>h4SrSSKJr SSKJr SSKJr SSKJr SSK J r SSK J r J r SSKrSSKrSS KJr SSKrSS KJr SS KJr SS KJr SS KJrJr SSKJrJ r J!r!J"r"J#r# SSK$J%r%J&r& SSK'J(r(J)r)J*r*J+r+J,r,J-r- SSK.J/r/ SSK0J1r1J2r2 SSK3J4r4J5r5 SSK6J7r7J8r8J9r9 \ \Rt\Rv\<\=4r>/SQr?\R"\R"\R5R5rDS2SjrES3S4SjjrF\"SS5S5Sj5rGSrHS6SjrIS7S8SjjrJS9S:SjjrK\"SS5S;SS jjrM\"SS5S?S!j5rN\"SS5S@SSS".S#jj5rOSAS$jrPSBS%jrQSCS&jrRSDS'jrSSESFS(jjrTSBS)jrUSGS*jrVS+rWSHSIS,jjrXS-rYS.rZSJS/jr["S0S15r\\\"5r]\]RR\]lg)Kz, Statistical tools for time series analysis ) annotations)lstsq)deprecate_kwarg)lzip) _next_regular)LiteralUnionN) LinAlgError)stats)interp1d) correlate)OLS yule_walker)CollinearityWarningInfeasibleTestErrorInterpolationWarningMissingDataError ValueWarning)Bunch add_constant) array_like bool_like dict_like float_likeint_like string_like)bds)innovations_algoinnovations_filter) mackinnoncrit mackinnonp) add_trendlagmat lagmat2ds)acovfacfpacfpacf_ywpacf_olsccovfccfq_statcointarma_order_select_icadfullerkpssr pacf_burgrrlevinson_durbin_pacflevinson_durbin zivot_andrewsrange_unit_root_testc R0n UR5n[X3U-S-5H'n U"XSS2SU 24/UQ76n U R5X'M) US:Xa#[SU R 555upOUS:Xa#[SU R 555upOzUS:XaeSnX4-n S n [X4-US- S 5HFn [ R "XRS 5n U n [ R "U 5U:dMF O O[S US 35eU(dX4$XU 4$) a Returns the results for the lag length that maximizes the info criterion. Parameters ---------- mod : Model class Model estimator class endog : array_like nobs array containing endogenous variable exog : array_like nobs by (startlag + maxlag) array containing lags and possibly other variables startlag : int The first zero-indexed column to hold a lag. See Notes. maxlag : int The highest lag order for lag length selection. method : {"aic", "bic", "t-stat"} aic - Akaike Information Criterion bic - Bayes Information Criterion t-stat - Based on last lag modargs : tuple, optional args to pass to model. See notes. fitargs : tuple, optional args to pass to fit. See notes. regresults : bool, optional Flag indicating to return optional return results Returns ------- icbest : float Best information criteria. bestlag : int The lag length that maximizes the information criterion. results : dict, optional Dictionary containing all estimation results Notes ----- Does estimation like mod(endog, exog[:,:i], *modargs).fit(*fitargs) where i goes from lagstart to lagstart+maxlag+1. Therefore, lags are assumed to be in contiguous columns from low to high lag length with the highest lag in the last column. Naicc3B# UHupURU4v M g7fN)r8.0kvs lC:\Users\julio\OneDrive\Documentos\Trabajo\Ideas Frescas\venv\Lib\site-packages\statsmodels/tsa/stattools.py _autolag..E_TQquuaj_bicc3B# UHupURU4v M g7fr:)rDr;s r?r@rArBrCt-statgjg RQ?gzInformation Criterion z not understood.) lowerrangefitminitemsnpabstvalues ValueError)modendogexogstartlagmaxlagmethodmodargsfitargs regresultsresultslag mod_instanceicbestbestlagstops r?_autolagr`Gs2tG \\^FX&01455q$3$w-:': #'') 6EW]]_EE 5EW]]_EE 8 !#*HqL"=CVVGL0045FGvvf~% >1&9IJKK ''c [US5n[USSS9n[USSS9n[USSS S 9n[US 5n[US 5nUR 5UR 5:Xa [ S 5eU(aSnSSSSS.nUb[U[5(aXbnUR5nURSnUS:wa [U5OSnUca[[R"S[R"US- S5-55n[ US-U- S- U5nUS:a [ S5eOXS-U- S- :a [ S5e[R"U5n [!U SS2S4USSS9n U RSnX*S- SU SS2S4'X*Sn U(a SS KJn U "5n U(aUS:wa ['XSS!9nOU nURSU RS- S-nU(d[)[*XXU5unnO[)[*U UUUUUS"9unnnUW lUU-n[!U SS2S4USSS9n U RSnX*S- SU SS2S4'X*Sn UnOUnSnUS:wa1[+U ['U SS2SUS-24U55R/5nO%[+XSS2SUS-245R/5nUR0Sn[3UUSS#9n[5SX'S$9nUSUSUSS%.nU(aJUW lXlUU lUU lUU lX}l S&U l!S'U l"UU l#S(U l$UUUU 4$U(dUUUUU4$UUUUUU4$))a` 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 The data series to test. maxlag : {None, int} Maximum lag which is included in test, default value of 12*(nobs/100)^{1/4} is used when ``None``. regression : {"c","ct","ctt","n"} Constant and trend order to include in regression. * "c" : constant only (default). * "ct" : constant and trend. * "ctt" : constant, and linear and quadratic trend. * "n" : no constant, no trend. autolag : {"AIC", "BIC", "t-stat", None} Method to use when automatically determining the lag length among the values 0, 1, ..., maxlag. * 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. * If None, then the number of included lags is set to maxlag. 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 The test statistic. pvalue : float MacKinnon's approximate p-value based on MacKinnon (1994, 2010). usedlag : int The number of lags used. nobs : int The 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. See the notebook `Stationarity and detrending (ADF/KPSS) <../examples/notebooks/generated/stationarity_detrending_adf_kpss.html>`__ for an overview. References ---------- .. [1] W. Green. "Econometric Analysis," 5th ed., Pearson, 2003. .. [2] Hamilton, J.D. "Time Series Analysis". Princeton, 1994. .. [3] MacKinnon, J.G. 1994. "Approximate asymptotic distribution functions for unit-root and cointegration tests. `Journal of Business and Economic Statistics` 12, 167-76. .. [4] 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 xrUToptional regression)cctcttnoptionsautolagr8rDrFrerlstorerYzInvalid input, x is constantrjrgrhri)Nrr7Nr(@Y@?rqr7z=sample size is too short to use selected regression componentzomaxlag must be less than (nobs/2 - 1 - ntrend) where n trend is the number of included deterministic regressorsbothin)trimoriginalrG ResultsStoreprepend)rYrfNr~rfnobs1%5%10%z8The coefficient on the lagged level equals 1 - unit rootz4The coefficient on the lagged level < 1 - stationaryz$Augmented Dickey-Fuller Test Results)%rrrrmaxrKrP isinstanceintrHshapelenrMceilpowerdiffr#statsmodels.stats.diagnosticrzr"r`rautolag_resultsrJrOr!r resolsrUusedlagadfstat critvaluesrH0HAr]_str)rcrUrfrmrprY trenddictrntrendxdiffxdallxdshortrzresstorefullRHSrTr]r^alresrrrpvaluers r?r/r/s~ 1cA fh 6FL*AJT3KG eW %E:|4Juuw!%%'788st6IZ C88* !!#J 771:D *c 1S_qF ~RWWTBHHTE\7$CCDETQY'!