def _partial_regression(endog, exog_i, exog_others): """Partial regression. regress endog on exog_i conditional on exog_others uses OLS Parameters ---------- endog : array_like exog : array_like exog_others : array_like Returns ------- res1c : OLS results instance (res1a, res1b) : tuple of OLS results instances results from regression of endog on exog_others and of exog_i on exog_others """ #FIXME: This function doesn't appear to be used. res1a = OLS(endog, exog_others).fit() res1b = OLS(exog_i, exog_others).fit() res1c = OLS(res1a.resid, res1b.resid).fit() return res1c, (res1a, res1b)
def reset_ramsey(res, degree=5): '''Ramsey's RESET specification test for linear models This is a general specification test, for additional non-linear effects in a model. Notes ----- The test fits an auxilliary OLS regression where the design matrix, exog, is augmented by powers 2 to degree of the fitted values. Then it performs an F-test whether these additional terms are significant. If the p-value of the f-test is below a threshold, e.g. 0.1, then this indicates that there might be additional non-linear effects in the model and that the linear model is mis-specified. References ---------- http://en.wikipedia.org/wiki/Ramsey_RESET_test ''' order = degree + 1 k_vars = res.model.exog.shape[1] #vander without constant and x: y_fitted_vander = np.vander(res.fittedvalues, order)[:, :-2] #drop constant exog = np.column_stack((res.model.exog, y_fitted_vander)) res_aux = OLS(res.model.endog, exog).fit() #r_matrix = np.eye(degree, exog.shape[1], k_vars) r_matrix = np.eye(degree-1, exog.shape[1], k_vars) #df1 = degree - 1 #df2 = exog.shape[0] - degree - res.df_model (without constant) return res_aux.f_test(r_matrix) #, r_matrix, res_aux
def coint(y1, y2, regression="c"): """ This is a simple cointegration test. Uses unit-root test on residuals to test for cointegrated relationship See Hamilton (1994) 19.2 Parameters ---------- y1 : array_like, 1d first element in cointegrating vector y2 : array_like remaining elements in cointegrating vector c : str {'c'} Included in regression * 'c' : Constant Returns ------- coint_t : float t-statistic of unit-root test on residuals pvalue : float MacKinnon's approximate p-value based on MacKinnon (1994) crit_value : dict Critical values for the test statistic at the 1 %, 5 %, and 10 % levels. 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 are obtained through regression surface approximation from MacKinnon 1994. References ---------- MacKinnon, J.G. 1994. "Approximate asymptotic distribution functions for unit-root and cointegration tests. `Journal of Business and Economic Statistics` 12, 167-76. """ regression = regression.lower() if regression not in ['c', 'nc', 'ct', 'ctt']: raise ValueError("regression option %s not understood") % regression y1 = np.asarray(y1) y2 = np.asarray(y2) if regression == 'c': y2 = add_constant(y2) st1_resid = OLS(y1, y2).fit().resid #stage one residuals lgresid_cons = add_constant(st1_resid[0:-1]) uroot_reg = OLS(st1_resid[1:], lgresid_cons).fit() coint_t = (uroot_reg.params[0] - 1) / uroot_reg.bse[0] pvalue = mackinnonp(coint_t, regression="c", N=2, lags=None) crit_value = mackinnoncrit(N=1, regression="c", nobs=len(y1)) return coint_t, pvalue, crit_value
def setupClass(cls): data = longley.load() data.exog = add_constant(data.exog) res1 = OLS(data.endog, data.exog).fit() R = np.array([[0, 1, 1, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0]]) q = np.array([0, 0, 0, 1, 0]) cls.Ftest1 = res1.f_test(R, q)
def setupClass(cls): data = longley.load() data.exog = add_constant(data.exog) res1 = OLS(data.endog, data.exog).fit() R = np.array([[0,1,1,0,0,0,0], [0,1,0,1,0,0,0], [0,1,0,0,0,0,0], [0,0,0,0,1,0,0], [0,0,0,0,0,1,0]]) q = np.array([0,0,0,1,0]) cls.Ftest1 = res1.f_test(R,q)
def setupClass(cls): from results.results_regression import Longley data = longley.load() data.exog = add_constant(data.exog) res1 = OLS(data.endog, data.exog).fit() res2 = Longley() res2.wresid = res1.wresid # workaround hack cls.res1 = res1 cls.res2 = res2 res_qr = OLS(data.endog, data.exog).fit(method="qr") cls.res_qr = res_qr
