"""
State Space Model
Author: Chad Fulton
License: Simplified-BSD
"""
from __future__ import division, absolute_import, print_function
import numpy as np
import pandas as pd
from scipy.stats import norm
from .kalman_filter import (
KalmanFilter, FilterResults, INVERT_UNIVARIATE, SOLVE_LU
)
import statsmodels.tsa.base.tsa_model as tsbase
import statsmodels.base.wrapper as wrap
from statsmodels.tools.numdiff import (
_get_epsilon, approx_hess_cs, approx_fprime_cs
)
from statsmodels.tools.decorators import cache_readonly, resettable_cache
from statsmodels.tools.eval_measures import aic, bic, hqic
[docs]class MLEModel(tsbase.TimeSeriesModel):
r"""
State space model for maximum likelihood estimation
Parameters
----------
endog : array_like
The observed time-series process :math:`y`
k_states : int
The dimension of the unobserved state process.
exog : array_like, optional
Array of exogenous regressors, shaped nobs x k. Default is no
exogenous regressors.
dates : array-like of datetime, optional
An array-like object of datetime objects. If a Pandas object is given
for endog, it is assumed to have a DateIndex.
freq : str, optional
The frequency of the time-series. A Pandas offset or 'B', 'D', 'W',
'M', 'A', or 'Q'. This is optional if dates are given.
**kwargs
Keyword arguments may be used to provide default values for state space
matrices or for Kalman filtering options. See `Representation`, and
`KalmanFilter` for more details.
Attributes
----------
ssm : KalmanFilter
Underlying state space representation.
Notes
-----
This class wraps the state space model with Kalman filtering to add in
functionality for maximum likelihood estimation. In particular, it adds
the concept of updating the state space representation based on a defined
set of parameters, through the `update` method or `updater` attribute (see
below for more details on which to use when), and it adds a `fit` method
which uses a numerical optimizer to select the parameters that maximize
the likelihood of the model.
The `start_params` `update` method must be overridden in the
child class (and the `transform` and `untransform` methods, if needed).
See Also
--------
MLEResults
statsmodels.tsa.statespace.kalman_filter.KalmanFilter
statsmodels.tsa.statespace.representation.Representation
"""
optim_hessian = 'cs'
def __init__(self, endog, k_states, exog=None, dates=None, freq=None,
**kwargs):
# Initialize the model base
super(MLEModel, self).__init__(endog=endog, exog=exog,
dates=dates, freq=freq,
missing='none')
# Store kwargs to recreate model
self._init_kwargs = kwargs
# Prepared the endog array: C-ordered, shape=(nobs x k_endog)
self.endog, self.exog = self.prepare_data()
# Dimensions
self.nobs = self.endog.shape[0]
self.k_states = k_states
# Initialize the state-space representation
self.initialize_statespace(**kwargs)
[docs] def prepare_data(self):
"""
Prepare data for use in the state space representation
"""
endog = np.array(self.data.orig_endog)
exog = self.data.orig_exog
if exog is not None:
exog = np.array(exog)
# Base class may allow 1-dim data, whereas we need 2-dim
if endog.ndim == 1:
endog.shape = (endog.shape[0], 1) # this will be C-contiguous
# Base classes data may be either C-ordered or F-ordered - we want it
# to be C-ordered since it will also be in shape (nobs, k_endog), and
# then we can just transpose it.
if not endog.flags['C_CONTIGUOUS']:
# TODO this breaks the reference link between the model endog
# variable and the original object - do we need a warn('')?
# This will happen often with Pandas DataFrames, which are often
# Fortran-ordered and in the long format
endog = np.ascontiguousarray(endog)
return endog, exog
[docs] def initialize_statespace(self, **kwargs):
"""
Initialize the state space representation
Parameters
----------
**kwargs
Additional keyword arguments to pass to the state space class
constructor.
