def _make_arma_names(data, k_trend, order):
k_ar, k_ma = order
exog = data.exog
if exog is not None:
exog_names = data._get_names(data._orig_exog) or []
else:
exog_names = []
ar_lag_names = util.make_lag_names(data.ynames, k_ar, 0)
ar_lag_names = [''.join(('ar.', i)) for i in ar_lag_names]
ma_lag_names = util.make_lag_names(data.ynames, k_ma, 0)
ma_lag_names = [''.join(('ma.', i)) for i in ma_lag_names]
trend_name = util.make_lag_names('', 0, k_trend)
exog_names = trend_name + exog_names + ar_lag_names + ma_lag_names
return exog_names
def _make_arma_names(data, k_trend, order):
k_ar, k_ma = order
exog = data.exog
if exog is not None:
exog_names = data._get_names(data._orig_exog) or []
else:
exog_names = []
ar_lag_names = util.make_lag_names(data.ynames, k_ar, 0)
ar_lag_names = ["".join(("ar.", i)) for i in ar_lag_names]
ma_lag_names = util.make_lag_names(data.ynames, k_ma, 0)
ma_lag_names = ["".join(("ma.", i)) for i in ma_lag_names]
trend_name = util.make_lag_names("", 0, k_trend)
exog_names = trend_name + exog_names + ar_lag_names + ma_lag_names
return exog_names
def __init__(self, endog, endog_lagged, params, sigma_u, lag_order,
model=None, trend='c', names=None, dates=None):
self.model = model
self.y = self.endog = endog #keep alias for now
self.ys_lagged = self.endog_lagged = endog_lagged #keep alias for now
self.dates = dates
self.n_totobs, neqs = self.y.shape
self.nobs = self.n_totobs - lag_order
k_trend = util.get_trendorder(trend)
if k_trend > 0: # make this the polynomial trend order
trendorder = k_trend - 1
else:
trendorder = None
self.k_trend = k_trend
self.trendorder = trendorder
self.exog_names = util.make_lag_names(names, lag_order, k_trend)
self.params = params
# Initialize VARProcess parent class
# construct coefficient matrices
# Each matrix needs to be transposed
reshaped = self.params[self.k_trend:]
reshaped = reshaped.reshape((lag_order, neqs, neqs))
# Need to transpose each coefficient matrix
intercept = self.params[0]
coefs = reshaped.swapaxes(1, 2).copy()
super(VARResults, self).__init__(coefs, intercept, sigma_u, names=names)
def __init__(self,
endog,
endog_lagged,
params,
sigma_u,
lag_order,
A=None,
B=None,
A_mask=None,
B_mask=None,
model=None,
trend='c',
names=None,
dates=None):
self.model = model
self.y = self.endog = endog #keep alias for now
self.ys_lagged = self.endog_lagged = endog_lagged #keep alias for now
self.dates = dates
self.n_totobs, self.neqs = self.y.shape
self.nobs = self.n_totobs - lag_order
k_trend = util.get_trendorder(trend)
if k_trend > 0: # make this the polynomial trend order
trendorder = k_trend - 1
else:
trendorder = None
self.k_trend = k_trend
self.k_exog = k_trend # now (0.9) required by VARProcess
self.trendorder = trendorder
self.exog_names = util.make_lag_names(names, lag_order, k_trend)
self.params = params
self.sigma_u = sigma_u
# Each matrix needs to be transposed
reshaped = self.params[self.k_trend:]
reshaped = reshaped.reshape((lag_order, self.neqs, self.neqs))
# Need to transpose each coefficient matrix
intercept = self.params[0]
coefs = reshaped.swapaxes(1, 2).copy()
#SVAR components
#TODO: if you define these here, you don't also have to define
#them in SVAR process, but I left them for now -ss
self.A = A
self.B = B
self.A_mask = A_mask
self.B_mask = B_mask
super(SVARResults, self).__init__(coefs,
intercept,
sigma_u,
A,
B,
names=names)
def fit(self, maxlags=None, method='ols', ic=None, trend='c',
verbose=False):
"""
Fit the VAR model
Parameters
----------
maxlags : int
Maximum number of lags to check for order selection, defaults to
12 * (nobs/100.)**(1./4), see select_order function
method : {'ols'}
Estimation method to use
ic : {'aic', 'fpe', 'hqic', 'bic', None}
Information criterion to use for VAR order selection.
aic : Akaike
fpe : Final prediction error
hqic : Hannan-Quinn
bic : Bayesian a.k.a. Schwarz
verbose : bool, default False
Print order selection output to the screen
trend : str {"c", "ct", "ctt", "nc"}
"c" - add constant
"ct" - constant and trend
"ctt" - constant, linear and quadratic trend
"nc" - co constant, no trend
Note that these are prepended to the columns of the dataset.