+V4 A:'   !)f$q( ( '  GGAJE 5D>6 FE ;;q>DEAI#E!Q$KEFmG =>  4@GG==#ekk!n4q8 &WxOFG&.%& "FGU(-H $8uQW~wVdK{{1~ B'ad -S YuQ 'A+ %56 C #% WA}1}$456::<nnQGJ!   H44FGT:= =FGT:vE EraunbiasedadjustedcP[US5n[US5n[USSS9n[USSS9n[US S S9n[US S S 9nUR 5nUS:XaSnO [ U5nU(a]US:Xa [ S5e[R"U5)nUS:XaUR5nSX)'OXnUR[5nU(a7U(a0XR5WR5- - n US:XaSU W)'OU(aXR5- n OUn [U5n Un UcU S - n OXZS - :a [S5eU(Gd6UGb2[R "U S -5n U R#U 5U S'[%U 5H%n XS -SR#U SU S -*5XS -'M' U(aUS:Xa.U(a X[R&"U S -5- -n U $X-n U $U(az[R "U S -[R(S9nWR5US'[%U 5H%n XS -SR#USU S -*5XS -'M' S XS:H'X-n U $U WR5-n U $U(a-U(a&US:Xa [R*"WUS5nS XS:H'OU(a<[R&"S U S -5n[R,"UUSSSSS245nOTU(a.WR5[R."SU -S - 5-nOU [R."SU -S - 5-nU(a[U 5n[1SU-S -5n [R2R3XS9n[R2R5U[R6"U5-5SUUUS - S- n U R8n O%[R*"XS5U S - SXS - S- n UbU SU S -R5$U $)ag Estimate autocovariances. Parameters ---------- x : array_like Time series data. Must be 1d. adjusted : bool, default False If True, then denominators is n-k, otherwise n. demean : bool, default True If True, then subtract the mean x from each element of x. fft : bool, default True If True, use FFT convolution. This method should be preferred for long time series. missing : str, default "none" A string in ["none", "raise", "conservative", "drop"] specifying how the NaNs are to be treated. "none" performs no checks. "raise" raises an exception if NaN values are found. "drop" removes the missing observations and then estimates the autocovariances treating the non-missing as contiguous. "conservative" computes the autocovariance using nan-ops so that nans are removed when computing the mean and cross-products that are used to estimate the autocovariance. When using "conservative", n is set to the number of non-missing observations. nlag : {int, None}, default None Limit the number of autocovariances returned. Size of returned array is nlag + 1. Setting nlag when fft is False uses a simple, direct estimator of the autocovariances that only computes the first nlag + 1 values. This can be much faster when the time series is long and only a small number of autocovariances are needed. Returns ------- ndarray The estimated autocovariances. References ---------- .. [1] Parzen, E., 1963. On spectral analysis with missing observations and amplitude modulation. Sankhya: The Indian Journal of Statistics, Series A, pp.383-392. rdemeanfftFrdmissingnoneraise conservativedroprknlagTrcr7ndimrrz!NaNs were encountered in the datarrNz"nlag must be smaller than nobs - 1rdtypefullrGrq)rj)rrrrrH has_missingrrMisnancopyastypersummeanrrPemptydotrIarangeint64r hstackonesrrifft conjugatereal)rcrrrrrdeal_with_masked notmask_bool notmask_intxorjlag_lenacovidivisordxirFrfs r?r%r%sX:.H vx (F C /C$MG D&4 0D1c"AmmoG& &q> g "#FG G | n $A Am A"))#.  " ;??,, , n $ !B }   \  AAG |a% A=>> 4#xx! $&&*QwAUW+//"ZQx.9DQK 7f#4BIIgk222   ((7Q;bhh?(__. wA%0Q%9%=%=#JAh/&GEN()*1 %  )) $N)B LLk6 :q&  YYq!a%  IIr2cr74R4=) *  OO A 2 2 A " " 2w !d(Q, 'ffjjj!vv{{3c!223ET:Qtaxz]Jyy||BF+AEG4qQzA Mgk"'')) Krac R[US5n[US5nUUS--[R"SU[R"S[ U5S-5- - US--5-n[ RRU[R"S[ U5S-55nX#4$)a Compute Ljung-Box Q Statistic. Parameters ---------- x : array_like Array of autocorrelation coefficients. Can be obtained from acf. nobs : int, optional Number of observations in the entire sample (ie., not just the length of the autocorrelation function results. Returns ------- q-stat : ndarray Ljung-Box Q-statistic for autocorrelation parameters. p-value : ndarray P-value of the Q statistic. See Also -------- statsmodels.stats.diagnostic.acorr_ljungbox Ljung-Box Q-test for autocorrelation in time series based on a time series rather than the estimated autocorrelation function. Notes ----- Designed to be used with acf. rcrrq?r7) rrrMcumsumrrr chi2sf)rcrretrs r?r,r,s< 1cA D& !D !8  ))SD299QA #;;<QF G H ::==bii3q6A:6 7D 9rac `[US5n[USSS9n[US5n[USSS9n[USSS9n[US S S 9n[ US 5nUR S nUc/[ [S[R"U5-5US- 5n[XSXGS9n U SUS-U S - n U(d U(dU $UbUOSn U(aU[R"U 5U- n S U S 'SU- U S'U SS===SS[R"U SSS-5---sss&OS[U5- n [RR!SU S- - 5[R""U 5-n [R$"['X- X-55nU(dX4$[)U SSUS9up?UbXX?4$XU4$)a& Calculate the autocorrelation function. Parameters ---------- x : array_like The time series data. adjusted : bool, default False If True, then denominators for autocovariance are n-k, otherwise n. nlags : int, optional Number of lags to return autocorrelation for. If not provided, uses min(10 * np.log10(nobs), nobs - 1). The returned value includes lag 0 (ie., 1) so size of the acf vector is (nlags + 1,). qstat : bool, default False If True, returns the Ljung-Box q statistic for each autocorrelation coefficient. See q_stat for more information. fft : bool, default True If True, computes the ACF via FFT. alpha : scalar, default None If a number is given, the confidence intervals for the given level are returned. For instance if alpha=.05, 95 % confidence intervals are returned where the standard deviation is computed according to Bartlett"s formula. bartlett_confint : bool, default True Confidence intervals for ACF values are generally placed at 2 standard errors around r_k. The formula used for standard error depends upon the situation. If the autocorrelations are being used to test for randomness of residuals as part of the ARIMA routine, the standard errors are determined assuming the residuals are white noise. The approximate formula for any lag is that standard error of each r_k = 1/sqrt(N). See section 9.4 of [2] for more details on the 1/sqrt(N) result. For more elementary discussion, see section 5.3.2 in [3]. For the ACF of raw data, the standard error at a lag k is found as if the right model was an MA(k-1). This allows the possible interpretation that if all autocorrelations past a certain lag are within the limits, the model might be an MA of order defined by the last