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 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):
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 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 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
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)
