"""Vector Autoregressive Moving Average with eXogenous regressors model (VARMAX)."""
__all__ = ["VARMAX"]
__author__ = ["KatieBuc"]
import warnings
import pandas as pd
from sktime.forecasting.base.adapters import _StatsModelsAdapter
[文档]class VARMAX(_StatsModelsAdapter):
r"""VARMAX forecasting model from statsmodels.
Direct interface to ``VARMAX`` from ``statsmodels.tsa.statespace.varmax``.
Vector Autoregressive Moving Average with eXogenous regressors model (VARMAX)
Parameters
----------
order : iterable
The (p,q) order of the model for the number of AR and MA parameters to
use.
trend : str{'n','c','t','ct'} or iterable, optional
Parameter controlling the deterministic trend polynomial :math:`A(t)`.
Can be specified as a string where 'c' indicates a constant (i.e. a
degree zero component of the trend polynomial), 't' indicates a
linear trend with time, and 'ct' is both. Can also be specified as an
iterable defining the non-zero polynomial exponents to include, in
increasing order. For example, ``[1,1,0,1]`` denotes
:math:`a + bt + ct^3`. Default is a constant trend component.
error_cov_type : {'diagonal', 'unstructured'}, optional
The structure of the covariance matrix of the error term, where
"unstructured" puts no restrictions on the matrix and "diagonal"
requires it to be a diagonal matrix (uncorrelated errors). Default is
"unstructured".
measurement_error : bool, optional
Whether or not to assume the endogenous observations ``endog`` were
measured with error. Default is False.
enforce_stationarity : bool, optional
Whether or not to transform the AR parameters to enforce stationarity
in the autoregressive component of the model. Default is True.
enforce_invertibility : bool, optional
Whether or not to transform the MA parameters to enforce invertibility
in the moving average component of the model. Default is True.
trend_offset : int, optional
The offset at which to start time trend values. Default is 1, so that
if ``trend='t'`` the trend is equal to 1, 2, ..., n_obs. Typically is only
set when the model created by extending a previous dataset.
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 : bool, optional
Whether or not start_params is already transformed. Default is True.
includes_fixed : bool, optional
If parameters were previously fixed with the fix_params method, this
argument describes whether or not start_params also includes the
fixed parameters, in addition to the free parameters. Default is False.
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)
- 'approx' for the observed information matrix estimator,
calculated using a numerical approximation of the Hessian matrix.
- 'robust' for an approximate (quasi-maximum likelihood) covariance
matrix that may be valid even in the presence of some
misspecifications. Intermediate calculations use the 'oim'
method.
- 'robust_approx' is the same as 'robust' except that the
intermediate calculations use the 'approx' method.
- 'none' for no covariance matrix calculation.
Default is 'opg' unless memory conservation is used to avoid computing the
loglikelihood values for each observation, in which case the default is
'approx'.
cov_kwds : dict or None, optional
A dictionary of arguments affecting covariance matrix computation.
opg, oim, approx, robust, robust_approx
- 'approx_complex_step' : bool, optional - If True, numerical
approximations are computed using complex-step methods. If False,
numerical approximations are computed using finite difference
methods. Default is True.
- 'approx_centered' : bool, optional - If True, numerical
approximations computed using finite difference methods use a
centered approximation. Default is False.
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.
maxiter : int, optional
The maximum number of iterations to perform.
full_output : bool, 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 : bool, 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 : bool, optional
Whether or not to return only the array of maximizing parameters.
Default is False.
optim_score : {'harvey', 'approx'} or None, optional
The method by which the score vector is calculated. 'harvey' uses
the method from Harvey (1989), 'approx' uses either finite
difference or complex step differentiation depending upon the
value of ``optim_complex_step``, and None uses the built-in gradient
approximation of the optimizer. Default is None. This keyword is
only relevant if the optimization method uses the score.
optim_complex_step : bool, optional
Whether or not to use complex step differentiation when
approximating the score; if False, finite difference approximation
is used. Default is True. This keyword is only relevant if
``optim_score`` is set to 'harvey' or 'approx'.
optim_hessian : {'opg','oim','approx'}, 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 'approx' uses numerical
approximation. This keyword is only relevant if the
optimization method uses the Hessian matrix.
low_memory : bool, optional
If set to True, techniques are applied to substantially reduce
memory usage. If used, some features of the results object will
not be available (including smoothed results and in-sample
prediction), although out-of-sample forecasting is possible.