def qqline(ax, line, x=None, y=None, dist=None, fmt='r-'): """ Plot a reference line for a qqplot. Parameters ---------- ax : matplotlib axes instance The axes on which to plot the line line : str {'45','r','s','q'} Options for the reference line to which the data is compared. '45' - 45-degree line 's' - standardized line, the expected order statistics are scaled by the standard deviation of the given sample and have the mean added to them 'r' - A regression line is fit 'q' - A line is fit through the quartiles. None - By default no reference line is added to the plot. x : array X data for plot. Not needed if line is '45'. y : array Y data for plot. Not needed if line is '45'. dist : scipy.stats.distribution A scipy.stats distribution, needed if line is 'q'. Notes ----- There is no return value. The line is plotted on the given `ax`. """ if line == '45': end_pts = zip(ax.get_xlim(), ax.get_ylim()) end_pts[0] = max(end_pts[0]) end_pts[1] = min(end_pts[1]) ax.plot(end_pts, end_pts, fmt) return # does this have any side effects? if x is None and y is None: raise ValueError("If line is not 45, x and y cannot be None.") elif line == 'r': # could use ax.lines[0].get_xdata(), get_ydata(), # but don't know axes are 'clean' y = OLS(y, add_constant(x)).fit().fittedvalues ax.plot(x,y,fmt) elif line == 's': m,b = y.std(), y.mean() ref_line = x*m + b ax.plot(x, ref_line, fmt) elif line == 'q': q25 = stats.scoreatpercentile(y, 25) q75 = stats.scoreatpercentile(y, 75) theoretical_quartiles = dist.ppf([.25,.75]) m = (q75 - q25) / np.diff(theoretical_quartiles) b = q25 - m*theoretical_quartiles[0] ax.plot(x, m*x + b, fmt)
def qqline(ax, line, x=None, y=None, dist=None, fmt='r-'): """ Plot a reference line for a qqplot. Parameters ---------- ax : matplotlib axes instance The axes on which to plot the line line : str {'45','r','s','q'} Options for the reference line to which the data is compared. '45' - 45-degree line 's' - standardized line, the expected order statistics are scaled by the standard deviation of the given sample and have the mean added to them 'r' - A regression line is fit 'q' - A line is fit through the quartiles. None - By default no reference line is added to the plot. x : array X data for plot. Not needed if line is '45'. y : array Y data for plot. Not needed if line is '45'. dist : scipy.stats.distribution A scipy.stats distribution, needed if line is 'q'. Notes ----- There is no return value. The line is plotted on the given `ax`. """ if line == '45': end_pts = zip(ax.get_xlim(), ax.get_ylim()) end_pts[0] = max(end_pts[0]) end_pts[1] = min(end_pts[1]) ax.plot(end_pts, end_pts, fmt) return # does this have any side effects? if x is None and y is None: raise ValueError("If line is not 45, x and y cannot be None.") elif line == 'r': # could use ax.lines[0].get_xdata(), get_ydata(), # but don't know axes are 'clean' y = OLS(y, add_constant(x)).fit().fittedvalues ax.plot(x, y, fmt) elif line == 's': m, b = y.std(), y.mean() ref_line = x * m + b ax.plot(x, ref_line, fmt) elif line == 'q': q25 = stats.scoreatpercentile(y, 25) q75 = stats.scoreatpercentile(y, 75) theoretical_quartiles = dist.ppf([.25, .75]) m = (q75 - q25) / np.diff(theoretical_quartiles) b = q25 - m * theoretical_quartiles[0] ax.plot(x, m * x + b, fmt)
def setupClass(cls): # if skipR: # raise SkipTest, "Rpy not installed" # try: # r.library('car') # except RPyRException: # raise SkipTest, "car library not installed for R" R = np.zeros(7) R[4:6] = [1, -1] # self.R = R data = longley.load() data.exog = add_constant(data.exog) res1 = OLS(data.endog, data.exog).fit() cls.Ttest1 = res1.t_test(R)
def setupClass(cls): # if skipR: # raise SkipTest, "Rpy not installed" # try: # r.library('car') # except RPyRException: # raise SkipTest, "car library not installed for R" R = np.zeros(7) R[4:6] = [1,-1] # self.R = R data = longley.load() data.exog = add_constant(data.exog) res1 = OLS(data.endog, data.exog).fit() cls.Ttest1 = res1.t_test(R)
def __init__(self): super(self.__class__, self).__init__() #initialize DGP nobs = self.nobs y_true, x, exog = self.y_true, self.x, self.exog np.random.seed(8765993) sigma_noise = 0.1 y = y_true + sigma_noise * np.random.randn(nobs) m = AdditiveModel(x) m.fit(y) res_gam = m.results #TODO: currently attached to class res_ols = OLS(y, exog).fit() #Note: there still are some naming inconsistencies self.res1 = res1 = Dummy() #for gam model #res2 = Dummy() #for benchmark self.res2 = res2 = res_ols #reuse existing ols results, will add additional res1.y_pred = res_gam.predict(x) res2.y_pred = res_ols.model.predict(res_ols.params, exog) res1.y_predshort = res_gam.predict(x[:10]) slopes = [i for ss in m.smoothers for i in ss.params[1:]] const = res_gam.alpha + sum([ss.params[1] for ss in m.smoothers]) #print const, slopes res1.params = np.array([const] + slopes)
def setupClass(cls): np.random.seed(54321) cls.endog_n_ = np.random.uniform(0, 20, size=30) cls.endog_n_one = cls.endog_n_[:, None] cls.exog_n_ = np.random.uniform(0, 20, size=30) cls.exog_n_one = cls.exog_n_[:, None] cls.degen_exog = cls.exog_n_one[:-1] cls.mod1 = OLS(cls.endog_n_one, cls.exog_n_one) cls.mod1.df_model += 1 #cls.mod1.df_resid -= 1 cls.res1 = cls.mod1.fit() # Note that these are created for every subclass.. # A little extra overhead probably cls.mod2 = OLS(cls.endog_n_one, cls.exog_n_one) cls.mod2.df_model += 1 cls.res2 = cls.mod2.fit()