significant autocorrelation. In this case, a moving average model is assumed for the data and the standard errors for the confidence intervals should be generated using Bartlett's formula. For more details on Bartlett formula result, see section 7.2 in [2]. missing : str, default "none" A string in ["none", "raise", "conservative", "drop"] specifying how the NaNs are to be treated. "none" performs no checks. "raise" raises an exception if NaN values are found. "drop" removes the missing observations and then estimates the autocovariances treating the non-missing as contiguous. "conservative" computes the autocovariance using nan-ops so that nans are removed when computing the mean and cross-products that are used to estimate the autocovariance. When using "conservative", n is set to the number of non-missing observations. Returns ------- acf : ndarray The autocorrelation function for lags 0, 1, ..., nlags. Shape (nlags+1,). confint : ndarray, optional Confidence intervals for the ACF at lags 0, 1, ..., nlags. Shape (nlags + 1, 2). Returned if alpha is not None. The confidence intervals are centered on the estimated ACF values. This behavior differs from plot_acf which centers the confidence intervals on 0. qstat : ndarray, optional The Ljung-Box Q-Statistic for lags 1, 2, ..., nlags (excludes lag zero). Returned if q_stat is True. pvalues : ndarray, optional The p-values associated with the Q-statistics for lags 1, 2, ..., nlags (excludes lag zero). Returned if q_stat is True. Notes ----- The acf at lag 0 (ie., 1) is returned. For very long time series it is recommended to use fft convolution instead. When fft is False uses a simple, direct estimator of the autocovariances that only computes the first nlag + 1 values. This can be much faster when the time series is long and only a small number of autocovariances are needed. If adjusted is true, the denominator for the autocovariance is adjusted for the loss of data. References ---------- .. [1] Parzen, E., 1963. On spectral analysis with missing observations and amplitude modulation. Sankhya: The Indian Journal of Statistics, Series A, pp.383-392. .. [2] Brockwell and Davis, 1987. Time Series Theory and Methods .. [3] Brockwell and Davis, 2010. Introduction to Time Series and Forecasting, 2nd edition. See Also -------- statsmodels.tsa.stattools.acf Estimate the autocorrelation function. statsmodels.graphics.tsaplots.plot_acf Plot autocorrelations and confidence intervals. rnlagsTrdqstatrFalpharrrkrcrN r7)rrrr皙?rrqrG@)r)rrrrrrrKrrMlog10r% ones_likerrr normppfsqrtarrayrr,)rcrrrrrbartlett_confintrravfr&_alphavaracfintervalconfintrs r?r&r&CsX:.H UGd 3E eW %E C /C ug 5E$MG 1cA 771:D }CRXXd^+,dQh7 Ts LC k SV #C U 'UTFc"T)q $Jq qr a!biiAb Q7777 s1vzz~~a&3,./"''&/AHhhtCNCN; # "s AC55 Dc[US5nU(aXR5- nURSnUbUO.[[ S[ R "U5-5US- 5n[US5nXCS- :a [S5e[ R"US-5nSURU5-US'[ R"US-5nUSSS2R5nUSSS2R5nUSSRUSS5USSRUSS5-US'SUS- USSRUSS5-US'[ R"U5n [ R"U5n [SU5H~n XySS&XSS&U SSXkU SS-- USS&U SSXkU SS-- USS&SXkS-- X[-XS-- USS-- X[S-'SX[S-- XS-SRX{S5-XkS-'M SUS-- U-S U[ R"SUS-5- -- n SUS'Xl4$) a Calculate Burg"s partial autocorrelation estimator. Parameters ---------- x : array_like Observations of time series for which pacf is calculated. nlags : int, optional Number of lags to return autocorrelation for. If not provided, uses min(10 * np.log10(nobs), nobs - 1). demean : bool, optional Flag indicating to demean that data. Set to False if x has been previously demeaned. Returns ------- pacf : ndarray Partial autocorrelations for lags 0, 1, ..., nlag. sigma2 : ndarray Residual variance estimates where the value in position m is the residual variance in an AR model that includes m lags. See Also -------- statsmodels.tsa.stattools.pacf Partial autocorrelation estimation. statsmodels.tsa.stattools.pacf_yw Partial autocorrelation estimation using Yule-Walker. statsmodels.tsa.stattools.pacf_ols Partial autocorrelation estimation using OLS. References ---------- .. [1] Brockwell, P.J. and Davis, R.A., 2016. Introduction to time series and forecasting. Springer. rcrNrr7z#nlags must be smaller than nobs - 1rqrGr)rrrrKrrMrrrPzerosrr empty_likerIr) rcrrrprr'ur>last_ulast_vrsigma2s r?r1r1s^N 1cA L 771:D"CRXXd^0C,DdQh(OA Aq A!8|>?? QA quuQx># "34rwwvF((4?@V | racp[US5n[US5n[US5n[US5n[USSS9n[U5nU(a%XR5- nXR5- nOUnUnU(a[R "USS 5nOUnU(aSOS n [ XgS U S 9US - SU- $)a Calculate the cross-covariance between two series. Parameters ---------- x, y : array_like The time series data to use in the calculation. adjusted : bool, optional If True, then denominators for cross-covariance are n-k, otherwise n. demean : bool, optional Flag indicating whether to demean x and y. fft : bool, default True If True, use FFT convolution. This method should be preferred for long time series. Returns ------- ndarray The estimated cross-covariance function: the element at index k is the covariance between {x[k], x[k+1], ..., x[n]} and {y[0], y[1], ..., y[m-k]}, where n and m are the lengths of x and y, respectively. rcyrrrFrdrrGdirectrrr7N)rrrrrMrr ) rcrrrrrjryorrVs r?r*r*<s0 1cA1cA:.H vx (F C /C AA \ \   IIaB  UxF RVF 3AEF ;a ??ra)rrc[US5n[US5n[US5n[USSS9n[XUSUS9nU[R"U5[R"U5-- nUS UnUbv[ R RS US - - 5[R"[U55- nURS S 5U[R"S S /5--n Xy4$U$)a The cross-correlation function. Parameters ---------- x, y : array_like The time series data to use in the calculation. adjusted : bool If True, then denominators for cross-correlation are n-k, otherwise n. fft : bool, default True If True, use FFT convolution. This method should be preferred for long time series. nlags : int, optional Number of lags to return cross-correlations for. If not provided, the number of lags equals len(x). alpha : float, optional If a number is given, the confidence intervals for the given level are