def _stackX(self, k_ar, trend):
"""
Private method to build the RHS matrix for estimation.
Columns are trend terms then lags.
"""
endog = self.endog
X = lagmat(endog, maxlag=k_ar, trim='both')
k_trend = util.get_trendorder(trend)
if k_trend:
X = add_trend(X, prepend=True, trend=trend)
self.k_trend = k_trend
return X
def _make_arma_exog(endog, exog, trend):
k_trend = 1 # overwritten if no constant
if exog is None and trend == 'c': # constant only
exog = np.ones((len(endog),1))
elif exog is not None and trend == 'c': # constant plus exogenous
exog = add_trend(exog, trend='c', prepend=True)
elif exog is not None and trend == 'nc':
# make sure it's not holding constant from last run
if exog.var() == 0:
exog = None
k_trend = 0
if trend == 'nc':
k_trend = 0
return k_trend, exog
def _make_arma_exog(endog, exog, trend):
k_trend = 1 # overwritten if no constant
if exog is None and trend == 'c': # constant only
exog = np.ones((len(endog), 1))
elif exog is not None and trend == 'c': # constant plus exogenous
exog = add_trend(exog, trend='c', prepend=True)
elif exog is not None and trend == 'nc':
# make sure it's not holding constant from last run
if exog.var() == 0:
exog = None
k_trend = 0
if trend == 'nc':
k_trend = 0
return k_trend, exog
def get_var_endog(y, lags, trend='c'):
"""
Make predictor matrix for VAR(p) process
Z := (Z_0, ..., Z_T).T (T x Kp)
Z_t = [1 y_t y_{t-1} ... y_{t - p + 1}] (Kp x 1)
Ref: Lutkepohl p.70 (transposed)
"""
nobs = len(y)
# Ravel C order, need to put in descending order
Z = np.array([y[t - lags:t][::-1].ravel() for t in xrange(lags, nobs)])
# Add constant, trend, etc.
if trend != 'nc':
Z = tsa.add_trend(Z, prepend=True, trend=trend)
return Z
def get_var_endog(y, lags, trend='c'):
"""
Make predictor matrix for VAR(p) process
Z := (Z_0, ..., Z_T).T (T x Kp)
Z_t = [1 y_t y_{t-1} ... y_{t - p + 1}] (Kp x 1)
Ref: Lutkepohl p.70 (transposed)
"""
nobs = len(y)
# Ravel C order, need to put in descending order
Z = np.array([y[t-lags : t][::-1].ravel() for t in xrange(lags, nobs)])
# Add constant, trend, etc.
if trend != 'nc':
Z = tsa.add_trend(Z, prepend=True, trend=trend)
return Z
def _stackX(self, k_ar, trend):
"""
Private method to build the RHS matrix for estimation.
Columns are trend terms, then exogenous, then lags.
"""
endog = self.endog
exog = self.exog
X = lagmat(endog, maxlag=k_ar, trim='both')
if exog is not None:
X = np.column_stack((exog[k_ar:, :], X))
# Handle trend terms
if trend == 'c':
k_trend = 1
elif trend == 'nc':
k_trend = 0
elif trend == 'ct':
k_trend = 2
elif trend == 'ctt':
k_trend = 3
if trend != 'nc':
X = add_trend(X, prepend=True, trend=trend)
self.k_trend = k_trend
return X
def _stackX(self, k_ar, trend):
"""
Private method to build the RHS matrix for estimation.
Columns are trend terms, then exogenous, then lags.
"""
endog = self.endog
exog = self.exog
X = lagmat(endog, maxlag=k_ar, trim='both')
if exog is not None:
X = np.column_stack((exog[k_ar:,:], X))
# Handle trend terms
if trend == 'c':
k_trend = 1
elif trend == 'nc':
k_trend = 0
elif trend == 'ct':
k_trend = 2
elif trend == 'ctt':
k_trend = 3
if trend != 'nc':
X = add_trend(X,prepend=True, trend=trend)
self.k_trend = k_trend
return X
def fit(
self,
order,
start_params=None,
trend="c",
method="css-mle",
transparams=True,
solver=None,
maxiter=35,
full_output=1,
disp=5,
callback=None,
**kwargs
):
"""
Fits ARMA(p,q) model using exact maximum likelihood via Kalman filter.
Parameters
----------
start_params : array-like, optional
Starting parameters for ARMA(p,q). If None, the default is given
by ARMA._fit_start_params. See there for more information.
transparams : bool, optional
Whehter or not to transform the parameters to ensure stationarity.