def pacf_ols(x, nlags=40): '''Calculate partial autocorrelations Parameters ---------- x : 1d array observations of time series for which pacf is calculated nlags : int Number of lags for which pacf is returned. Lag 0 is not returned. Returns ------- pacf : 1d array partial autocorrelations, maxlag+1 elements Notes ----- This solves a separate OLS estimation for each desired lag. ''' #TODO: add warnings for Yule-Walker #NOTE: demeaning and not using a constant gave incorrect answers? #JP: demeaning should have a better estimate of the constant #maybe we can compare small sample properties with a MonteCarlo xlags, x0 = lagmat(x, nlags, original='sep') #xlags = sm.add_constant(lagmat(x, nlags), prepend=True) xlags = add_constant(xlags, prepend=True) pacf = [1.] for k in range(1, nlags + 1): res = OLS(x0[k:], xlags[k:, :k + 1]).fit() #np.take(xlags[k:], range(1,k+1)+[-1], pacf.append(res.params[-1]) return np.array(pacf)
def setupClass(cls): data = longley.load() data.exog = add_constant(data.exog) ols_res = OLS(data.endog, data.exog).fit() gls_res = GLS(data.endog, data.exog).fit() cls.res1 = gls_res cls.res2 = ols_res
def fitbygroups(self): '''Fit OLS regression for each group separately. Returns ------- results are attached olsbygroup : dictionary of result instance the returned regression results for each group sigmabygroup : array (ngroups,) (this should be called sigma2group ??? check) mse_resid for each group weights : array (nobs,) standard deviation of group extended to the original observations. This can be used as weights in WLS for group-wise heteroscedasticity. ''' olsbygroup = {} sigmabygroup = [] for gi, group in enumerate( self.unique): #np.arange(len(self.unique))): groupmask = self.groupsint == gi #group index res = OLS(self.endog[groupmask], self.exog[groupmask]).fit() olsbygroup[group] = res sigmabygroup.append(res.mse_resid) self.olsbygroup = olsbygroup self.sigmabygroup = np.array(sigmabygroup) self.weights = np.sqrt( self.sigmabygroup[self.groupsint]) #TODO:chk sqrt
def spec_hausman(self, dof=None): '''Hausman's specification test See Also -------- spec_hausman : generic function for Hausman's specification test ''' #use normalized cov_params for OLS resols = OLS(endog, exog).fit() normalized_cov_params_ols = resols.model.normalized_cov_params se2 = resols.mse_resid params_diff = self._results.params - resols.params cov_diff = np.linalg.pinv(self.xhatprod) - normalized_cov_params_ols #TODO: the following is very inefficient, solves problem (svd) twice #use linalg.lstsq or svd directly #cov_diff will very often be in-definite (singular) if not dof: dof = tools.rank(cov_diff) cov_diffpinv = np.linalg.pinv(cov_diff) H = np.dot(params_diff, np.dot(cov_diffpinv, params_diff))/se2 pval = stats.chi2.sf(H, dof) return H, pval, dof
def plot_partregress_ax(endog, exog_i, exog_others, varname='', title_fontsize=None, ax=None): """Plot partial regression for a single regressor. Parameters ---------- endog : ndarray endogenous or response variable exog_i : ndarray exogenous, explanatory variable exog_others : ndarray other exogenous, explanatory variables, the effect of these variables will be removed by OLS regression varname : str name of the variable used in the title ax : Matplotlib AxesSubplot instance, optional If given, this subplot is used to plot in instead of a new figure being created. Return ------ fig : Matplotlib figure instance If `ax` is None, the created figure. Otherwise the figure to which `ax` is connected. See Also -------- plot_partregress : Plot partial regression for a set of regressors. """ fig, ax = utils.create_mpl_ax(ax) res1a = OLS(endog, exog_others).fit() res1b = OLS(exog_i, exog_others).fit() ax.plot(res1b.resid, res1a.resid, 'o') res1c = OLS(res1a.resid, res1b.resid).fit() ax.plot(res1b.resid, res1c.fittedvalues, '-', color='k') ax.set_title('Partial Regression plot %s' % varname, fontsize=title_fontsize) # + namestr) return fig
def fitpooled(self): '''fit the pooled model, which assumes there are no differences across groups ''' if self.het: if not hasattr(self, 'weights'): self.fitbygroups() weights = self.weights res = WLS(self.endog, self.exog, weights=weights).fit() else: res = OLS(self.endog, self.exog).fit() self.lspooled = res
def __init__(self): super(self.__class__, self).__init__() #initialize DGP y, x, exog = self.y, self.x, self.exog #use order = 2 in regression pmod = smoothers.PolySmoother(2, x) pmod.fit(y) #no return self.res_ps = pmod self.res2 = OLS(y, exog[:,:2+1]).fit()