"""
# (Now self.endog is C-ordered and in long format (nobs x k_endog). To
# get F-ordered and in wide format just need to transpose)
endog = self.endog.T
# Instantiate the state space object
self.ssm = KalmanFilter(endog.shape[0], self.k_states, **kwargs)
# Bind the data to the model
self.ssm.bind(endog)
# Other dimensions, now that `ssm` is available
self.k_endog = self.ssm.k_endog
[docs] def fit(self, start_params=None, transformed=True, cov_type='opg',
cov_kwds=None, method='lbfgs', maxiter=50, full_output=1,
disp=5, callback=None, return_params=False,
optim_hessian=None, **kwargs):
"""
Fits the model by maximum likelihood via Kalman filter.
Parameters
----------
start_params : array_like, optional
Initial guess of the solution for the loglikelihood maximization.
If None, the default is given by Model.start_params.
transformed : boolean, optional
Whether or not `start_params` is already transformed. Default is
True.
method : str, optional
The `method` determines which solver from `scipy.optimize`
is used, and it can be chosen from among the following strings:
- 'newton' for Newton-Raphson, 'nm' for Nelder-Mead
- 'bfgs' for Broyden-Fletcher-Goldfarb-Shanno (BFGS)
- 'lbfgs' for limited-memory BFGS with optional box constraints
- 'powell' for modified Powell's method
- 'cg' for conjugate gradient
- 'ncg' for Newton-conjugate gradient
- 'basinhopping' for global basin-hopping solver
The explicit arguments in `fit` are passed to the solver,
with the exception of the basin-hopping solver. Each
solver has several optional arguments that are not the same across
solvers. See the notes section below (or scipy.optimize) for the
available arguments and for the list of explicit arguments that the
basin-hopping solver supports.
cov_type : str, optional
The `cov_type` keyword governs the method for calculating the
covariance matrix of parameter estimates. Can be one of:
- 'opg' for the outer product of gradient estimator
- 'oim' for the observed information matrix estimator, calculated
using the method of Harvey (1989)
- 'cs' for the observed information matrix estimator, calculated
using a numerical (complex step) approximation of the Hessian
matrix.
- 'delta' for the observed information matrix estimator, calculated
using a numerical (complex step) approximation of the Hessian
along with the delta method (method of propagation of errors)
applied to the parameter transformation function
`transform_params`.
- 'robust' for an approximate (quasi-maximum likelihood) covariance
matrix that may be valid even in the presense of some
misspecifications. Intermediate calculations use the 'oim'
method.
- 'robust_cs' is the same as 'robust' except that the intermediate
calculations use the 'cs' method.
cov_kwds : dict or None, optional
See `MLEResults.get_robustcov_results` for a description required
keywords for alternative covariance estimators
maxiter : int, optional
The maximum number of iterations to perform.
full_output : boolean, optional
Set to True to have all available output in the Results object's
mle_retvals attribute. The output is dependent on the solver.
See LikelihoodModelResults notes section for more information.
disp : boolean, optional
Set to True to print convergence messages.
callback : callable callback(xk), optional
Called after each iteration, as callback(xk), where xk is the
current parameter vector.
return_params : boolean, optional
Whether or not to return only the array of maximizing parameters.
Default is False.
optim_hessian : {'opg','oim','cs'}, optional
The method by which the Hessian is numerically approximated. 'opg'
uses outer product of gradients, 'oim' uses the information
matrix formula from Harvey (1989), and 'cs' uses second-order
complex step differentiation. This keyword is only relevant if the
optimization method uses the Hessian matrix.
**kwargs
Additional keyword arguments to pass to the optimizer.