returned. For instance if alpha=.05, 95 % confidence intervals are returned where the standard deviation is computed according to 1/sqrt(len(x)). Returns ------- ndarray The cross-correlation function of x and y: the element at index k is the correlation between {x[k], x[k+1], ..., x[n]} and {y[0], y[1], ..., y[m-k]}, where n and m are the lengths of x and y, respectively. confint : ndarray, optional Confidence intervals for the CCF at lags 0, 1, ..., nlags-1 using the level given by alpha and the standard deviation calculated as 1/sqrt(len(x)) [1]. Shape (nlags, 2). Returned if alpha is not None. Notes ----- If adjusted is True, the denominator for the cross-correlation is adjusted. References ---------- .. [1] Brockwell and Davis, 2016. Introduction to Time Series and Forecasting, 3rd edition, p. 242. rcrrrFrdT)rrrNrrrGr7) rrr*rMstdr rrrrreshaper) rcrrrrrcvfrrrs r?r+r+jsV 1cA1cA:.H C /C x# >C RVVAY& 'C fu+C ::>># "34rwws1vF++b!$x"((B72C'CC| rac [US5n[US5n[US5nUnU(aUnO[USS9SUS-n[R "US-US-4S5n[R "US-5nUSUS - US 'US US US-- US'[ S US-5HnXG[R"USU2US- 4USUSSS 25- XgS- - XWU4'[ SU5H$nXXUS- 4XWU4XWU- US- 4-- XXU4'M& XgS- SXWU4S -- -Xg'M US n USS2S 4n [R"U5R5n S U S 'XXU4$)a Levinson-Durbin recursion for autoregressive processes. Parameters ---------- s : array_like If isacov is False, then this is the time series. If iasacov is true then this is interpreted as autocovariance starting with lag 0. nlags : int, optional The largest lag to include in recursion or order of the autoregressive process. isacov : bool, optional Flag indicating whether the first argument, s, contains the autocovariances or the data series. Returns ------- sigma_v : float The estimate of the error variance. arcoefs : ndarray The estimate of the autoregressive coefficients for a model including nlags. pacf : ndarray The partial autocorrelation function. sigma : ndarray The entire sigma array from intermediate result, last value is sigma_v. phi : ndarray The entire phi array from intermediate result, last column contains autoregressive coefficients for AR(nlags). Notes ----- This function returns currently all results, but maybe we drop sigma and phi from the returns. If this function is called with the time series (isacov=False), then the sample autocovariance function is calculated with the default options (biased, no fft). srrF)rNr7rr)r7r7rqrGr) rrrr%rMrrIrdiagr) r rrordersxx_mphisigr=jsigma_varcoefspacf_s r?r3r3sP 1cA UG $E vx (F E aU#Keai0 ((EAIuqy)3 /C ((519 Ca58#CI 1XD E!H, ,CF 1eai  Hrvvc!A#q1u*ouQqz$B$/?@ @ AJqD q!Aq1uH qD CAq1u 4E(EEC1IUq3!t9>12 !"gG!"b&kG GGCL   EE!H U ,,rac[US5n[USSS9n[R"[R"U55nUSS:wa [ S5eUSSnUR SnUb$X:a [ S 5eUSUnUR Sn[R"US-5nUSUS'[R"SUS -- 5nUR5n[SU5H^nUSX&- *R5nXuUUSSS 2-- USX&- *&XVXFS- -URUSX&- *SSS 25-X6S-'M` SUS'XS4$) a Levinson-Durbin algorithm that returns the acf and ar coefficients. Parameters ---------- pacf : array_like Partial autocorrelation array for lags 0, 1, ... p. nlags : int, optional Number of lags in the AR model. If omitted, returns coefficients from an AR(p) and the first p autocorrelations. Returns ------- arcoefs : ndarray AR coefficients computed from the partial autocorrelations. acf : ndarray The acf computed from the partial autocorrelations. Array returned contains the autocorrelations corresponding to lags 0, 1, ..., p. References ---------- .. [1] Brockwell, P.J. and Davis, R.A., 2016. Introduction to time series and forecasting. Springer. r'rTrdrr7zCThe first entry of the pacf corresponds to lags 0 and so must be 1.NzIMust provide at least as many values from the pacf as the number of lags.rqrG) rrrMrasarrayrPrrcumprodrrIr)r'rrjr&nur(rprevs r?r2r2s|2 dF #D UGd 3E ::bjj& 'D Aw!|    8D 1 A  9. FU| JJqM ((1q5/C !WCF A M "BiikG 1a[z15"'')"QZ$tt*%<< AE(Z"U)+dhhs1x7H27N.OOE CF <rac^^^^[R"U[S9S-nURS:XaUR SS5n[ U5nSUs=:aS:a%O O"[ [R"XQ-55nO[U5[ LaUS:aUnUW*Sn[R"U5)RSS9m[R"USS9n[T5H7upU S:dM [R"SU -SS 9 [RX'M9 USUn [R"U 5)RSS9m[R"U SS9n [T5H7upU S:dM [R"S U -SS 9 [RX'M9 X- n U(aSS KJm UUU4S jnUUU4S jnOSSKJm UUU4SjnUUU4SjnUR'5nUS;a U"U 5nOLUS;aSU - n U"U 5nO8US;a'S[R("U"U 5U"U 55-nO [+S5e[ U 5S:Xa U SUS4$U U4$)a_ Test for heteroskedasticity of residuals Tests whether the sum-of-squares in the first subset of the sample is significantly different than the sum-of-squares in the last subset of the sample. Analogous to a Goldfeld-Quandt test. The null hypothesis is of no heteroskedasticity. Parameters ---------- resid : array_like Residuals of a time series model. The shape is 1d (nobs,) or 2d (nobs, nvars). subset_length : {int, float} Length of the subsets to test (h in Notes below). If a float in 0 < subset_length < 1, it is interpreted as fraction. Default is 1/3. alternative : str, 'increasing', 'decreasing' or 'two-sided' This specifies the alternative for the p-value calculation. Default is two-sided. use_f : bool, optional Whether or not to compare against the asymptotic distribution (chi-squared) or the approximate small-sample distribution (F). Default is True (i.e. default is to compare against an F distribution). Returns ------- test_statistic : {float, ndarray} Test statistic(s) H(h). p_value : {float, ndarray} p-value(s) of test statistic(s). Notes ----- The null hypothesis is of no heteroskedasticity. That means different things depending on which alternative is selected: - Increasing: Null hypothesis is that the variance is not increasing throughout the sample; that the sum-of-squares in the later subsample is *not* greater than the sum-of-squares in the earlier subsample. - Decreasing: Null hypothesis is that the variance is not decreasing throughout the sample; that the sum-of-squares in the earlier subsample is *not* greater than the sum-of-squares in the later subsample. - Two-sided: Null hypothesis is that the variance is not changing throughout the sample. Both that the sum-of-squares in the earlier subsample is not greater than the sum-of-squares in the later subsample *and* that the sum-of-squares in the later subsample is not greater than the sum-of-squares in the earlier subsample. For :math:`h = [T/3]`, the test statistic is: .. math:: H(h) = \sum_{t=T-h+1}^T \tilde v_t^2 \Bigg / \sum_{t=1}^{h} \tilde v_t^2 This statistic can be tested against an :math:`F(h,h)` distribution. Alternatively, :math:`h H(h)` is asymptotically distributed according to :math:`\chi_h^2`; this second test can be applied by passing `use_f=False` as an argument. See section 5.4 of [1]_ for the above formula and discussion, as well as additional details. References ---------- .. [1] Harvey, Andrew C. 1990. *Forecasting, Structural Time Series* *Models and the Kalman Filter.