def _fit_start_params_hr(self, order):
"""
Get starting parameters for fit.
Parameters
----------
order : iterable
(p,q,k) - AR lags, MA lags, and number of exogenous variables
including the constant.
Returns
-------
start_params : array
A first guess at the starting parameters.
Notes
-----
If necessary, fits an AR process with the laglength selected according
to best BIC. Obtain the residuals. Then fit an ARMA(p,q) model via
OLS using these residuals for a first approximation. Uses a separate
OLS regression to find the coefficients of exogenous variables.
References
----------
Hannan, E.J. and Rissanen, J. 1982. "Recursive estimation of mixed
autoregressive-moving average order." `Biometrika`. 69.1.
"""
p,q,k = order
start_params = zeros((p+q+k))
endog = self.endog.copy() # copy because overwritten
exog = self.exog
if k != 0:
ols_params = GLS(endog, exog).fit().params
start_params[:k] = ols_params
endog -= np.dot(exog, ols_params).squeeze()
if q != 0:
if p != 0:
armod = AR(endog).fit(ic='bic', trend='nc')
arcoefs_tmp = armod.params
p_tmp = armod.k_ar
resid = endog[p_tmp:] - np.dot(lagmat(endog, p_tmp,
trim='both'), arcoefs_tmp)
if p < p_tmp + q:
endog_start = p_tmp + q - p
resid_start = 0
else:
endog_start = 0
resid_start = p - p_tmp - q
lag_endog = lagmat(endog, p, 'both')[endog_start:]
lag_resid = lagmat(resid, q, 'both')[resid_start:]
# stack ar lags and resids
X = np.column_stack((lag_endog, lag_resid))
coefs = GLS(endog[max(p_tmp+q,p):], X).fit().params
start_params[k:k+p+q] = coefs
else:
start_params[k+p:k+p+q] = yule_walker(endog, order=q)[0]
if q==0 and p != 0:
arcoefs = yule_walker(endog, order=p)[0]
start_params[k:k+p] = arcoefs
return start_params
def _fit_start_params_hr(self, order):
"""
Get starting parameters for fit.
Parameters
----------
order : iterable
(p,q,k) - AR lags, MA lags, and number of exogenous variables
including the constant.
Returns
-------
start_params : array
A first guess at the starting parameters.
Notes
-----
If necessary, fits an AR process with the laglength selected according
to best BIC. Obtain the residuals. Then fit an ARMA(p,q) model via
OLS using these residuals for a first approximation. Uses a separate
OLS regression to find the coefficients of exogenous variables.
References
----------
Hannan, E.J. and Rissanen, J. 1982. "Recursive estimation of mixed
autoregressive-moving average order." `Biometrika`. 69.1.
"""
p, q, k = order
start_params = zeros((p + q + k))
endog = self.endog.copy() # copy because overwritten
exog = self.exog
if k != 0:
ols_params = GLS(endog, exog).fit().params
start_params[:k] = ols_params
endog -= np.dot(exog, ols_params).squeeze()
if q != 0:
if p != 0:
armod = AR(endog).fit(ic='bic', trend='nc')
arcoefs_tmp = armod.params
p_tmp = armod.k_ar
resid = endog[p_tmp:] - np.dot(
lagmat(endog, p_tmp, trim='both'), arcoefs_tmp)
X = np.column_stack(
(lagmat(endog, p, 'both')[p_tmp + (q - p):],
lagmat(resid, q, 'both'))) # stack ar lags and resids
coefs = GLS(endog[p_tmp + q:], X).fit().params
start_params[k:k + p + q] = coefs
else:
start_params[k + p:k + p + q] = yule_walker(endog, order=q)[0]
if q == 0 and p != 0:
arcoefs = yule_walker(endog, order=p)[0]
start_params[k:k + p] = arcoefs
return start_params
def setupClass(cls):
from scikits.statsmodels.datasets.sunspots import load
data = load()
cls.rho, cls.sigma = yule_walker(data.endog, order=4,
method="mle")
cls.R_params = [1.2831003105694765, -0.45240924374091945,
-0.20770298557575195, 0.047943648089542337]
def pacf_yw(x, nlags=40, method='unbiased'):
'''Partial autocorrelation estimated with non-recursive yule_walker
Parameters
----------
x : 1d array
observations of time series for which pacf is calculated
maxlag : int
largest lag for which pacf is returned
method : 'unbiased' (default) or 'mle'
method for the autocovariance calculations in yule walker
Returns
-------
pacf : 1d array
partial autocorrelations, maxlag+1 elements
Notes
-----
This solves yule_walker for each desired lag and contains
currently duplicate calculations.