Uses the transformation suggested in Jones (1980). If False,
no checking for stationarity or invertibility is done.
method : str {'css-mle','mle','css'}
This is the loglikelihood to maximize. If "css-mle", the
conditional sum of squares likelihood is maximized and its values
are used as starting values for the computation of the exact
likelihood via the Kalman filter. If "mle", the exact likelihood
is maximized via the Kalman Filter. If "css" the conditional sum
of squares likelihood is maximized. All three methods use
`start_params` as starting parameters. See above for more
information.
trend : str {'c','nc'}
Whehter to include a constant or not. 'c' includes constant,
'nc' no constant.
solver : str or None, optional
Solver to be used. The default is 'l_bfgs' (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'.
The limited memory BFGS uses m=30 to approximate the Hessian,
projected gradient tolerance of 1e-7 and factr = 1e3. These
cannot currently be changed for l_bfgs. See notes for more
information.
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 printed. For the default
l_bfgs_b solver, disp controls the frequency of the output during
the iterations. disp < 0 means no output in this case.
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.
Returns
-------
`scikits.statsmodels.tsa.arima.ARMAResults` class
See also
--------
scikits.statsmodels.model.LikelihoodModel.fit for more information
on using the solvers.
Notes
------
If fit by 'mle', it is assumed for the Kalman Filter that the initial
unkown state is zero, and that the inital variance is
P = dot(inv(identity(m**2)-kron(T,T)),dot(R,R.T).ravel('F')).reshape(r,
r, order = 'F')
The below is the docstring from
`scikits.statsmodels.LikelihoodModel.fit`
"""
# enforce invertibility
self.transparams = transparams
self.method = method.lower()
# get model order
k_ar, k_ma = map(int, order)
k_lags = max(k_ar, k_ma + 1)
self.k_ar = k_ar
self.k_ma = k_ma
self.k_lags = k_lags
endog = self.endog
exog = self.exog
k_exog = self.k_exog
self.nobs = len(endog) # this is overwritten if method is 'css'
# handle exogenous variables
k_trend = 1 # overwritten if no constant
if exog is None and trend == "c": # constant only
exog = np.ones((len(endog), 1))
elif exog is not None and trend == "c": # constant plus exogenous
exog = add_trend(exog, trend="c", prepend=True)
elif exog is not None and trend == "nc":
# make sure it's not holding constant from last run
if exog.var() == 0:
exog = None
k_trend = 0
if trend == "nc":
k_trend = 0
self.k_trend = k_trend
self.exog = exog # overwrites original exog from __init__
k = k_trend + k_exog
# choose objective function
if method.lower() in ["mle", "css-mle"]:
loglike = lambda params: -self.loglike_kalman(params)
self.loglike = self.loglike_kalman
if method.lower() == "css":
loglike = lambda params: -self.loglike_css(params)
self.loglike = self.loglike_css
self.nobs = len(endog) - k_ar # nobs for CSS excludes pre-sample
if start_params is not None:
start_params = np.asarray(start_params)
else:
if method.lower() != "css-mle": # use Hannan-Rissanen start_params
start_params = self._fit_start_params((k_ar, k_ma, k))
else: # use Hannan-Rissanen to get CSS start_params
func = lambda params: -self.loglike_css(params)
# start_params = [.1]*(k_ar+k_ma+k_exog) # different one for k?
start_params = self._fit_start_params((k_ar, k_ma, k))
if transparams:
start_params = self._invtransparams(start_params)
bounds = [(None,) * 2] * (k_ar + k_ma + k)
mlefit = optimize.fmin_l_bfgs_b(
func, start_params, approx_grad=True, m=12, pgtol=1e-7, factr=1e3, bounds=bounds, iprint=-1
)
start_params = self._transparams(mlefit[0])
if transparams: # transform initial parameters to ensure invertibility
start_params = self._invtransparams(start_params)
if solver is None: # use default limited memory bfgs
bounds = [(None,) * 2] * (k_ar + k_ma + k)
mlefit = optimize.fmin_l_bfgs_b(
loglike, start_params, approx_grad=True, m=12, pgtol=1e-8, factr=1e2, bounds=bounds, iprint=disp
)
self.mlefit = mlefit
params = mlefit[0]
else: # call the solver from LikelihoodModel
mlefit = super(ARMA, self).fit(
start_params,
method=solver,
maxiter=maxiter,
full_output=full_output,
disp=disp,
callback=callback,
**kwargs
)
self.mlefit = mlefit
params = mlefit.params
if transparams: # transform parameters back
params = self._transparams(params)
self.transparams = False # set to false so methods don't expect transf.
normalized_cov_params = None # TODO: fix this
return ARMAResults(self, params, normalized_cov_params)
def fit(self, order, start_params=None, trend='c', method = "css-mle",
transparams=True, solver=None, maxiter=35, full_output=1,
disp=5, callback=None, **kwargs):
"""
Fits ARMA(p,q) model using exact maximum likelihood via Kalman filter.
Parameters
----------
start_params : array-like, optional
Starting parameters for ARMA(p,q). If None, the default is given
by ARMA._fit_start_params. See there for more information.
transparams : bool, optional
Whehter or not to transform the parameters to ensure stationarity.