Returns
-------
MLEResults
See also
--------
statsmodels.base.model.LikelihoodModel.fit
MLEResults
"""
if start_params is None:
start_params = self.start_params
transformed = True
# Update the hessian method
if optim_hessian is not None:
self.optim_hessian = optim_hessian
# Unconstrain the starting parameters
if transformed:
start_params = self.untransform_params(np.array(start_params))
if method == 'lbfgs' or method == 'bfgs':
# kwargs.setdefault('pgtol', 1e-8)
# kwargs.setdefault('factr', 1e2)
# kwargs.setdefault('m', 12)
kwargs.setdefault('approx_grad', True)
kwargs.setdefault('epsilon', 1e-5)
# Maximum likelihood estimation
fargs = (False,) # (sets transformed=False)
mlefit = super(MLEModel, self).fit(start_params, method=method,
fargs=fargs,
maxiter=maxiter,
full_output=full_output,
disp=disp, callback=callback,
skip_hessian=True, **kwargs)
# Just return the fitted parameters if requested
if return_params:
return self.transform_params(mlefit.params)
# Otherwise construct the results class if desired
else:
res = self.filter(mlefit.params, transformed=False,
cov_type=cov_type, cov_kwds=cov_kwds)
res.mlefit = mlefit
res.mle_retvals = mlefit.mle_retvals
res.mle_settings = mlefit.mle_settings
return res
[docs] def filter(self, params, transformed=True, cov_type=None, cov_kwds=None,
return_ssm=False, **kwargs):
"""
Kalman filtering
Parameters
----------
params : array_like
Array of parameters at which to evaluate the loglikelihood
function.
transformed : boolean, optional
Whether or not `params` is already transformed. Default is True.
return_ssm : boolean,optional
Whether or not to return only the state space output or a full
results object. Default is to return a full results object.
cov_type : str, optional
See `MLEResults.fit` for a description of covariance matrix types
for results object.
cov_kwds : dict or None, optional
See `MLEResults.get_robustcov_results` for a description required
keywords for alternative covariance estimators
**kwargs
Additional keyword arguments to pass to the Kalman filter. See
`KalmanFilter.filter` for more details.
"""
params = np.array(params, ndmin=1)
if not transformed:
params = self.transform_params(params)
self.update(params, transformed=True)
# Save the parameter names
self.data.param_names = self.param_names
# Get the state space output
result = self.ssm.filter(**kwargs)
# Wrap in a results object
if not return_ssm:
result_kwargs = {}
if cov_type is not None:
result_kwargs['cov_type'] = cov_type
result = MLEResultsWrapper(
MLEResults(self, params, result, **result_kwargs)
)
return result
[docs] def loglike(self, params, transformed=True, **kwargs):
"""
Loglikelihood evaluation
Parameters
----------
params : array_like
Array of parameters at which to evaluate the loglikelihood
function.
transformed : boolean, optional
Whether or not `params` is already transformed. Default is True.
**kwargs
Additional keyword arguments to pass to the Kalman filter. See
`KalmanFilter.filter` for more details.
Notes
-----
[1]_ recommend maximizing the average likelihood to avoid scale issues;
this is done automatically by the base Model fit method.
References
----------
.. [1] Koopman, Siem Jan, Neil Shephard, and Jurgen A. Doornik. 1999.
Statistical Algorithms for Models in State Space Using SsfPack 2.2.
Econometrics Journal 2 (1): 107-60. doi:10.1111/1368-423X.00023.
See Also
--------
update : modifies the internal state of the state space model to
reflect new params
"""
if not transformed:
params = self.transform_params(params)
self.update(params, transformed=True)
loglike = self.ssm.loglike(**kwargs)
# Koopman, Shephard, and Doornik recommend maximizing the average
# likelihood to avoid scale issues, but the averaging is done
# automatically in the base model `fit` method
return loglike
[docs] def loglikeobs(self, params, transformed=True, **kwargs):
"""
Loglikelihood evaluation
Parameters
----------
params : array_like
Array of parameters at which to evaluate the loglikelihood
function.
transformed : boolean, optional
Whether or not `params` is already transformed. Default is True.
**kwargs
Additional keyword arguments to pass to the Kalman filter. See
`KalmanFilter.filter` for more details.
Notes
-----
[1]_ recommend maximizing the average likelihood to avoid scale issues;
this is done automatically by the base Model fit method.
References
----------
.. [1] Koopman, Siem Jan, Neil Shephard, and Jurgen A. Doornik. 1999.
Statistical Algorithms for Models in State Space Using SsfPack 2.2.
Econometrics Journal 2 (1): 107-60. doi:10.1111/1368-423X.00023.
See Also
--------
update : modifies the internal state of the Model to reflect new params
"""
if not transformed:
params = self.transform_params(params)
self.update(params, transformed=True)
return self.ssm.loglikeobs(**kwargs)
[docs] def score(self, params, *args, **kwargs):
"""
Compute the score function at params.