def __init__(self): super(self.__class__, self).__init__() #initialize DGP y, x, exog = self.y, self.x, self.exog #use order = 3 in regression pmod = smoothers.PolySmoother(3, x) #pmod.fit(y) #no return pmod.smooth(y) #no return, use alias for fit self.res_ps = pmod self.res2 = OLS(y, exog[:,:3+1]).fit()
def fit(self): alpha0 = 0.1 #startvalue func = self.fit_conditional fitres = optimize.fmin(func, alpha0) # fit_conditional only returns ssr for now alpha = fitres[0] y = self.ar1filter(self.endog, alpha) x = self.ar1filter(self.exog, alpha) reso = OLS(y, x).fit() return fitres, reso
def setupClass(cls): from results.results_regression import LongleyGls data = longley.load() exog = add_constant(np.column_stack(\ (data.exog[:,1],data.exog[:,4]))) tmp_results = OLS(data.endog, exog).fit() rho = np.corrcoef(tmp_results.resid[1:], tmp_results.resid[:-1])[0][1] # by assumption order = toeplitz(np.arange(16)) sigma = rho**order GLS_results = GLS(data.endog, exog, sigma=sigma).fit() cls.res1 = GLS_results cls.res2 = LongleyGls()
def setupClass(cls): super(TestNxNxOne, cls).setupClass() cls.mod2 = OLS(cls.endog_n_, cls.exog_n_one) cls.mod2.df_model += 1 cls.res2 = cls.mod2.fit()
def fit(self, maxlag=None, method='cmle', ic=None, trend='c', transparams=True, start_params=None, solver=None, maxiter=35, full_output=1, disp=1, callback=None, **kwargs): """ Fit the unconditional maximum likelihood of an AR(p) process. Parameters ---------- maxlag : int If `ic` is None, then maxlag is the lag length used in fit. If `ic` is specified then maxlag is the highest lag order used to select the correct lag order. If maxlag is None, the default is round(12*(nobs/100.)**(1/4.)) method : str {'cmle', 'mle'}, optional cmle - Conditional maximum likelihood using OLS mle - Unconditional (exact) maximum likelihood. See `solver` and the Notes. ic : str {'aic','bic','hic','t-stat'} Criterion used for selecting the optimal lag length. aic - Akaike Information Criterion bic - Bayes Information Criterion t-stat - Based on last lag hq - Hannan-Quinn Information Criterion If any of the information criteria are selected, the lag length which results in the lowest value is selected. If t-stat, the model starts with maxlag and drops a lag until the highest lag has a t-stat that is significant at the 95 % level. trend : str {'c','nc'} Whether to include a constant or not. 'c' - include constant. 'nc' - no constant. The below can be specified if method is 'mle' transparams : bool, optional Whether or not to transform the parameters to ensure stationarity. Uses the transformation suggested in Jones (1980). start_params : array-like, optional A first guess on the parameters. Default is cmle estimates. solver : str or None, optional Solver to be used. The default is 'l_bfgs' (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'. The limited memory BFGS uses m=30 to approximate the Hessian, projected gradient tolerance of 1e-7 and factr = 1e3. These cannot currently be changed for l_bfgs. See notes for more information. maxiter : int, optional The maximum number of function evaluations. Default is 35. tol : float The convergence tolerance. Default is 1e-08. full_output : bool, optional If True, all output from solver will be available in the Results object's mle_retvals attribute. Output is dependent on the solver. See Notes for more information. disp : bool, optional If True, convergence information is output. callback : function, optional Called after each iteration as callback(xk) where xk is the current parameter vector. kwargs See Notes for keyword arguments that can be passed to fit. References ---------- Jones, R.H. 1980 "Maximum likelihood fitting of ARMA models to time series with missing observations." `Technometrics`. 22.3. 389-95. See also -------- scikits.statsmodels.model.LikelihoodModel.fit for more information on using the solvers. Notes ------ The below is the docstring from scikits.statsmodels.LikelihoodModel.fit """ self.transparams = transparams method = method.lower() if method not in ['cmle', 'yw', 'mle']: raise ValueError("Method %s not recognized" % method) self.method = method nobs = len(self.endog) # overwritten if method is 'cmle' if maxlag is None: maxlag = int(round(12 * (nobs / 100.)