Notes
-----
Lutkepohl pp. 146-153
Returns
-------
est : VARResults
"""
lags = maxlags
if trend not in ['c', 'ct', 'ctt', 'nc']:
raise ValueError("trend '{}' not supported for VAR".format(trend))
if ic is not None:
selections = self.select_order(maxlags=maxlags, verbose=verbose)
if ic not in selections:
raise Exception("%s not recognized, must be among %s"
% (ic, sorted(selections)))
lags = selections[ic]
if verbose:
print('Using %d based on %s criterion' % (lags, ic))
else:
if lags is None:
lags = 1
k_trend = util.get_trendorder(trend)
self.exog_names = util.make_lag_names(self.endog_names, lags, k_trend)
self.nobs = len(self.endog) - lags
return self._estimate_var(lags, trend=trend)
def fit(self, maxlags=None, method='ols', ic=None, trend='c',
verbose=False):
"""
Fit the VAR model
Parameters
----------
maxlags : int
Maximum number of lags to check for order selection, defaults to
12 * (nobs/100.)**(1./4), see select_order function
method : {'ols'}
Estimation method to use
ic : {'aic', 'fpe', 'hqic', 'bic', None}
Information criterion to use for VAR order selection.
aic : Akaike
fpe : Final prediction error
hqic : Hannan-Quinn
bic : Bayesian a.k.a. Schwarz
verbose : bool, default False
Print order selection output to the screen
trend, str {"c", "ct", "ctt", "nc"}
"c" - add constant
"ct" - constant and trend
"ctt" - constant, linear and quadratic trend
"nc" - co constant, no trend
Note that these are prepended to the columns of the dataset.
Notes
-----
Lutkepohl pp. 146-153
Returns
-------
est : VARResults
"""
lags = maxlags
if trend not in ['c', 'ct', 'ctt', 'nc']:
raise ValueError("trend '{}' not supported for VAR".format(trend))
if ic is not None:
selections = self.select_order(maxlags=maxlags, verbose=verbose)
if ic not in selections:
raise Exception("%s not recognized, must be among %s"
% (ic, sorted(selections)))
lags = selections[ic]
if verbose:
print('Using %d based on %s criterion' % (lags, ic))
else:
if lags is None:
lags = 1
k_trend = util.get_trendorder(trend)
self.exog_names = util.make_lag_names(self.endog_names, lags, k_trend)
self.nobs = len(self.endog) - lags
return self._estimate_var(lags, trend=trend)
def __init__(
self,
endog,
endog_lagged,
params,
sigma_u,
lag_order,
A=None,
B=None,
A_mask=None,
B_mask=None,
model=None,
trend="c",
names=None,
dates=None,
):
self.model = model
self.y = self.endog = endog # keep alias for now
self.ys_lagged = self.endog_lagged = endog_lagged # keep alias for now
self.dates = dates
self.n_totobs, self.neqs = self.y.shape
self.nobs = self.n_totobs - lag_order
k_trend = util.get_trendorder(trend)
if k_trend > 0: # make this the polynomial trend order
trendorder = k_trend - 1
else:
trendorder = None
self.k_trend = k_trend
self.trendorder = trendorder
self.exog_names = util.make_lag_names(names, lag_order, k_trend)
self.params = params
self.sigma_u = sigma_u
# Each matrix needs to be transposed
reshaped = self.params[self.k_trend :]
reshaped = reshaped.reshape((lag_order, self.neqs, self.neqs))
# Need to transpose each coefficient matrix
intercept = self.params[0]
coefs = reshaped.swapaxes(1, 2).copy()
# SVAR components
# TODO: if you define these here, you don't also have to define
# them in SVAR process, but I left them for now -ss
self.A = A
self.B = B
self.A_mask = A_mask
self.B_mask = B_mask
super(SVARResults, self).__init__(coefs, intercept, sigma_u, A, B, names=names)
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)
names=['Y1', 'Y2'],
trend=trend,
dates=data.dates,
model=self,
exog=exog)
result = VARResultsWrapper(varfit)
#return VARResultsWrapper(varfit)
#end
for k, v in result.info_criteria.items:
ics[k].append(v)
selected_orders = dict((k, mat(v).argmin()) for k, v in ics.items)
if verbose:
output.print_ic_table(ics, selected_orders)
selections = selected_orders
#end
if ic not in selections:
raise Exception("%s not recognized, must be among %s" %
(ic, sorted(selections)))
lags = selections[ic]
if verbose:
print('Using %d based on %s criterion' % (lags, ic))
k_trend = 1 #'C'
exog_names = util.make_lag_names(endog_names, lags, k_trend)
nobs = len(endog) - lags