* Cambridge University Press. rrqr7rGrNaxiszfEarly subset of data for variable %d has too few non-missing observations to calculate test statistic. stacklevelzfLater subset of data for variable %d has too few non-missing observations to calculate test statistic.)fc*>TRUTT5$r:cdftest_statistics denom_dofr4 numer_dofs r?2breakvar_heteroskedasticity_test..sQUU Y . rac*>TRUTT5$r:rr8s r?r<r=sQTT Y . ra)rc.>TRTU-T5$r:r6r9rr:r;s r?r<r=sTXX  '. rac.>TRTU-T5$r:r?rAs r?r<r=sTWW  '. ra)rinc increasing)rdec decreasingr)2z2-sided two-sidedzInvalid alternative.)rMr+floatrrrrroundtyperrnansum enumeraterwarnnan scipy.statsr4rrHminimumrP)resid subset_length alternativeuse_f squared_residrh numer_residnumer_squared_sumrdof denom_residdenom_squared_sumtest_statistic pval_lower pval_upperp_valuerr:r4r;s @@@@r? breakvar_heteroskedasticity_testra(s`VJJuE2a7MQ%--b!4 u:D=1 -. / m  # (: $K((;'',,!,4I +A6I& 7 MM-/01   $&66  ' #K((;'',,!,4I +A6I& 7 MM-/01   $&66  '':N !   %  ##%K00^, 2 2~-^, 5 5bjj ~ & >(B  /00 >aa '!*,, 7 ""rac  [USSS9n[R"U5R5(d [ S5e[ US5nUb([ US5n[ R"S[5 OS n[US 5nUS ::a [ S 5e[R"S US -5nUR"S SU-[U5-::aB[ SR%[UR"S [U5- S- 5S - 55e0nUGHn0nU(a['S5 ['SU5 Un [)X SS S9n U(a[+U SS2S U S -24SS9n [+U SS2S S24SS9n U R"S U R"S S - :Xd5U RS 5U RS 5:HR-5S :wa [/S5eO [1S5e[3U SS2S 4U 5R55n [3U SS2S 4U 5R55nUR6R8(a UR:nO UR<nUS :XdUR>S :Xd[R@"URB5(d_UR>U- [RD"[F5RH:d*URJR"S U R"S :wa [/S5eU R>UR>- UR>- U - URL-nU(aD['SU[NRPRSUXRL5URLU 4-5 U[NRPRSUXRL5URLU 4US'U RTU R>UR>- -UR>- nU(a/['SU[NRVRSUU 5U 4-5 U[NRVRSUU 5U 4US'SU RXURX- -nU(a/['SU[NRVRSUU 5U 4-5 U[NRVRSUU 5U 4US '[RZ"[R\"X45[R^"X5[R\"U S 4545nURaU5nU(a:['S!URbURdURfURh4-5 [Rj"URb5S"[Rj"URd5S"URfURh4US#'XUU/4Xi'GM U$![ay [R"UVs/sHn[U5PM Os snfsn5nUR5nUR5S ::dUR S :Xa [ S5eGNf=f)$a` Four tests for granger non causality of 2 time series. All four tests give similar results. `params_ftest` and `ssr_ftest` are equivalent based on F test which is identical to lmtest:grangertest in R. Parameters ---------- x : array_like The data for testing whether the time series in the second column Granger causes the time series in the first column. Missing values are not supported. maxlag : {int, Iterable[int]} If an integer, computes the test for all lags up to maxlag. If an iterable, computes the tests only for the lags in maxlag. addconst : bool Include a constant in the model. verbose : bool Print results. Deprecated .. deprecated: 0.14 verbose is deprecated and will be removed after 0.15 is released Returns ------- dict All test results, dictionary keys are the number of lags. For each lag the values are a tuple, with the first element a dictionary with test statistic, pvalues, degrees of freedom, the second element are the OLS estimation results for the restricted model, the unrestricted model and the restriction (contrast) matrix for the parameter f_test. Notes ----- TODO: convert to class and attach results properly The Null hypothesis for grangercausalitytests is that the time series in the second column, x2, does NOT Granger cause the time series in the first column, x1. Grange causality means that past values of x2 have a statistically significant effect on the current value of x1, taking past values of x1 into account as regressors. We reject the null hypothesis that x2 does not Granger cause x1 if the pvalues are below a desired size of the test. The null hypothesis for all four test is that the coefficients corresponding to past values of the second time series are zero. `params_ftest`, `ssr_ftest` are based on F distribution `ssr_chi2test`, `lrtest` are based on chi-square distribution References ---------- .. [1] https://en.wikipedia.org/wiki/Granger_causality .. [2] Greene: Econometric Analysis Examples -------- >>> import statsmodels.api as sm >>> from statsmodels.tsa.stattools import grangercausalitytests >>> import numpy as np >>> data = sm.datasets.macrodata.load_pandas() >>> data = data.data[["realgdp", "realcons"]].pct_change().dropna() All lags up to 4 >>> gc_res = grangercausalitytests(data, 4) Only lag 4 >>> gc_res = grangercausalitytests(data, [4]) rcrqrzx contains NaN or inf values.addconstNverbosez>verbose is deprecated since functions should not print resultsTrUrz!maxlag must be a positive integerr7zAmaxlag must be a non-empty list containing only positive integersz6Insufficient observations. Maximum allowable lag is {}z Granger Causalityznumber of lags (no zero)ru)rwdropexFr{z`The x values include a column with constant values and so the test statistic cannot be computed.zNot ImplementedzfThe Granger causality test statistic cannot be computed because the VAR has a perfect fit of the data.zDssr based F test: F=%-8.4f, p=%-8.4f, df_denom=%d, df_num=%d ssr_ftestz3ssr based chi2 test: chi2=%-8.4f, p=%-8.4f, df=%d ssr_chi2testz3likelihood ratio test: chi2=%-8.4f, p=%-8.4f, df=%dlrtestzDparameter F test: F=%-8.4f, p=%-8.4f, df_denom=%d, df_num=%d params_ftest)6rrMisfiniteallrPrrrN FutureWarningrr TypeErrorrrrrKsizerformatprintr$rrrNotImplementedErrorrrJmodel k_constant centered_tssuncentered_tssssrrrsquaredfinforIepsrdf_residr r4rrrllf column_stackreyef_testfvaluerdf_denomdf_numr)rcrUrcrdlagsr[reslimlgresultmxlgdtadtaowndtajointres2down res2djointtssfgc1fgc2lrrconstrftress r?grangercausalitytestsrsZ 1c"A ;;q>    899:.HGY/ L   &(+ Q;@A AyyFQJ' wwqzQZ#h-// sAGGAJX$>!