**(1 / 4.))) endog = self.endog exog = self.exog k_ar = maxlag # stays this if ic is None # select lag length if ic is not None: ic = ic.lower() if ic not in ['aic', 'bic', 'hqic', 't-stat']: raise ValueError("ic option %s not understood" % ic) # make Y and X with same nobs to compare ICs Y = endog[maxlag:] self.Y = Y # attach to get correct fit stats X = self._stackX(maxlag, trend) # sets k_trend self.X = X startlag = self.k_trend # k_trend set in _stackX if exog is not None: startlag += exog.shape[1] # add dim happens in super? startlag = max(1, startlag) # handle if startlag is 0 results = {} if ic != 't-stat': for lag in range(startlag, maxlag + 1): # have to reinstantiate the model to keep comparable models endog_tmp = endog[maxlag - lag:] fit = AR(endog_tmp).fit(maxlag=lag, method=method, full_output=full_output, trend=trend, maxiter=maxiter, disp=disp) results[lag] = eval('fit.' + ic) bestic, bestlag = min( (res, k) for k, res in results.iteritems()) else: # choose by last t-stat. stop = 1.6448536269514722 # for t-stat, norm.ppf(.95) for lag in range(maxlag, startlag - 1, -1): # have to reinstantiate the model to keep comparable models endog_tmp = endog[maxlag - lag:] fit = AR(endog_tmp).fit(maxlag=lag, method=method, full_output=full_output, trend=trend, maxiter=maxiter, disp=disp) if np.abs(fit.tvalues[-1]) >= stop: bestlag = lag break k_ar = bestlag # change to what was chosen by fit method self.k_ar = k_ar # redo estimation for best lag # make LHS Y = endog[k_ar:, :] # make lagged RHS X = self._stackX(k_ar, trend) # sets self.k_trend k_trend = self.k_trend self.Y = Y self.X = X if solver: solver = solver.lower() if method == "cmle": # do OLS arfit = OLS(Y, X).fit() params = arfit.params self.nobs = nobs - k_ar if method == "mle": self.nobs = nobs if not start_params: start_params = OLS(Y, X).fit().params start_params = self._invtransparams(start_params) loglike = lambda params: -self.loglike(params) if solver == None: # use limited memory bfgs bounds = [(None, ) * 2] * (k_ar + k_trend) mlefit = optimize.fmin_l_bfgs_b(loglike, start_params, approx_grad=True, m=30, pgtol=1e-7, factr=1e3, bounds=bounds, iprint=1) self.mlefit = mlefit params = mlefit[0] else: mlefit = super(AR, self).fit(start_params=start_params, method=solver, maxiter=maxiter, full_output=full_output, disp=disp, callback=callback, **kwargs) self.mlefit = mlefit params = mlefit.params if self.transparams: params = self._transparams(params) self.transparams = False # turn off now for other results # don't use yw, because we can't estimate the constant # elif method == "yw": # params, omega = yule_walker(endog, order=maxlag, # method="mle", demean=False) # how to handle inference after Yule-Walker? # self.params = params #TODO: don't attach here # self.omega = omega pinv_exog = np.linalg.pinv(X) normalized_cov_params = np.dot(pinv_exog, pinv_exog.T) arfit = ARResults(self, params, normalized_cov_params) self._results = arfit return arfit
#using GMM and IV2SLS classes #---------------------------- mod = IVGMM(endog, exog, instrument, nmoms=instrument.shape[1]) res = mod.fit() modgmmols = IVGMM(endog, exog, exog, nmoms=exog.shape[1]) resgmmols = modgmmols.fit() #the next is the same as IV2SLS, (Z'Z)^{-1} as weighting matrix modgmmiv = IVGMM(endog, exog, instrument, nmoms=instrument.shape[1]) #same as mod resgmmiv = modgmmiv.fitgmm(np.ones(exog.shape[1], float), weights=np.linalg.inv(np.dot(instrument.T, instrument))) modls = IV2SLS(endog, exog, instrument) resls = modls.fit() modols = OLS(endog, exog) resols = modols.fit() print '\nIV case' print 'params' print 'IV2SLS', resls.params print 'GMMIV ', resgmmiv # .params print 'GMM ', res.params print 'diff ', res.params - resls.params print 'OLS ', resols.params print 'GMMOLS', resgmmols.params print '\nbse' print 'IV2SLS', resls.bse print 'GMM ', mod.bse #bse currently only attached to model not results print 'diff ', mod.bse - resls.bse
def fitjoint(self): '''fit a joint fixed effects model to all observations The regression results are attached as `lsjoint`. The contrasts for overall and pairwise tests for equality of coefficients are attached as a dictionary `contrasts`. This also includes the contrasts for the test that the coefficients of a level are zero. :: >>> res.contrasts.keys() [(0, 1), 1, 'all', 3, (1, 2), 2, (1, 3), (2, 3), (0, 3), (0, 2)] The keys are based on the original names or labels of the groups. TODO: keys can be numpy scalars and then the keys cannot be sorted ''' if not hasattr(self, 'weights'): self.fitbygroups() groupdummy = (self.groupsint[:, None] == self.uniqueint).astype(int) #order of dummy variables by variable - not used #dummyexog = self.exog[:,:,None]*groupdummy[:,None,1:] #order of dummy variables by grous - used dummyexog = self.exog[:, None, :] * groupdummy[:, 1:, None] exog = np.c_[self.exog, dummyexog.reshape(self.exog.shape[0], -1)] #self.nobs ?? #Notes: I changed to drop first group from dummy #instead I want one full set dummies if