Uses the transformation suggested in Jones (1980). If False,
no checking for stationarity or invertibility is done.
method : str {'css-mle','mle','css'}
This is the loglikelihood to maximize. If "css-mle", the
conditional sum of squares likelihood is maximized and its values
are used as starting values for the computation of the exact
likelihood via the Kalman filter. If "mle", the exact likelihood
is maximized via the Kalman Filter. If "css" the conditional sum
of squares likelihood is maximized. All three methods use
`start_params` as starting parameters. See above for more
information.
trend : str {'c','nc'}
Whehter to include a constant or not. 'c' includes constant,
'nc' no constant.
solver : str or None, optional
Solver to be used. The default is 'l_bfgs' (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'.
The limited memory BFGS uses m=30 to approximate the Hessian,
projected gradient tolerance of 1e-7 and factr = 1e3. These
cannot currently be changed for l_bfgs. See notes for more
information.
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 printed. For the default
l_bfgs_b solver, disp controls the frequency of the output during
the iterations. disp < 0 means no output in this case.
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.
Returns
-------
`scikits.statsmodels.tsa.arima.ARMAResults` class
See also
--------
scikits.statsmodels.model.LikelihoodModel.fit for more information
on using the solvers.
Notes
------
If fit by 'mle', it is assumed for the Kalman Filter that the initial
unkown state is zero, and that the inital variance is
P = dot(inv(identity(m**2)-kron(T,T)),dot(R,R.T).ravel('F')).reshape(r,
r, order = 'F')
The below is the docstring from
`scikits.statsmodels.LikelihoodModel.fit`
"""
# enforce invertibility
self.transparams = transparams
self.method = method.lower()
# get model order
k_ar,k_ma = map(int,order)
k_lags = max(k_ar,k_ma+1)
self.k_ar = k_ar
self.k_ma = k_ma
self.k_lags = k_lags
endog = self.endog
exog = self.exog
k_exog = self.k_exog
self.nobs = len(endog) # this is overwritten if method is 'css'
# handle exogenous variables
k_trend = 1 # overwritten if no constant
if exog is None and trend == 'c': # constant only
exog = np.ones((len(endog),1))
elif exog is not None and trend == 'c': # constant plus exogenous
exog = add_trend(exog, trend='c', prepend=True)
elif exog is not None and trend == 'nc':
# make sure it's not holding constant from last run
if exog.var() == 0:
exog = None
k_trend = 0
if trend == 'nc':
k_trend = 0
self.k_trend = k_trend
self.exog = exog # overwrites original exog from __init__
k = k_trend + k_exog
# choose objective function
if method.lower() in ['mle','css-mle']:
loglike = lambda params: -self.loglike_kalman(params)
self.loglike = self.loglike_kalman
if method.lower() == 'css':
loglike = lambda params: -self.loglike_css(params)
self.loglike = self.loglike_css
self.nobs = len(endog) - k_ar #nobs for CSS excludes pre-sample
if start_params is not None:
start_params = np.asarray(start_params)
else:
if method.lower() != 'css-mle': # use Hannan-Rissanen start_params
start_params = self._fit_start_params((k_ar,k_ma,k))
else: # use Hannan-Rissanen to get CSS start_params
func = lambda params: -self.loglike_css(params)
#start_params = [.1]*(k_ar+k_ma+k_exog) # different one for k?
start_params = self._fit_start_params((k_ar,k_ma,k))
if transparams:
start_params = self._invtransparams(start_params)
bounds = [(None,)*2]*(k_ar+k_ma+k)
mlefit = optimize.fmin_l_bfgs_b(func, start_params,
approx_grad=True, m=12, pgtol=1e-7, factr=1e3,
bounds = bounds, iprint=-1)
start_params = self._transparams(mlefit[0])
if transparams: # transform initial parameters to ensure invertibility
start_params = self._invtransparams(start_params)
if solver is None: # use default limited memory bfgs
bounds = [(None,)*2]*(k_ar+k_ma+k)
mlefit = optimize.fmin_l_bfgs_b(loglike, start_params,
approx_grad=True, m=12, pgtol=1e-8, factr=1e2,
bounds=bounds, iprint=disp)
self.mlefit = mlefit
params = mlefit[0]
else: # call the solver from LikelihoodModel
mlefit = super(ARMA, self).fit(start_params, method=solver,
maxiter=maxiter, full_output=full_output, disp=disp,
callback = callback, **kwargs)
self.mlefit = mlefit
params = mlefit.params
if transparams: # transform parameters back
params = self._transparams(params)
self.transparams = False # set to false so methods don't expect transf.
normalized_cov_params = None #TODO: fix this
return ARMAResults(self, params, normalized_cov_params)