Parameters
----------
params : array_like
Array of parameters at which to evaluate the score.
*args, **kwargs
Additional arguments to the `loglike` method.
Returns
----------
score : array
Score, evaluated at `params`.
Notes
-----
This is a numerical approximation, calculated using first-order complex
step differentiation on the `loglike` method.
Both \*args and \*\*kwargs are necessary because the optimizer from
`fit` must call this function and only supports passing arguments via
\*args (for example `scipy.optimize.fmin_l_bfgs`).
"""
transformed = (
args[0] if len(args) > 0 else kwargs.get('transformed', False)
)
score = approx_fprime_cs(params, self.loglike, kwargs={
'transformed': transformed
})
return score
[docs] def score_obs(self, params, **kwargs):
"""
Compute the score per observation, evaluated at params
Parameters
----------
params : array_like
Array of parameters at which to evaluate the score.
*args, **kwargs
Additional arguments to the `loglike` method.
Returns
----------
score : array (nobs, k_vars)
Score per observation, evaluated at `params`.
Notes
-----
This is a numerical approximation, calculated using first-order complex
step differentiation on the `loglikeobs` method.
"""
self.update(params)
return approx_fprime_cs(params, self.loglikeobs, kwargs=kwargs)
[docs] def hessian(self, params, *args, **kwargs):
"""
Hessian matrix of the likelihood function, evaluated at the given
parameters
Parameters
----------
params : array_like
Array of parameters at which to evaluate the hessian.
*args, **kwargs
Additional arguments to the `loglike` method.
Returns
-------
hessian : array
Hessian matrix evaluated at `params`
Notes
-----
This is a numerical approximation.
Both \*args and \*\*kwargs are necessary because the optimizer from
`fit` must call this function and only supports passing arguments via
\*args (for example `scipy.optimize.fmin_l_bfgs`).
"""
if self.optim_hessian == 'cs':
hessian = self._hessian_cs(params, *args, **kwargs)
elif self.optim_hessian == 'oim':
hessian = self._hessian_oim(params)
elif self.optim_hessian == 'opg':
hessian = self._hessian_opg(params)
else:
raise NotImplementedError('Invalid Hessian calculation method.')
return hessian
def _hessian_oim(self, params):
"""
Hessian matrix computed using the Harvey (1989) information matrix
"""
return -self.observed_information_matrix(params)
def _hessian_opg(self, params):
"""
Hessian matrix computed using the outer product of gradients
information matrix
"""
return -self.opg_information_matrix(params)
def _hessian_cs(self, params, *args, **kwargs):
"""
Hessian matrix computed by second-order complex-step differentiation
on the `loglike` function.
"""
transformed = (
args[0] if len(args) > 0 else kwargs.get('transformed', False)
)
f = lambda params, **kwargs: self.loglike(params, **kwargs) / self.nobs
hessian = approx_hess_cs(params, f, kwargs={
'transformed': transformed
})
return hessian
@property
def start_params(self):
"""
(array) Starting parameters for maximum likelihood estimation.
"""
if hasattr(self, '_start_params'):
return self._start_params
else:
raise NotImplementedError
@property
def param_names(self):
"""
(list of str) List of human readable parameter names (for parameters
actually included in the model).
"""
if hasattr(self, '_param_names'):
return self._param_names
else:
try:
names = ['param.%d' % i for i in range(len(self.start_params))]
except NotImplementedError:
names = []
return names
[docs] def update(self, params, transformed=True):
"""
Update the parameters of the model
Parameters
----------
params : array_like
Array of new parameters.
transformed : boolean, optional
Whether or not `params` is already transformed. If set to False,
`transform_params` is called. Default is True.
Returns
-------
params : array_like
Array of parameters.
Notes
-----
Since Model is a base class, this method should be overridden by
subclasses to perform actual updating steps.
"""
params = np.array(params, ndmin=1)
if not transformed:
params = self.transform_params(params)
return params
@classmethod
[docs]class MLEResults(tsbase.TimeSeriesModelResults):
r"""
Class to hold results from fitting a state space model.
