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 non causality of 2 timeseries
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, 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, 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
----------
http://en.wikipedia.org/wiki/Granger_causality
Greene: Econometric Analysis
'''
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 non causality of 2 timeseries
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, 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, 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
----------
http://en.wikipedia.org/wiki/Granger_causality
Greene: Econometric Analysis
"""
from scipy import stats
x = np.asarray(x)
if x.shape[0] <= 3 * maxlag + int(addconst):
raise ValueError(
"Insufficient observations. Maximum allowable "
"lag is {0}".format(int((x.shape[0] - int(addconst)) / 3) - 1))
resli = {}
for mlg in range(1, maxlag + 1):
result = {}
if verbose:
print '\nGranger Causality'
print 'number of lags (no zero)', mlg
mxlg = mlg
# 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)], prepend=False)
dtajoint = add_constant(dta[:, 1:], prepend=False)
else:
raise NotImplementedError('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, 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