self.het: weights = self.weights res = WLS(self.endog, exog, weights=weights).fit() else: res = OLS(self.endog, exog).fit() self.lsjoint = res contrasts = {} nvars = self.exog.shape[1] nparams = exog.shape[1] ndummies = nparams - nvars contrasts['all'] = np.c_[np.zeros((ndummies, nvars)), np.eye(ndummies)] for groupind, group in enumerate( self.unique[1:]): #need enumerate if groups != groupsint groupind = groupind + 1 contr = np.zeros((nvars, nparams)) contr[:, nvars * groupind:nvars * (groupind + 1)] = np.eye(nvars) contrasts[group] = contr #save also for pairs, see next contrasts[(self.unique[0], group)] = contr #Note: I'm keeping some duplication for testing pairs = np.triu_indices(len(self.unique), 1) for ind1, ind2 in zip( *pairs): #replace with group1, group2 in sorted(keys) if ind1 == 0: continue # need comparison with benchmark/normalization group separate g1 = self.unique[ind1] g2 = self.unique[ind2] group = (g1, g2) contr = np.zeros((nvars, nparams)) contr[:, nvars * ind1:nvars * (ind1 + 1)] = np.eye(nvars) contr[:, nvars * ind2:nvars * (ind2 + 1)] = -np.eye(nvars) contrasts[group] = contr self.contrasts = contrasts
def adfuller(x, maxlag=None, regression="c", autolag='AIC', store=False, regresults=False): '''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 : str {'c','ct','ctt','nc'} Constant and trend order to include in regression * 'c' : constant only * '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' or 'BIC', then the number of lags is chosen to minimize the corresponding information criterium * 't-stat' based choice of maxlag. Starts with maxlag and drops a lag until the t-statistic on the last lag length is significant at the 95 % level. store : bool If True, then a result instance is returned additionally to the adf statistic regresults : bool If True, the full regression results are returned. Returns ------- adf : float Test statistic pvalue : float MacKinnon's approximate p-value based on MacKinnon (1994) 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. regresults : RegressionResults instance The resstore : (optional) instance of ResultStore an instance of 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 accept or reject the null. Examples -------- see example script References ---------- Greene Hamilton P-Values (regression surface approximation) MacKinnon, J.G. 1994. "Approximate asymptotic distribution functions for unit-root and cointegration tests. `Journal of Business and Economic Statistics` 12, 167-76. Critical values 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 ''' trenddict = {None: 'nc', 0: 'c', 1: 'ct', 2: 'ctt'} if regression is None or isinstance(regression, int): regression = trenddict[regression] regression = regression.lower() if regression not in ['c', 'nc', 'ct', 'ctt']: raise ValueError("regression option %s not understood") % regression x = np.asarray(x) nobs = x.shape[0] if maxlag is None: #from Greene referencing Schwert 1989 maxlag = int(round(12. * np.power(nobs / 100., 1 / 4.))) xdiff = np.diff(x) xdall = lagmat(xdiff[:, None], maxlag, trim='both', original='in') nobs = xdall.shape[0] xdall[:, 0] = x[-nobs - 1:-1] # replace 0 xdiff with level of x xdshort = xdiff[-nobs:] if store: resstore = ResultsStore() if autolag: if regression != 'nc': fullRHS = add_trend(xdall, regression, prepend=True) else: fullRHS = xdall startlag = fullRHS.shape[1] - xdall.shape[1] + 1 # 1 for level #search for lag length with highest information criteria #Note: use the same number of observations to have comparable IC icbest, bestlag = _autolag(OLS, xdshort, fullRHS, startlag, maxlag, autolag) #rerun ols with best autolag xdall = lagmat(xdiff[:, None], bestlag, trim='both', original='in') nobs = xdall.shape[0] xdall[:, 0] = x[-nobs - 1:-1] # replace 0 xdiff with level of x xdshort = xdiff[-nobs:] usedlag = bestlag else: usedlag = maxlag icbest = None if regression != 'nc': resols = OLS(xdshort, add_trend(xdall[:, :usedlag + 1], regression)).fit() else: resols = OLS(xdshort, xdall[:, :usedlag + 1]).fit() adfstat = resols.tvalues[0] # adfstat = (resols.params[0]-1.0)/resols.bse[0] # the "asymptotically correct" z statistic is obtained as # nobs/(1-np.sum(resols.params[1:-(trendorder+1)])) (resols.params[0] - 1) # I think this is the statistic that is used for series that are integrated # for orders higher than I(1), ie., not ADF but cointegration tests. # Get approx p-value and critical values pvalue = mackinnonp(adfstat, regression=regression, N=1) critvalues = mackinnoncrit(N=1, regression=regression, nobs=nobs) critvalues = { "1%": critvalues[0], "5%": critvalues[1], "10%": critvalues[2] } if store: resstore.resols = resols resstore.usedlag = usedlag resstore.adfstat = adfstat resstore.critvalues = critvalues resstore.nobs = nobs resstore.H0 = "The coefficient on the lagged level equals 1" resstore.HA = "The coefficient on the lagged level < 1" resstore.icbest = icbest return adfstat, pvalue, critvalues, resstore else: if not autolag: return adfstat, pvalue, usedlag, nobs, critvalues else: return adfstat, pvalue, usedlag, nobs, critvalues, icbest