Parameters
----------
model : MLEModel instance
The fitted model instance
params : array
Fitted parameters
filter_results : KalmanFilter instance
The underlying state space model and Kalman filter output
Attributes
----------
model : Model instance
A reference to the model that was fit.
filter_results : KalmanFilter instance
The underlying state space model and Kalman filter output
nobs : float
The number of observations used to fit the model.
params : array
The parameters of the model.
scale : float
This is currently set to 1.0 and not used by the model or its results.
See Also
--------
MLEModel
statsmodels.tsa.statespace.kalman_filter.FilterResults
statsmodels.tsa.statespace.representation.FrozenRepresentation
"""
def __init__(self, model, params, filter_results, cov_type='opg',
cov_kwds=None, **kwargs):
self.data = model.data
tsbase.TimeSeriesModelResults.__init__(self, model, params,
normalized_cov_params=None,
scale=1.)
# Save the state space representation output
self.filter_results = filter_results
# Dimensions
self.nobs = model.nobs
# Setup covariance matrix notes dictionary
if not hasattr(self, 'cov_kwds'):
self.cov_kwds = {}
self.cov_type = cov_type
# Setup the cache
self._cache = resettable_cache()
# Handle covariance matrix calculation
if cov_kwds is None:
cov_kwds = {}
self._get_robustcov_results(cov_type=cov_type, use_self=True,
**cov_kwds)
def _get_robustcov_results(self, cov_type='opg', **kwargs):
"""
Create new results instance with specified covariance estimator as
default
Note: creating new results instance currently not supported.
Parameters
----------
cov_type : string
the type of covariance matrix estimator to use. See Notes below
kwargs : depends on cov_type
Required or optional arguments for covariance calculation.
See Notes below.
Returns
-------
results : results instance
This method creates a new results instance with the requested
covariance as the default covariance of the parameters.
Inferential statistics like p-values and hypothesis tests will be
based on this covariance matrix.
Notes
-----
The following covariance types and required or optional arguments are
currently available:
- 'opg' for the outer product of gradient estimator
- 'oim' for the observed information matrix estimator, calculated
using the method of Harvey (1989)
- 'cs' for the observed information matrix estimator, calculated
using a numerical (complex step) approximation of the Hessian
matrix.
- 'delta' for the observed information matrix estimator, calculated
using a numerical (complex step) approximation of the Hessian along
with the delta method (method of propagation of errors)
applied to the parameter transformation function `transform_params`.
- 'robust' for an approximate (quasi-maximum likelihood) covariance
matrix that may be valid even in the presense of some
misspecifications. Intermediate calculations use the 'oim'
method.
- 'robust_cs' is the same as 'robust' except that the intermediate
calculations use the 'cs' method.
"""
import statsmodels.stats.sandwich_covariance as sw
use_self = kwargs.pop('use_self', False)
if use_self:
res = self
else:
raise NotImplementedError
res = self.__class__(
self.model, self.params,
normalized_cov_params=self.normalized_cov_params,
scale=self.scale)
# Set the new covariance type
res.cov_type = cov_type
res.cov_kwds = {}
# Calculate the new covariance matrix
if len(self.params) == 0:
res.cov_params_default = np.zeros((0,0))
res.cov_kwds['cov_type'] = (
'No parameters estimated.')
elif self.cov_type == 'cs':
res.cov_params_default = res.cov_params_cs
res.cov_kwds['description'] = (
'Covariance matrix calculated using numerical (complex-step)'
' differentiation.')
elif self.cov_type == 'delta':
res.cov_params_default = res.cov_params_delta
res.cov_kwds['description'] = (
'Covariance matrix calculated using numerical differentiation'
' and the delta method (method of propagation of errors)'
' applied to the parameter transformation function.')
elif self.cov_type == 'oim':
res.cov_params_default = res.cov_params_oim
res.cov_kwds['description'] = (
'Covariance matrix calculated using the observed information'
' matrix described in Harvey (1989).')
elif self.cov_type == 'opg':
res.cov_params_default = res.cov_params_opg
res.cov_kwds['description'] = (
'Covariance matrix calculated using the outer product of'
' gradients.'
