } } }}}}}}|rÔt||ƒn tjd ƒ}tj ||t ƒ|d}|| | | || |d}|jdkrFt |||ƒ}ntj t ||||ƒ}||d 8}|||||d }||||fS(sê Calculates the four kurtosis measures in Kim & White Parameters ---------- y : array-like axis : int or None, optional Axis along which the kurtoses are computed. If `None`, the entire array is used. ab: iterable, optional Contains 100*(alpha, beta) in the kr3 measure where alpha is the tail quantile cut-off for measuring the extreme tail and beta is the central quantile cutoff for the standardization of the measure db: iterable, optional Contains 100*(delta, gamma) in the kr4 measure where delta is the tail quantile for measuring extreme values and gamma is the central quantile used in the the standardization of the measure excess : bool, optional If true (default), computed values are excess of those for a standard normal distribution. Returns ------- kr1 : ndarray The standard kurtosis estimator. kr2 : ndarray Kurtosis estimator based on octiles. kr3 : ndarray Kurtosis estimators based on exceedence expectations. kr4 : ndarray Kurtosis measure based on the spread between high and low quantiles. Notes ----- The robust kurtosis measures are defined .. math:: KR_{2}=\frac{\left(\hat{q}_{.875}-\hat{q}_{.625}\right) +\left(\hat{q}_{.375}-\hat{q}_{.125}\right)} {\hat{q}_{.75}-\hat{q}_{.25}} .. math:: KR_{3}=\frac{\hat{E}\left(y|y>\hat{q}_{1-\alpha}\right) -\hat{E}\left(y|y<\hat{q}_{\alpha}\right)} {\hat{E}\left(y|y>\hat{q}_{1-\beta}\right) -\hat{E}\left(y|y<\hat{q}_{\beta}\right)} .. math:: KR_{4}=\frac{\hat{q}_{1-\delta}-\hat{q}_{\delta}} {\hat{q}_{1-\gamma}-\hat{q}_{\gamma}} where :math:`\hat{q}_{p}` is the estimated quantile at :math:`p`. .. [*] Tae-Hwan Kim and Halbert White, "On more robust estimation of skewness and kurtosis," Finance Research Letters, vol. 1, pp. 56-73, March 2004. iig)@g9@gÀB@g@O@gÀR@gàU@gY@RiiiN( RtsqueezetndimRRRROR>RRtFalseR=tapply_along_axis(R%RRCRDtexcessR2R3RERFR4te1te2te3te5te6te7tfdtf1mdtfgtf1mgRGtkr1tkr2tkr3tkr4((s:lib/python2.7/site-packages/statsmodels/stats/stattools.pytrobust_kurtosiss&= $    '$"c Cs²tjtj|ƒƒ}|jdkr6tdƒ‚ntj|ƒ}|jd}|ddkr‡||dd||dd}n||dd}||}||dk}||dk}|dd…df}||}tj|dk|dkƒ}tj ||<||}||} tj |dkƒ} | r¥tj | | fƒtj | ƒ} | dtj | ƒ8} tj| ƒ} | | d| …| d…f10000). .. [*] M. Huberta and E. Vandervierenb, "An adjusted boxplot for skewed distributions" Computational Statistics & Data Analysis, vol. 52, pp. 5186-5201, August 2008. is#y must be squeezable to a 1-d arrayiigN(RRPRRQt ValueErrorRR Rt logical_andtinfRtonesteyettriutfliplrtmedian( R%Rtmftztlowertuppertstandardizationtis_zerotspreadthtnum_tiest replacements((s:lib/python2.7/site-packages/statsmodels/stats/stattools.pyt _medcouple_1dvs0 %     " cCsGtj|dtjƒ}|dkr4t|jƒƒStjt||ƒS(sÐ Calculates the medcouple robust measure of skew. Parameters ---------- y : array-like axis : int or None, optional Axis along which the medcouple statistic is computed. If `None`, the entire array is used. Returns ------- mc : ndarray The medcouple statistic with the same shape as `y`, with the specified axis removed. Notes ----- The current algorithm requires a O(N**2) memory allocations, and so may not work for very large arrays (N>10000). .. [*] M. Huberta and E. Vandervierenb, "An adjusted boxplot for skewed distributions" Computational Statistics & Data Analysis, vol. 52, pp. 5186-5201, August 2008. tdtypeN(RRtdoubleRRvRRS(R%R((s:lib/python2.7/site-packages/statsmodels/stats/stattools.pyt medcouple³s (g@gI@(g@g9@(g@gI@(g@g9@(t__doc__tscipyRtnumpyRtstatsmodels.tools.sm_exceptionsRR RRR1R=ROtTrueRcRvRy(((s:lib/python2.7/site-packages/statsmodels/stats/stattools.pyts  #  5 L#-X =