Default is False.
dynamic : bool, 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.
information_set : str, optional
The information set to condition each prediction on. Default is
"predicted", which computes predictions of period t values
conditional on observed data through period t-1; these are
one-step-ahead predictions, and correspond with the typical
``fittedvalues`` results attribute. Alternatives are "filtered",
which computes predictions of period t values conditional on
observed data through period t, and "smoothed", which computes
predictions of period t values conditional on the entire dataset
(including also future observations t+1, t+2, ...).
signal_only : bool, optional
Whether to compute predictions of only the "signal" component of
the observation equation. Default is False. For example, the
observation equation of a time-invariant model is
:math:`y_t = d + Z \alpha_t + \varepsilon_t`, and the "signal"
component is then :math:`Z \alpha_t`. If this argument is set to
True, then predictions of the "signal" :math:`Z \alpha_t` will be
returned. Otherwise, the default is for predictions of :math:`y_t`
to be returned.
suppress_warnings : bool, optional
Many warnings might be thrown inside of statsmodels. If
``suppress_warnings`` is True, all of these warnings will be squelched.
Default is False.
Notes
-----
Generically, the VARMAX model is specified (see for example chapter 18 of
[1]_):
.. math::
y_t = A(t) + A_1 y_{t-1} + \dots + A_p y_{t-p} + B x_t + \epsilon_t +
M_1 \epsilon_{t-1} + \dots M_q \epsilon_{t-q}
where :math:`\epsilon_t \sim N(0, \Omega)`, and where :math:`y_t` is a
``k_endog x 1`` vector. Additionally, this model allows considering the case
where the variables are measured with error.
Note that in the full VARMA(p,q) case there is a fundamental identification
problem in that the coefficient matrices :math:`\{A_i, M_j\}` are not
generally unique, meaning that for a given time series process there may
be multiple sets of matrices that equivalently represent it. See Chapter 12
of [1]_ for more information. Although this class can be used to estimate
VARMA(p,q) models, a warning is issued to remind users that no steps have
been taken to ensure identification in this case.
References
----------
.. [1] Lütkepohl, Helmut. 2007.
New Introduction to Multiple Time Series Analysis.
Berlin: Springer.
Examples
--------
>>> from sktime.forecasting.varmax import VARMAX
>>> from sktime.datasets import load_macroeconomic
>>> from sktime.split import temporal_train_test_split
>>> y = load_macroeconomic() # doctest: +SKIP
>>> forecaster = VARMAX(suppress_warnings=True) # doctest: +SKIP
>>> forecaster.fit(y[['realgdp', 'unemp']]) # doctest: +SKIP
VARMAX(...)
>>> y_pred = forecaster.predict(fh=[1,4,12]) # doctest: +SKIP
"""
_tags = {
# packaging info
# --------------
"authors": ["ChadFulton", "bashtage", "KatieBuc"],
# ChadFulton and bashtage for statsnodels VARMAX
# "python_dependencies": "statsmodels" - inherited from _StatsModelsAdapter
# estimator type
# --------------
"scitype:y": "multivariate",
"ignores-exogeneous-X": False,
"handles-missing-data": False,
"y_inner_mtype": "pd.DataFrame",
"X_inner_mtype": "pd.DataFrame",
"requires-fh-in-fit": False,
"X-y-must-have-same-index": True,
"enforce_index_type": None,
"capability:pred_int": False,
"capability:pred_int:insample": False,
}
def __init__(
self,
order=(1, 0),
trend="c",
error_cov_type="unstructured",
measurement_error=False,
enforce_stationarity=True,
enforce_invertibility=True,
trend_offset=1,
start_params=None,
transformed=True,
includes_fixed=False,
cov_type=None,
cov_kwds=None,
method="lbfgs",
maxiter=50,
full_output=1,
disp=False,
callback=None,
return_params=False,
optim_score=None,
optim_complex_step=None,
optim_hessian=None,
flags=None,
low_memory=False,
dynamic=False,
information_set="predicted",
signal_only=False,
suppress_warnings=False,
):
# Model parameters
self.order = order
self.trend = trend
self.error_cov_type = error_cov_type
self.measurement_error = measurement_error
self.enforce_stationarity = enforce_stationarity
self.enforce_invertibility = enforce_invertibility
self.trend_offset = trend_offset
self.start_params = start_params
self.transformed = transformed
self.includes_fixed = includes_fixed
self.cov_type = cov_type
self.cov_kwds = cov_kwds
self.method = method
self.maxiter = maxiter
self.full_output = full_output
self.disp = disp
self.callback = callback
self.return_params = return_params
self.optim_score = optim_score
self.optim_complex_step = optim_complex_step
self.optim_hessian = optim_hessian
self.flags = flags
self.low_memory = low_memory
self.dynamic = dynamic
self.information_set = information_set
self.signal_only = signal_only
self.suppress_warnings = suppress_warnings
super().__init__()
def _fit_forecaster(self, y, X=None):
"""Fit forecaster to training data.