#CDqHI  E  ' ( ,c 2fQ7 !#adQh&7"8%HF#C12J>Hq!ciilQ&67LLOx||A6;;=B)>C&&78 8 s1a4y&)--/QTH-113     & &))C++C 1H~~"xx ++,,$(;(;;  &&q)X^^A->>%A  \\JNN *nn  !! "  GGJJtT+>+>?''    GGJJtT#6#6 7      {}} z~~ =>O  tT!:DAB #' dD(A4!H~8<<*..0 1  Euzz}}R.56  b$ 7>x// XXtl #RVVD%74)9L M !!'*  <<u~~u||LM  JJu|| $R ( JJu|| $R ( NN LL " ~*g>? ad LG xxV4VcSV45 88:?dii1n$ -s:7WY"=X A Y"!Y"cN[US5n[USSS9n[USSS9n[USS S9 [US S S 9n[US S SS9n[USS S 9nURupxUS- nUS:XaUn O [ XSS9n [ X 5R5n U RSS[-- :a[U RXESS9n O,[R"S[SS9 [R *4n US:Xa[R"/S-n O [%XUS- S9n ['U SX(S9n U SX4$)a Test for no-cointegration of a univariate equation. The null hypothesis is no cointegration. Variables in y0 and y1 are assumed to be integrated of order 1, I(1). This uses the augmented Engle-Granger two-step cointegration test. Constant or trend is included in 1st stage regression, i.e. in cointegrating equation. **Warning:** The autolag default has changed compared to statsmodels 0.8. In 0.8 autolag was always None, no the keyword is used and defaults to "aic". Use `autolag=None` to avoid the lag search. Parameters ---------- y0 : array_like The first element in cointegrated system. Must be 1-d. y1 : array_like The remaining elements in cointegrated system. trend : str {"c", "ct"} The trend term included in regression for cointegrating equation. * "c" : constant. * "ct" : constant and linear trend. * also available quadratic trend "ctt", and no constant "n". method : {"aeg"} Only "aeg" (augmented Engle-Granger) is available. maxlag : None or int Argument for `adfuller`, largest or given number of lags. autolag : str Argument for `adfuller`, lag selection criterion. * If None, then maxlag lags are used without lag search. * 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. return_results : bool For future compatibility, currently only tuple available. If True, then a results instance is returned. Otherwise, a tuple with the test outcome is returned. Set `return_results=False` to avoid future changes in return. Returns ------- coint_t : float The t-statistic of unit-root test on residuals. pvalue : float MacKinnon"s approximate, asymptotic p-value based on MacKinnon (1994). crit_value : dict Critical values for the test statistic at the 1 %, 5 %, and 10 % levels based on regression curve. This depends on the number of observations. Notes ----- The Null hypothesis is that there is no cointegration, the alternative hypothesis is that there is cointegrating relationship. If the pvalue is small, below a critical size, then we can reject the hypothesis that there is no cointegrating relationship. P-values and critical values are obtained through regression surface approximation from MacKinnon 1994 and 2010. If the two series are almost perfectly collinear, then computing the test is numerically unstable. However, the two series will be cointegrated under the maintained assumption that they are integrated. In this case the t-statistic will be set to -inf and the pvalue to zero. TODO: We could handle gaps in data by dropping rows with nans in the Auxiliary regressions. Not implemented yet, currently assumes no nans and no gaps in time series. References ---------- .. [1] MacKinnon, J.G. 1994 "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests." Journal of Business & Economics Statistics, 12.2, 167-76. .. [2] MacKinnon, J.G. 2010. "Critical Values for Cointegration Tests." Queen"s University, Dept of Economics Working Papers 1227. http://ideas.repec.org/p/qed/wpaper/1227.html y0y1rqrtrend)rgrjrhrirkrV)aegrUTrdrmrnroreturn_resultsr7rjF)rr|d)rUrmrfzZy0 and y1 are (almost) perfectly colinear.Cointegration test is not reliable in this case.r2rerrr})rrrrrr"rrJrzSQRTEPSr/rRrrNrrMinfrOr r!)rrrrVrUrmrrk_varsxxres_cores_adfcritpval_asys r?r-r-sD| B B B1 %B w0G HE(3 fh 6FT3KG~/?$ON88LD aKF |  r 6 [__ F S7]** LLS    ?   FF7* |x!|vdQhG'!*AH 1:x %%rac HSSKJn U"U4SU0UDSU0D6R"S SU0UD6$![a g[aanUbSnAgSUR S;dS[ U5;a-S/[U5-nUS:XaS/U-n[XX#XE5sSnA$SnAgSnAf g=f) Nr)ARIMAr"r start_paramsinitial皙?rgrk) statsmodels.tsa.arima.modelrrJr rPargsstrr_safe_arma_fit)rr"model_kwrfit_kwrrerrors r?rr2s1Q=e=x=u=AA % )/       #  ejjm +yCJ/F53u:-L| #u|3 !(6  s& ) B! B!BA BB!B!c [US5n[US5n[USSS9n[USSS9n[US SS9n[US -5Vs/sHowPM nn[US -5Vs/sHowPM n n[ U[ 5(aU/nO&[ U[ [45(d [S 5e[R"[U5US -US -45n Uc0OUnUc0OUn[US SS9n UH[n U HRn [XSU 4XTU5nUc[RU S S 2X4'M/[U5Hup[!X5XX4'M MT M] U Vs/sHn["R$"UXS9PM nn['[)UU55n0nUR+5Hunn[R,"[R."UR15R15U- 55nUR2S n[R4"U5nUR7US-UU-UU-405 M UR7U5 [9S0UD6$s snfs snfs snf)a Compute information criteria for many ARMA models. Parameters ---------- y : array_like Array of time-series data. max_ar : int Maximum number of AR lags to use. Default 4. max_ma : int Maximum number of MA lags to use. Default 2. ic : str, list Information criteria to report. Either a single string or a list of different criteria is possible. trend : str The trend to use when fitting the ARMA models. model_kw : dict Keyword arguments to be passed to the ``ARMA`` model. fit_kw : dict Keyword arguments to be passed to ``ARMA.fit``. Returns ------- Bunch Dict-like object with attribute access. Each ic is an attribute with a DataFrame for the results. The AR order used is the row index. The ma order used is the column index. The minimum orders are available as ``ic_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. Examples -------- >>> 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="n") >>> res.aic_min_order >>> res.bic_min_order max_armax_mar)rjrgrkrTrdrr7z.Need a list or a tuple for ic if not a string.Nr) contiguousr)columnsindex _min_orderrk)rrrrIrrlisttuplerPrMrrrrrOrMgetattrpd DataFramedictziprLascontiguousarrayrNrKrargminupdater)rrricrrrrar_rangema_rangerZy_arrarmarQcriteriaresdfsmin_resrdeltancolslocs r?r.r.OsJvfh 'F fh 'F w ;E:=H vx$ 7F !,-,a,H- !,-,a,H-"cT T5M * *IJJhhB!VaZ89G%r8H>RvF q#$ /EB Q XfMC{%'VV2 "(} %,S%;2 " - HO GN S(;w  s2s| CGYY[ 6$$RVVFJJL,<,<,>,G%HI AiiL(3%<u*EFG ! JJw <3<I.