nobs = 100 lb, ub = -1, 2 x = np.linspace(lb, ub, nobs) x = np.sin(x) exog = x[:, None]**np.arange(order + 1) y_true = exog.sum(1) y = y_true + sigma_noise * np.random.randn(nobs) #xind = np.argsort(x) pmod = smoothers.PolySmoother(2, x) pmod.fit(y) #no return y_pred = pmod.predict(x) error = y - y_pred mse = (error * error).mean() print mse res_ols = OLS(y, exog[:, :3]).fit() print np.squeeze(pmod.coef) - res_ols.params weights = np.ones(nobs) weights[:nobs // 3] = 0.1 weights[-nobs // 5:] = 2 pmodw = smoothers.PolySmoother(2, x) pmodw.fit(y, weights=weights) #no return y_predw = pmodw.predict(x) error = y - y_predw mse = (error * error).mean() print mse res_wls = WLS(y, exog[:, :3], weights=weights).fit() print np.squeeze(pmodw.coef) - res_wls.params
def setupClass(cls): data = longley.load() data.exog = add_constant(data.exog) res1 = OLS(data.endog, data.exog).fit() R2 = [[0, 1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 1, -1, 0]] cls.Ftest1 = res1.f_test(R2)
def fit_conditional(self, alpha): y = self.ar1filter(self.endog, alpha) x = self.ar1filter(self.exog, alpha) res = OLS(y, x).fit() return res.ssr #res.llf
def setupClass(cls): data = longley.load() data.exog = add_constant(data.exog) res1 = OLS(data.endog, data.exog).fit() R2 = [[0,1,-1,0,0,0,0],[0, 0, 0, 0, 1, -1, 0]] cls.Ftest1 = res1.f_test(R2)
z = y_true #alias check d = x y = y_true + sigma_noise * np.random.randn(nobs) example = 1 if example == 1: m = AdditiveModel(d) m.fit(y) y_pred = m.results.predict(d) for ss in m.smoothers: print ss.params res_ols = OLS(y, exog_reduced).fit() print res_ols.params #assert_almost_equal(y_pred, res_ols.fittedvalues, 3) if example > 0: import matplotlib.pyplot as plt plt.figure() plt.plot(exog) y_pred = m.results.mu # + m.results.alpha #m.results.predict(d) plt.figure() plt.subplot(2, 2, 1) plt.plot(y, '.', alpha=0.25) plt.plot(y_true, 'k-', label='true')
def grangercausalitytests(x, maxlag, addconst=True, verbose=True): '''four tests for granger causality of 2 timeseries all four tests give similar results `params_ftest` and `ssr_ftest` are equivalent based of F test which is identical to lmtest:grangertest in R Parameters ---------- x : array, 2d, (nobs,2) data for test whether the time series in the second column Granger causes the time series in the first column maxlag : integer the Granger causality test results are calculated for all lags up to maxlag verbose : bool print results if true Returns ------- results : dictionary 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 teststatistic, 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, Granger causes the time series in the first column, x1. This means that past values of x2 have a statistically significant effect on the current value of x1, taking also past values of x1 into account, as regressors. We reject the null hypothesis of x2 Granger causing x1 if the pvalues are below a desired size of the test. 'params_ftest', 'ssr_ftest' are based on F test 'ssr_chi2test', 'lrtest' are based on chi-square test ''' from scipy import stats # lazy import resli = {} for mlg in range(1, maxlag + 1): result = {} if verbose: print '\nGranger Causality' print 'number of lags (no zero)', mlg mxlg = mlg #+ 1 # Note number of lags starting at zero in lagmat # create lagmat of both time series dta = lagmat2ds(x, mxlg, trim='both', dropex=1) #add constant if addconst: dtaown = add_constant(dta[:, 1:mxlg + 1]) dtajoint = add_constant(dta[:, 1:]) else: raise ValueError('Not Implemented') dtaown = dta[:, 1:mxlg] dtajoint = dta[:, 1:] #run ols on both models without and with lags of second variable res2down = OLS(dta[:, 0], dtaown).fit() res2djoint = OLS(dta[:, 0], dtajoint).fit() #print results #for ssr based tests see: http://support.sas.com/rnd/app/examples/ets/granger/index.htm #the other tests are made-up # Granger Causality test using ssr (F statistic) fgc1 = (res2down.ssr - res2djoint.ssr) / res2djoint.ssr / (mxlg) * res2djoint.df_resid if verbose: print 'ssr based F test: F=%-8.4f, p=%-8.4f, df_denom=%d, df_num=%d' % \ (fgc1, stats.f.sf(fgc1, mxlg, res2djoint.df_resid), res2djoint.df_resid, mxlg) result['ssr_ftest'] = (fgc1, stats.f.sf(fgc1, mxlg, res2djoint.df_resid), res2djoint.df_resid, mxlg) # Granger