Writes to self:
Sets fitted model attributes ending in "_".
Parameters
----------
y : array_like
The observed time-series process :math:`y`, shaped n_obs x k_endog.
X : array_like, optional (default=None)
Array of exogenous regressors, shaped n_obs x k.
Returns
-------
self : reference to self
"""
if self.suppress_warnings:
warnings.filterwarnings("ignore")
from statsmodels.tsa.statespace.varmax import VARMAX as _VARMAX
self._forecaster = _VARMAX(
endog=y,
exog=X,
order=self.order,
trend=self.trend,
error_cov_type=self.error_cov_type,
measurement_error=self.measurement_error,
enforce_stationarity=self.enforce_stationarity,
enforce_invertibility=self.enforce_invertibility,
trend_offset=self.trend_offset,
)
self._fitted_forecaster = self._forecaster.fit(
start_params=self.start_params,
transformed=self.transformed,
includes_fixed=self.includes_fixed,
cov_type=self.cov_type,
cov_kwds=self.cov_kwds,
method=self.method,
maxiter=self.maxiter,
full_output=self.full_output,
disp=self.disp,
callback=self.callback,
return_params=self.return_params,
optim_score=self.optim_score,
optim_complex_step=self.optim_complex_step,
optim_hessian=self.optim_hessian,
flags=self.flags,
low_memory=self.low_memory,
)
return self
# defining `_predict`, instead of inheriting from `_StatsModelsAdapter`,
# for two reasons:
# 1. to pass in `dynamic`, `information_set` and `signal_only`
# 2. to deal with statsmodel integer indexing issue
def _predict(self, fh, X):
"""Wrap Statmodel's VARMAX forecast method.
Parameters
----------
fh : ForecastingHorizon
The forecasters horizon with the steps ahead to to predict.
Default is one-step ahead forecast,
i.e. np.array([1])
X : pd.DataFrame, optional (default=None)
Exogenous variables.
Returns
-------
y_pred : np.ndarray
Returns series of predicted values.
"""
abs_idx = fh.to_absolute_int(self._y.index[0], self.cutoff)
start, end = abs_idx[[0, -1]]
full_range = pd.RangeIndex(start=start, stop=end + 1)
y_pred = self._fitted_forecaster.predict(
start=start,
end=end,
dynamic=self.dynamic,
information_set=self.information_set,
signal_only=self.signal_only,
exog=X,
)
y_pred.index = full_range
y_pred = y_pred.loc[abs_idx.to_pandas()]
y_pred.index = fh.to_absolute_index(self.cutoff)
return y_pred
[文档] @classmethod
def get_test_params(cls, parameter_set="default"):
"""Return testing parameter settings for the estimator.
Parameters
----------
parameter_set : str, default="default"
Name of the set of test parameters to return, for use in tests. If no
special parameters are defined for a value, will return ``"default"`` set.
There are currently no reserved values for forecasters.
Returns
-------
params : dict or list of dict, default = {}
Parameters to create testing instances of the class
Each dict are parameters to construct an "interesting" test instance, i.e.,
``MyClass(**params)`` or ``MyClass(**params[i])`` creates a valid test
instance.
``create_test_instance`` uses the first (or only) dictionary in ``params``
"""
params = [
{"order": (1, 0)},
{"order": (0, 1)},
{"order": (1, 1)},
]
return params