)
elif self.cov_type == 'robust' or self.cov_type == 'robust_oim':
res.cov_params_default = res.cov_params_robust_oim
res.cov_kwds['description'] = (
'Quasi-maximum likelihood covariance matrix used for'
' robustness to some misspecifications; calculated using the'
' observed information matrix described in Harvey (1989).')
elif self.cov_type == 'robust_cs':
res.cov_params_default = res.cov_params_robust_cs
res.cov_kwds['description'] = (
'Quasi-maximum likelihood covariance matrix used for'
' robustness to some misspecifications; calculated using'
' numerical (complex-step) differentiation.')
else:
raise NotImplementedError('Invalid covariance matrix type.')
return res
@cache_readonly
[docs] def aic(self):
"""
(float) Akaike Information Criterion
"""
# return -2*self.llf + 2*self.params.shape[0]
return aic(self.llf, self.nobs, self.params.shape[0])
@cache_readonly
[docs] def bic(self):
"""
(float) Bayes Information Criterion
"""
# return -2*self.llf + self.params.shape[0]*np.log(self.nobs)
return bic(self.llf, self.nobs, self.params.shape[0])
@cache_readonly
[docs] def cov_params_cs(self):
"""
(array) The variance / covariance matrix. Computed using the numerical
Hessian computed without using parameter transformations.
"""
nobs = (self.model.nobs - self.filter_results.loglikelihood_burn)
# When using complex-step methods, cannot rely on Cholesky inversion
# because variance parameters will then have a complex component which
# which implies non-positive-definiteness.
inversion_method = INVERT_UNIVARIATE | SOLVE_LU
evaluated_hessian = self.model._hessian_cs(
self.params, transformed=True, inversion_method=inversion_method
)
self.model.update(self.params)
return -np.linalg.inv(nobs * evaluated_hessian)
@cache_readonly
[docs] def cov_params_delta(self):
"""
(array) The variance / covariance matrix. Computed using the numerical
Hessian computed using parameter transformations and the Delta method
(method of propagation of errors).
"""
nobs = (self.model.nobs - self.filter_results.loglikelihood_burn)
unconstrained = self.model.untransform_params(self.params)
jacobian = self.model.transform_jacobian(unconstrained)
cov_cs = -np.linalg.inv(
nobs * self.model._hessian_cs(unconstrained, transformed=False)
)
return np.dot(np.dot(jacobian, cov_cs), jacobian.transpose())
@cache_readonly
[docs] def cov_params_oim(self):
"""
(array) The variance / covariance matrix. Computed using the method
from Harvey (1989).
"""
nobs = (self.model.nobs - self.filter_results.loglikelihood_burn)
return np.linalg.inv(
nobs * self.model.observed_information_matrix(self.params)
)
@cache_readonly
[docs] def cov_params_opg(self):
"""
(array) The variance / covariance matrix. Computed using the outer
product of gradients method.
"""
nobs = (self.model.nobs - self.filter_results.loglikelihood_burn)
# When using complex-step methods, cannot rely on Cholesky inversion
# because variance parameters will then have a complex component which
# which implies non-positive-definiteness.
inversion_method = INVERT_UNIVARIATE | SOLVE_LU
return np.linalg.inv(
nobs *
self.model.opg_information_matrix(
self.params, inversion_method=inversion_method
)
)
@cache_readonly
[docs] def cov_params_robust(self):
"""
(array) The QMLE variance / covariance matrix. Alias for
`cov_params_robust_oim`
"""
return self.cov_params_robust_oim
@cache_readonly
[docs] def cov_params_robust_oim(self):
"""
(array) The QMLE variance / covariance matrix. Computed using the
method from Harvey (1989) as the evaluated hessian.
"""
nobs = (self.model.nobs - self.filter_results.loglikelihood_burn)
cov_opg = self.cov_params_opg
evaluated_hessian = (
nobs * self.model.observed_information_matrix(self.params)
)
return np.linalg.inv(
np.dot(np.dot(evaluated_hessian, cov_opg), evaluated_hessian)
)
@cache_readonly
[docs] def cov_params_robust_cs(self):
"""
(array) The QMLE variance / covariance matrix. Computed using the
numerical Hessian computed without using parameter transformations as
the evaluated hessian.