Causality test using ssr (ch2 statistic) fgc2 = res2down.nobs * (res2down.ssr - res2djoint.ssr) / res2djoint.ssr if verbose: print 'ssr based chi2 test: chi2=%-8.4f, p=%-8.4f, df=%d' % \ (fgc2, stats.chi2.sf(fgc2, mxlg), mxlg) result['ssr_chi2test'] = (fgc2, stats.chi2.sf(fgc2, mxlg), mxlg) #likelihood ratio test pvalue: lr = -2 * (res2down.llf - res2djoint.llf) if verbose: print 'likelihood ratio test: chi2=%-8.4f, p=%-8.4f, df=%d' % \ (lr, stats.chi2.sf(lr, mxlg), mxlg) result['lrtest'] = (lr, stats.chi2.sf(lr, mxlg), mxlg) # F test that all lag coefficients of exog are zero rconstr = np.column_stack((np.zeros((mxlg-1,mxlg-1)), np.eye(mxlg-1, mxlg-1),\ np.zeros((mxlg-1, 1)))) rconstr = np.column_stack((np.zeros((mxlg,mxlg)), np.eye(mxlg, mxlg),\ np.zeros((mxlg, 1)))) ftres = res2djoint.f_test(rconstr) if verbose: print 'parameter F test: F=%-8.4f, p=%-8.4f, df_denom=%d, df_num=%d' % \ (ftres.fvalue, ftres.pvalue, ftres.df_denom, ftres.df_num) result['params_ftest'] = (np.squeeze(ftres.fvalue)[()], np.squeeze(ftres.pvalue)[()], ftres.df_denom, ftres.df_num) resli[mxlg] = (result, [res2down, res2djoint, rconstr]) return resli
def setupClass(cls): data = longley.load() data.exog = add_constant(data.exog) cls.res1 = OLS(data.endog, data.exog).fit() cls.res2 = WLS(data.endog, data.exog).fit()
def setupClass(cls): data = longley.load() data.exog = add_constant(data.exog) cls.res1 = OLS(data.endog, data.exog).fit() R = np.identity(7) cls.Ttest = cls.res1.t_test(R)
def grangercausalitytests(x, maxlag, addconst=True, verbose=True): '''four tests for granger causality of 2 timeseries all four tests give similar results `params_ftest` and `ssr_ftest` are equivalent based of F test which is identical to lmtest:grangertest in R Parameters ---------- x : array, 2d, (nobs,2) data for test whether the time series in the second column Granger causes the time series in the first column maxlag : integer the Granger causality test results are calculated for all lags up to maxlag verbose : bool print results if true Returns ------- results : dictionary 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 teststatistic, 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 'params_ftest', 'ssr_ftest' are based on F test 'ssr_chi2test', 'lrtest' are based on chi-square test ''' from scipy import stats # lazy import resli = {} for mlg in range(1, maxlag+1): result = {} if verbose: print '\nGranger Causality' print 'number of lags (no zero)', mlg mxlg = mlg #+ 1 # Note number of lags starting at zero in lagmat # create lagmat of both time series dta = lagmat2ds(x, mxlg, trim='both', dropex=1) #add constant if addconst: dtaown = add_constant(dta[:,1:mxlg+1]) dtajoint = add_constant(dta[:,1:]) else: raise ValueError('Not Implemented') dtaown = dta[:,1:mxlg] dtajoint = dta[:,1:] #run ols on both models without and with lags of second variable res2down = OLS(dta[:,0], dtaown).fit() res2djoint = OLS(dta[:,0], dtajoint).fit() #print results #for ssr based tests see: http://support.sas.com/rnd/app/examples/ets/granger/index.htm #the other tests are made-up # Granger Causality test using ssr (F statistic) fgc1 = (res2down.ssr-res2djoint.ssr)/res2djoint.ssr/(mxlg)*res2djoint.df_resid if verbose: print 'ssr based F test: F=%-8.4f, p=%-8.4f, df_denom=%d, df_num=%d' % \ (fgc1, stats.f.sf(fgc1, mxlg, res2djoint.df_resid), res2djoint.df_resid, mxlg) result['ssr_ftest'] = (fgc1, stats.f.sf(fgc1, mxlg, res2djoint.df_resid), res2djoint.df_resid, mxlg) # Granger Causality test using ssr (ch2 statistic) fgc2 = res2down.nobs*(res2down.ssr-res2djoint.ssr)/res2djoint.ssr if verbose: print 'ssr based chi2 test: chi2=%-8.4f, p=%-8.4f, df=%d' % \ (fgc2, stats.chi2.sf(fgc2, mxlg), mxlg) result['ssr_chi2test'] = (fgc2, stats.chi2.sf(fgc2, mxlg), mxlg) #likelihood ratio test pvalue: lr = -2*(res2down.llf-res2djoint.llf) if verbose: print 'likelihood ratio test: chi2=%-8.4f, p=%-8.4f, df=%d' % \ (lr, stats.chi2.sf(lr, mxlg), mxlg) result['lrtest'] = (lr, stats.chi2.sf(lr, mxlg), mxlg) # F test that all lag coefficients of exog are zero rconstr = np.column_stack((np.zeros((mxlg-1,mxlg-1)), np.eye(mxlg-1, mxlg-1),\ np.zeros((mxlg-1, 1)))) rconstr = np.column_stack((np.zeros((mxlg,mxlg)), np.eye(mxlg, mxlg),\ np.zeros((mxlg, 1)))) ftres = res2djoint.f_test(rconstr) if verbose: print 'parameter F test: F=%-8.4f, p=%-8.4f, df_denom=%d, df_num=%d' % \ (ftres.fvalue, ftres.pvalue, ftres.df_denom, ftres.df_num) result['params_ftest'] = (np.squeeze(ftres.fvalue)[()], np.squeeze(ftres.pvalue)[()], ftres.df_denom, ftres.df_num) resli[mxlg] = (result, [res2down, res2djoint, rconstr]) return resli