-( s I' IIcV[R"[R"U55$)zB Returns True if "data" contains missing entries, otherwise False )rMrr)datas r?rrs 88BFF4L !!rac V[US5n[USSS9n[US5nURSnUnX@R:wa[ SURS35eUS :XaJ[ U[[R"S US -555R5Rn/S QnOXR5- n/S QnUS :XaI[[R"S[R"US- S5-55n[!X$S - 5nOUS:XdUc7Uc["R$"S[&SS9 [)Xd5n[!X$S - 5nOB[+U[,5(a [ S5e[/USSS9nX$:a[ SUSUS35e/SQn[R0"UR35S-5US-- n [5XdU5n X- n [R6"XU5n Sn XS:Xa(["R$"U R9SS 9[:SS9 O/XS:Xa'["R$"U R9S!S 9[:SS9 USUS USUS"S#.nU(a@SS$KJn U"5nUUl UUl!US%:XaS&OS'nS(US)3Ul"S*US)3Ul#XUU4$XX.4$)+a4 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 The data series to test. regression : str{"c", "ct"} The null hypothesis for the KPSS test. * "c" : The data is stationary around a constant (default). * "ct" : The data is stationary around a trend. nlags : {str, int}, optional Indicates the number of lags to be used. If "auto" (default), 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 "legacy", 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. See the notebook `Stationarity and detrending (ADF/KPSS) <../examples/notebooks/generated/stationarity_detrending_adf_kpss.html>`__ for an overview. References ---------- .. [1] Andrews, D.W.K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59: 817-858. .. [2] Hobijn, B., Frances, B.H., & Ooms, M. (2004). Generalizations of the KPSS-test for stationarity. Statistica Neerlandica, 52: 483-502. .. [3] 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. .. [4] Newey, W.K., & West, K.D. (1994). Automatic lag selection in covariance matrix estimation. Review of Economic Studies, 61: 631-653. .. [5] Schwert, G. W. (1989). Tests for unit roots: A Monte Carlo investigation. Journal of Business and Economic Statistics, 7 (2): 147-159. rcrf)rgrhrkrpr x of shape  not understoodrhr7)gX9v?g㥛 ?gI +?gS?)gh|?5?goʡ?g|?5^?gS?legacyrrrsrtautozpNone is not a valid value for nlags. It must be an integer, 'auto' or 'legacy'. None will raise starting in 0.14rqr2z0nvals must be 'auto' or 'legacy' when not an intrFrdzlags (z$) must be < number of observations (r)rr皙?{Gz?The test statistic is outside of the range of p-values available in the look-up table. The actual p-value is {direction} than the p-value returned. rGsmaller directiongreaterrerrz2.5%rryrglevelrzThe series is z stationaryzThe series is not )$rrrrrqrPrrrMrrJrRrrrrrKrrNro _kpss_autolagrrrrr_sigma_est_kpssinterprrrrrzrrrr)rcrfrrprhyporesidsrpvalsetas_hat kpss_statr`warn_msg crit_dictrzrstorestationary_types r?r0r0sf 1cAZ{KJ eW %E 771:D D vv~;qwwi?@@ t|Q RYYq$(%;<=AACII+VVX+ BGGD288D5L'#BBCDE!8$ &EM = MMG  f+E!8$ E3  KLL%8 =CD6K  &E &&A% &$!) 4C F% 0E Iii /GH) OOiO 0  !H  OOiO 0  QtAwQtAwOI =  %)S['g$_$5[A ((9E 9f44533rac[R"US-5n[SUS-5H4n[R"XSUSX- 5nUSU-SXBS-- - -- nM6 X1- $)zo Computes equation 10, p. 164 of Kwiatkowski et al. (1992). This is the consistent estimator for the variance. rqr7Nr)rMrrIr)rrrrr resids_prods r?rrlsq FF6Q; E 1dQh ffVBZ $();<  [C1s +;$<==  <rac[[R"US55n[R"US-5U- nSn[ SUS-5H3n[R "XSUSX- 5nXaS- -nX6- nXEU-- nM5 XC- nSnS[R"Xw-U5-n [U [R"X5-5n U $) z 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. gqq?rqrr7NrUUUUUU?g{P?)rrMrrrIr) rrcovlagss0s1rrrpwr gamma_hatautolagss r?rrxs "((4+,G ! t #B B 1gk "ffVBZ $();< cz!   +o # GE C%-55I9rxx223H Orac[US5n[US5nURSnX R:wa[ SURS35e/SQn[ R "/SQ5n[ R "/SQ/S Q/S Q/S Q/S Q/S Q/SQ/SQ/SQ/SQ/SQ/SQ/ 5n[ R"SURS45n[URS5H"n[XESS2U45nU"U5USU4'M$ [R"U5n U RS5R5RS5n U RS5R5RS5n X:R!5X:R!5-n U [ R""[%U55- n [%U5S- n[[%U5S- SS5HnXSU4:aUnM O X>nSnSnXS:XaSnO XS:XaSnU(a'[&R("UR+US9[,SS9 USUSUS US!S".nU(a'SS#KJn U"5nUUlS$UlS%UlXUU4$XU4$)&aE Range unit-root test for stationarity. Computes the Range Unit-Root (RUR) test for the null hypothesis that x is stationary. Parameters ---------- x : array_like, 1d The data series to test. store : bool If True, then a result instance is returned additionally to the RUR statistic (default is False). Returns ------- rur_stat : float The RUR test statistic. p_value : float The p-value of the test. The p-value is interpolated from Table 1 in Aparicio et al. (2006), and a boundary point is returned if the test statistic is outside the table of critical values, that is, if the p-value is outside the interval (0.01, 0.1). crit : dict The critical values at 10%, 5%, 2.5% and 1%. Based on Aparicio et al. (2006). resstore : (optional) instance of ResultStore An instance of a dummy class with results attached as attributes. Notes ----- The p-values are interpolated from Table 1 of Aparicio et al. (2006). If the computed statistic is outside the table of critical values, then a warning message is generated. Missing values are not handled. References ---------- .. [1] Aparicio, F., Escribano A., Sipols, A.E. (2006). Range Unit-Root (RUR) tests: robust against nonlinearities, error distributions, structural breaks and outliers. Journal of Time Series Analysis, 27 (4): 545-576. rcrprrr)rrrr?gffffff?) 2riiii ii)gJ4?gX?g`vOj?gkw#?g[ A@g}b@)gI&†?gB?g?gMSt$?gDt@g( @)g/$?gOec?gcZB?gW[?ge`TR@gQI @)gaTR'?g&S:?gZڊ?g48E?go!