"""
nobs = (self.model.nobs - self.filter_results.loglikelihood_burn)
cov_opg = self.cov_params_opg
# When using complex-step methods, cannot rely on Cholesky inversion
# because variance parameters will then have a complex component which
# which implies non-positive-definiteness.
inversion_method = INVERT_UNIVARIATE | SOLVE_LU
evaluated_hessian = (
nobs *
self.model._hessian_cs(self.params, transformed=True,
inversion_method=inversion_method)
)
return np.linalg.inv(
np.dot(np.dot(evaluated_hessian, cov_opg), evaluated_hessian)
)
[docs] def fittedvalues(self):
"""
(array) The predicted values of the model.
"""
return self.filter_results.forecasts
@cache_readonly
[docs] def hqic(self):
"""
(float) Hannan-Quinn Information Criterion
"""
# return -2*self.llf + 2*np.log(np.log(self.nobs))*self.params.shape[0]
return hqic(self.llf, self.nobs, self.params.shape[0])
@cache_readonly
[docs] def llf_obs(self):
"""
(float) The value of the log-likelihood function evaluated at `params`.
"""
return self.model.loglikeobs(self.params)
@cache_readonly
[docs] def llf(self):
"""
(float) The value of the log-likelihood function evaluated at `params`.
"""
return self.llf_obs[self.filter_results.loglikelihood_burn:].sum()
@cache_readonly
[docs] def loglikelihood_burn(self):
"""
(float) The number of observations during which the likelihood is not
evaluated.
"""
return self.filter_results.loglikelihood_burn
@cache_readonly
[docs] def pvalues(self):
"""
(array) The p-values associated with the z-statistics of the
coefficients. Note that the coefficients are assumed to have a Normal
distribution.
"""
return norm.sf(np.abs(self.zvalues)) * 2
[docs] def resid(self):
"""
(array) The model residuals.
"""
return self.filter_results.forecasts_error
@cache_readonly
[docs] def zvalues(self):
"""
(array) The z-statistics for the coefficients.
"""
return self.params / self.bse
[docs] def predict(self, start=None, end=None, dynamic=False, full_results=False,
**kwargs):
"""
In-sample prediction and out-of-sample forecasting
Parameters
----------
start : int, str, or datetime, optional
Zero-indexed observation number at which to start forecasting, ie.,
the first forecast is start. Can also be a date string to
parse or a datetime type. Default is the the zeroth observation.
end : int, str, or datetime, optional
Zero-indexed observation number at which to end forecasting, ie.,
the last forecast is end. Can also be a date string to
parse or a datetime type. However, if the dates index does not
have a fixed frequency, end must be an integer index if you
want out of sample prediction. Default is the last observation in
the sample.
dynamic : boolean, int, str, or datetime, optional
Integer offset relative to `start` at which to begin dynamic
prediction. Can also be an absolute date string to parse or a
datetime type (these are not interpreted as offsets).
Prior to this observation, true endogenous values will be used for
prediction; starting with this observation and continuing through
the end of prediction, forecasted endogenous values will be used
instead.
full_results : boolean, optional
If True, returns a FilterResults instance; if False returns a
tuple with forecasts, the forecast errors, and the forecast error
covariance matrices. Default is False.
**kwargs
Additional arguments may required for forecasting beyond the end
of the sample. See `FilterResults.predict` for more details.
Returns
-------
forecast : array
Array of out of sample forecasts.
