def fit(self, maxlag=None, method='cmle', ic=None, trend='c',
transparams=True, start_params=None, solver='lbfgs', 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
hqic - 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 if method is 'mle'. The default is 'lbfgs'
(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'.
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
--------
statsmodels.base.model.LikelihoodModel.fit
"""
method = method.lower()
if method not in ['cmle', 'yw', 'mle']:
raise ValueError("Method %s not recognized" % method)
self.method = method
self.trend = trend
self.transparams = transparams
nobs = len(self.endog) # overwritten if method is 'cmle'
endog = self.endog
if maxlag is None:
maxlag = int(round(12*(nobs/100.)**(1/4.)))
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)
k_ar = self.select_order(k_ar, ic, trend, method)
self.k_ar = k_ar # change to what was chosen by ic
# 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.exog_names = util.make_lag_names(self.endog_names, k_ar, k_trend)
self.Y = Y
self.X = X
if method == "cmle": # do OLS
arfit = OLS(Y, X).fit()
params = arfit.params
self.nobs = nobs - k_ar
self.sigma2 = arfit.ssr/arfit.nobs # needed for predict fcasterr
elif method == "mle":
solver = solver.lower()
self.nobs = nobs
if start_params is None:
start_params = OLS(Y, X).fit().params
else:
if len(start_params) != k_trend + k_ar:
raise ValueError("Length of start params is %d. There"
" are %d parameters." %
(len(start_params), k_trend + k_ar))
start_params = self._invtransparams(start_params)
if solver == 'lbfgs':
kwargs.setdefault('pgtol', 1e-8)
kwargs.setdefault('factr', 1e2)
kwargs.setdefault('m', 12)
kwargs.setdefault('approx_grad', True)
mlefit = super(AR, self).fit(start_params=start_params,
method=solver, maxiter=maxiter,
full_output=full_output, disp=disp,
callback=callback, **kwargs)
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)
if method == 'mle' and full_output:
arfit.mle_retvals = mlefit.mle_retvals
arfit.mle_settings = mlefit.mle_settings
return ARResultsWrapper(arfit)
def fit(self, maxlag=None, method='cmle', ic=None, trend='c',
transparams=True, start_params=None, solver='lbfgs', 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
hqic - 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 if method is 'mle'. The default is 'lbfgs'
(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'.
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
--------
statsmodels.base.model.LikelihoodModel.fit
"""
method = method.lower()
if method not in ['cmle', 'yw', 'mle']:
raise ValueError("Method %s not recognized" % method)
self.method = method
self.trend = trend
self.transparams = transparams
nobs = len(self.endog) # overwritten if method is 'cmle'
endog = self.endog
if maxlag is None:
maxlag = int(round(12*(nobs/100.)**(1/4.)))
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)
k_ar = self.select_order(k_ar, ic, trend, method)
self.k_ar = k_ar # change to what was chosen by ic
# 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.exog_names = util.make_lag_names(self.endog_names, k_ar, k_trend)
self.Y = Y
self.X = X
if method == "cmle": # do OLS
arfit = OLS(Y, X).fit()
params = arfit.params
self.nobs = nobs - k_ar
self.sigma2 = arfit.ssr/arfit.nobs # needed for predict fcasterr
elif method == "mle":
solver = solver.lower()
self.nobs = nobs
if start_params is None:
start_params = OLS(Y, X).fit().params
else:
if len(start_params) != k_trend + k_ar:
raise ValueError("Length of start params is %d. There"
" are %d parameters." %
(len(start_params), k_trend + k_ar))
start_params = self._invtransparams(start_params)
if solver == 'lbfgs':
kwargs.setdefault('pgtol', 1e-8)
kwargs.setdefault('factr', 1e2)
kwargs.setdefault('m', 12)
kwargs.setdefault('approx_grad', True)
mlefit = super(AR, self).fit(start_params=start_params,
method=solver, maxiter=maxiter,
full_output=full_output, disp=disp,
callback=callback, **kwargs)
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)
if method == 'mle' and full_output:
arfit.mle_retvals = mlefit.mle_retvals
arfit.mle_settings = mlefit.mle_settings
return ARResultsWrapper(arfit)