'''
xm = x - x.mean()
pacf = [1.]
for k in range(1, nlags + 1):
pacf.append(yule_walker(x, k, method=method)[0][-1])
return np.array(pacf)
def pacf_yw(x, nlags=40, method='unbiased'):
'''Partial autocorrelation estimated with non-recursive yule_walker
Parameters
----------
x : 1d array
observations of time series for which pacf is calculated
maxlag : int
largest lag for which pacf is returned
method : 'unbiased' (default) or 'mle'
method for the autocovariance calculations in yule walker
Returns
-------
pacf : 1d array
partial autocorrelations, maxlag+1 elements
Notes
-----
This solves yule_walker for each desired lag and contains
currently duplicate calculations.
'''
xm = x - x.mean()
pacf = [1.]
for k in range(1, nlags+1):
pacf.append(yule_walker(x, k, method=method)[0][-1])
return np.array(pacf)
def setupClass(cls):
from scikits.statsmodels.datasets.sunspots import load
data = load()
cls.rho, cls.sigma = yule_walker(data.endog, order=4,
method="mle")
cls.R_params = [1.2831003105694765, -0.45240924374091945,
-0.20770298557575195, 0.047943648089542337]
examples_all = range(10) + ['test_copy']
examples = examples_all #[5]
if 0 in examples:
print '\n Example 0'
X = np.arange(1,8)
X = sm.add_constant(X)
Y = np.array((1, 3, 4, 5, 8, 10, 9))
rho = 2
model = GLSAR(Y, X, 2)
for i in range(6):
results = model.fit()
print "AR coefficients:", model.rho
rho, sigma = yule_walker(results.resid, order = model.order)
model = GLSAR(Y, X, rho)
par0 = results.params
print par0
model0if = GLSAR(Y, X, 2)
res = model0if.iterative_fit(6)
print 'iterativefit beta', res.params
results.tvalues # is this correct? it does equal params/bse
# but isn't the same as the AR example (which was wrong in the first place..)
print results.t_test([0,1]) # are sd and t correct? vs
print results.f_test(np.eye(2))
rhotrue = [0.5, 0.2]
rhotrue = np.asarray(rhotrue)
examples_all = range(10) + ['test_copy']
examples = examples_all #[5]
if 0 in examples:
print '\n Example 0'
X = np.arange(1, 8)
X = sm.add_constant(X)
Y = np.array((1, 3, 4, 5, 8, 10, 9))
rho = 2
model = GLSAR(Y, X, 2)
for i in range(6):
results = model.fit()
print "AR coefficients:", model.rho
rho, sigma = yule_walker(results.resid, order=model.order)
model = GLSAR(Y, X, rho)
par0 = results.params
print par0
model0if = GLSAR(Y, X, 2)
res = model0if.iterative_fit(6)
print 'iterativefit beta', res.params
results.tvalues # is this correct? it does equal params/bse
# but isn't the same as the AR example (which was wrong in the first place..)
print results.t_test([0, 1]) # are sd and t correct? vs
print results.f_test(np.eye(2))
rhotrue = [0.5, 0.2]
rhotrue = np.asarray(rhotrue)
nlags = np.size(rhotrue)