@gkw @)gŏ1w?g ?g;Nё\?gSt$?g58EGr@gHP @)g[ A?gX?g62r * A& &A  + hGHI) !H   OOiO 0  $4  I = 2 . )V33)++racP\rSrSrSrSrS SjrSrSrSr S S jr S S jr S r g)ZivotAndrewsUnitRooti zA Class wrapper for Zivot-Andrews structural-break unit-root test cJ0UlSUl[R"UR5URS'SUl[R"UR5URS'SUl[R"UR 5URS'g)z Critical values for the three different models specified for the Zivot-Andrews unit-root test. Notes ----- The p-values are generated through Monte Carlo simulation using 100,000 replications and 2000 data points. )0)MbP?g3P>#)rg#S)皙?g(IL)333333?gV)皙?g>d )?g=)333333?g)^Ҙ)ffffff?g&"p)皙?g;)T)rgٙB56)rg9])@g3")@gdF >)@gMJA)$@gݘC))@g[B>).@g\ʞ)1@gz[)4@gUN )6@gF)9@g؁sF);@gE|')>@gd#W)@@@g%䃞-)A@g2%)B@ght)D@g|])@E@g"2 )F@gm)G@gR q)I@g AJ))@J@gA}R )K@g rh )L@go_G )N@g)W )@P@g Ac] )Q@g6qr )R@giW!' )T@g16T )@U@g!A 3m )V@g_LU) W@g{)W@gd)X@gY)@X@gek})X@gv)X@g4)皙X@g ܺ:rg)0)r g3T)rgMSt+)r g߾C")r gytM)rgjn)rg=$@)rg~:)rg9ֿ)rgm)rgQ)rg<#)rg:̗)rg )rg 0)rgj)rgǺ&)rgec)rgӼ )rgC)rgeN)rg.= )rgt. )rgZ )rgjHci )r gGȰ )r!gJRЭ )r"gKqU )r#g:H )r$g$ )r%gY )r&g->x )r'g" )r(g"^ )r)g  )r*gdw)r+gz6>)r,g҇n)r-g+j)r.g(D!T)r/gsF)r0g )r1g.9N)r2gŏ1w)r3gJR)r4gn2d)r5gAf)r6g"^F)r7gHht)0)r gX9C)rg%jj)r gC5vJ)r g)rg=s)rgu7O)rg)rg9z)rg^ D)rgGȰj)rgÙ_M)rgUj@+0)rg%eK)rg2Y)rgt3N)rg7)rgFx )rgQ[)rg46<)rgM)rgP1)rgt~)rg1N)rg )r g)r!g /)r"goʡ)r#g|Sz)r$gmJR)r%g9}+)r&gLOX)r'gkC8)r(g~jt)r)gF()r*g.)r+gb=9)r,gڏa )r-g` )r.gq2 )r/g_LU )r0gG=D;H )r1gN )r2gk}Ж)r3gp>?)r4g1)r5gԷ)r6g c)r7gR%MrhN)_za_critical_values_crMr+_t_ct)selfs r?__init__ZivotAndrewsUnitRoot.__init__ s$& 1 d)+ 477(;  %1 d)+ 477(;  %1 d*,DHH)=  &racURUnUSS2S4nUSS2S4n[R"XU5S- n/SQn[R"XtU5nUSUSUSS.n Xi4$)a Linear interpolation for Zivot-Andrews p-values and critical values Parameters ---------- stat : float The ZA test statistic model : {"c","t","ct"} The model used when computing the ZA statistic. "c" is default. Returns ------- pvalue : float The interpolated p-value cvdict : dict Critical values for the test statistic at the 1%, 5%, and 10% levels Notes ----- The p-values are linear interpolated from the quantiles of the simulated ZA test statistic distribution Nrr7rs)rrrrqr)r9rMr) r=statrutablepcntsr rcv crit_valuecvdicts r?_za_critZivotAndrewsUnitRoot._za_crit s~0((/ad ad 4.6 YYr%0 Q-Q-a=  ~rac[RRURR U55nURR U5nUR upVUR U5nXR U5- nURR U5XV- - n U[R "[R"X-55- $)z9 Minimal implementation of LS estimator for internal use )rMlinalginvTrrrr!) r=rRrSxpxixpyrk_exogbers r? _quick_olsZivotAndrewsUnitRoot._quick_ols syy}}TVVZZ-.ffjjzz  HHSM HHQK t}-2772776=1222rac[R"USS9nU[R"URR U55-nU[R"URR U55- n[R "XvSR SXV-45nX8SS2S4'XUS- USS2US- 4'[XvSS9XhR SU-USS2US24'Xx4$)zn Create the endog/exog data for the auxiliary regressions from the original (standardized) series under test. rr0Nr7r)rw)rMrrrLrrrr#) r=seriesrconstrcolsrrRrSs r?_format_regression_data,ZivotAndrewsUnitRoot._format_regression_data s Q' U+,,"''&((,,v"677xxu++A. <=QT "4!85Qq[&9 ::a=4' QX{rac X8S-- n US:waCSUSU 2S4'XQU S2S4'XhS-US-USS2S4'US:XaSUSU 2S4'USXC- S-XS2S4'U$XhS-US-USS2S4'SUSU S- 2S4'USXC- S-XS- S2S4'U$)z0 Update the exog array for the next regression. r7r8rNrqrhrerk) r=rSrfperiodrrVrrWrcutoffs r?_update_regression_exog,ZivotAndrewsUnitRoot._update_regression_exog s !8$   D&! $! qTAX7DAJT!#$WfWaZ #(dma.?#AWaZ  qTAX7DAJ&'DFQJ" #&+A1B&DD1*" # raNc *[US[RSS9n[US5n[ USSS9n[ USS S 9n[ US S SS 9nUS:dUS:a [ S5eURSnU(a[XSUS9nUSnO0U(aUnO&[S[R"US- S5-5n[Xb-5n U n Xi- n US:XaSn OSn S[R"U5- n [R"SUS-5nU[R"S5US-- -nURXXX5unn[R"U S-[R5n[!U S-U S-5HnUR#UUUUU UU U5nUU S-:Xa[%XSUSS9R'5nUR(URSS- :a5[ SR+URSS- UR(55eUR,U S- UU'MUR/XSU5U S- UU'M [R0"U5n[R2"U5S- nUR5UU5nUSnUSnUUUUU4$)a Zivot-Andrews structural-break unit-root test. The Zivot-Andrews test tests for a unit root in a univariate process in the presence of serial correlation and a single structural break. Parameters ---------- x : array_like The data series to test. trim : float The percentage of series at begin/end to exclude from break-period calculation in range [0, 0.333] (default=0.15). maxlag : int The maximum lag which is included in test, default is 12*(nobs/100)^{1/4} (Schwert, 1989). regression : {"c","t","ct"} Constant and trend order to include in regression. * "c" : constant only (default). * "t" : trend only. * "ct" : constant and trend. autolag : {"AIC", "BIC", "t-stat", None} The method to select the lag length when using automatic selection. * 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. Returns ------- zastat : float The test statistic. pvalue : float The pvalue based on MC-derived critical values. cvdict : dict The critical values for the test statistic at the 1%, 5%, and 10% levels. baselag : int The number of lags used for period regressions. bpidx : int The index of x corresponding to endogenously calculated break period with values in the range [0..nobs-1]. Notes ----- H0 = unit root with a single structural break Algorithm follows Baum (2004/2015) approximation to original Zivot-Andrews method. Rather than performing an autolag regression at each candidate break period (as per the original paper), a single autolag regression is run up-front on the base model (constant + trend with no dummies) to determine the best lag length. This lag length is then used for all subsequent break-period regressions. This results in significant run time reduction but also slightly more pessimistic test statistics than the original Zivot-Andrews method, although no attempt has been made to characterize the size/power trade-off. References ---------- .. [1] Baum, C.F. (2004). ZANDREWS: Stata module to calculate Zivot-Andrews unit root test in presence of structural break," Statistical Software Components S437301, Boston College Department of Economics, revised 2015. .. [2] Schwert, G.W. (1989). Tests for unit roots: A Monte Carlo investigation. Journal of Business & Economic Statistics, 7: 147-159. .. [3] Zivot, E., and Andrews, D.W.K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. 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