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