"""
if start is None:
start = 0
# Handle start and end (e.g. dates)
start = self.model._get_predict_start(start)
end, out_of_sample = self.model._get_predict_end(end)
# Handle string dynamic
dates = self.data.dates
if isinstance(dynamic, str):
if dates is None:
raise ValueError("Got a string for dynamic and dates is None")
dtdynamic = self.model._str_to_date(dynamic)
try:
dynamic_start = self.model._get_dates_loc(dates, dtdynamic)
dynamic = dynamic_start - start
except KeyError:
raise ValueError("Dynamic must be in dates. Got %s | %s" %
(str(dynamic), str(dtdynamic)))
# Perform the prediction
results = self.filter_results.predict(
start, end+out_of_sample+1, dynamic, full_results, **kwargs
)
# Note: to be consistent with Statsmodels, return only the forecasts
# unless full_results is specified. Confidence intervals and the date
# indices are left out for now, but will likely be moved to a separate
# function in the future.
if full_results:
return results
else:
forecasts = results
return forecasts
[docs] def forecast(self, steps=1, **kwargs):
"""
Out-of-sample forecasts
Parameters
----------
steps : int, optional
The number of out of sample forecasts from the end of the
sample. Default is 1.
**kwargs
Additional arguments may required for forecasting beyond the end
of the sample. See `FilterResults.predict` for more details.
Returns
-------
forecast : array
Array of out of sample forecasts.
"""
return self.predict(start=self.nobs, end=self.nobs+steps-1, **kwargs)
[docs] def summary(self, alpha=.05, start=None, model_name=None):
"""
Summarize the Model
Parameters
----------
alpha : float, optional
Significance level for the confidence intervals. Default is 0.05.
start : int, optional
Integer of the start observation. Default is 0.
model_name : string
The name of the model used. Default is to use model class name.
Returns
-------
summary : Summary instance
This holds the summary table and text, which can be printed or
converted to various output formats.
See Also
--------
statsmodels.iolib.summary.Summary
"""
from statsmodels.iolib.summary import Summary
model = self.model
title = 'Statespace Model Results'
if start is None:
start = 0
if self.data.dates is not None:
dates = self.data.dates
d = dates[start]
sample = ['%02d-%02d-%02d' % (d.month, d.day, d.year)]
d = dates[-1]
sample += ['- ' + '%02d-%02d-%02d' % (d.month, d.day, d.year)]
else:
sample = [str(start), ' - ' + str(self.model.nobs)]
if model_name is None:
model_name = model.__class__.__name__
top_left = [
('Dep. Variable:', None),
('Model:', [model_name]),
('Date:', None),
('Time:', None),
('Sample:', [sample[0]]),
('', [sample[1]])
]
top_right = [
('No. Observations:', [self.model.nobs]),
('Log Likelihood', ["%#5.3f" % self.llf]),
('AIC', ["%#5.3f" % self.aic]),
('BIC', ["%#5.3f" % self.bic]),
('HQIC', ["%#5.3f" % self.hqic])
]
if hasattr(self, 'cov_type'):
top_left.append(('Covariance Type:', [self.cov_type]))
summary = Summary()
summary.add_table_2cols(self, gleft=top_left, gright=top_right,
title=title)
if len(self.params) > 0:
summary.add_table_params(self, alpha=alpha,
xname=self.data.param_names, use_t=False)
# Add warnings/notes, added to text format only
etext = []
if hasattr(self, 'cov_type') and 'description' in self.cov_kwds:
etext.append(self.cov_kwds['description'])
if etext:
etext = ["[{0}] {1}".format(i + 1, text)
for i, text in enumerate(etext)]
etext.insert(0, "Warnings:")
summary.add_extra_txt(etext)
return summary
class MLEResultsWrapper(wrap.ResultsWrapper):
_attrs = {}
_wrap_attrs = wrap.union_dicts(tsbase.TimeSeriesResultsWrapper._wrap_attrs,
_attrs)
# TODO right now, predict with full_results=True can return something other
# than a time series, so the `attach_dates` call will fail if we have
# 'predict': 'dates' here. In the future, remove `full_results` and replace
# it with new methods, e.g. get_prediction, get_forecast, and likely will
# want those to be a subclass of FilterResults with e.g. confidence
# intervals calculated and dates attached.
# Also, need to modify `attach_dates` to account for DataFrames.
_methods = {'predict': None}
_wrap_methods = wrap.union_dicts(tsbase.TimeSeriesResultsWrapper._wrap_methods,
_methods)
wrap.populate_wrapper(MLEResultsWrapper, MLEResults)