Source code for statsmodels.tsa.statespace.simulation_smoother
"""
State Space Representation, Kalman Filter, Smoother, and Simulation Smoother
Author: Chad Fulton
License: Simplified-BSD
"""
import numbers
import warnings
import numpy as np
from .kalman_smoother import KalmanSmoother
from .cfa_simulation_smoother import CFASimulationSmoother
from . import tools
SIMULATION_STATE = 0x01
SIMULATION_DISTURBANCE = 0x04
SIMULATION_ALL = (
SIMULATION_STATE | SIMULATION_DISTURBANCE
)
# Based on scipy.states._qmc.check_random_state
def check_random_state(seed=None):
"""Turn `seed` into a `numpy.random.Generator` instance.
Parameters
----------
seed : {None, int, Generator, RandomState}, optional
If `seed` is None (or `np.random`), the `numpy.random.RandomState`
singleton is used.
If `seed` is an int, a new ``numpy.random.RandomState`` instance
is used, seeded with `seed`.
If `seed` is already a ``numpy.random.Generator`` or
``numpy.random.RandomState`` instance then that instance is used.
Returns
-------
seed : {`numpy.random.Generator`, `numpy.random.RandomState`}
Random number generator.
"""
if seed is None or isinstance(seed, (numbers.Integral, np.integer)):
return np.random.default_rng(seed)
elif isinstance(seed, (np.random.RandomState, np.random.Generator)):
return seed
else:
raise ValueError(f'{seed!r} cannot be used to seed a'
' numpy.random.Generator instance')
[docs]
class SimulationSmoother(KalmanSmoother):
r"""
State space representation of a time series process, with Kalman filter
and smoother, and with simulation smoother.
Parameters
----------
k_endog : {array_like, int}
The observed time-series process :math:`y` if array like or the
number of variables in the process if an integer.
k_states : int
The dimension of the unobserved state process.
k_posdef : int, optional
The dimension of a guaranteed positive definite covariance matrix
describing the shocks in the measurement equation. Must be less than
or equal to `k_states`. Default is `k_states`.
simulation_smooth_results_class : class, optional
Default results class to use to save output of simulation smoothing.
Default is `SimulationSmoothResults`. If specified, class must extend
from `SimulationSmoothResults`.
simulation_smoother_classes : dict, optional
Dictionary with BLAS prefixes as keys and classes as values.
**kwargs
Keyword arguments may be used to provide default values for state space
matrices, for Kalman filtering options, for Kalman smoothing
options, or for Simulation smoothing options.
See `Representation`, `KalmanFilter`, and `KalmanSmoother` for more
details.
"""
simulation_outputs = [
'simulate_state', 'simulate_disturbance', 'simulate_all'
]
def __init__(self, k_endog, k_states, k_posdef=None,
simulation_smooth_results_class=None,
simulation_smoother_classes=None, **kwargs):
super().__init__(
k_endog, k_states, k_posdef, **kwargs
)
if simulation_smooth_results_class is None:
simulation_smooth_results_class = SimulationSmoothResults
self.simulation_smooth_results_class = simulation_smooth_results_class
self.prefix_simulation_smoother_map = (
simulation_smoother_classes
if simulation_smoother_classes is not None
else tools.prefix_simulation_smoother_map.copy())
# Holder for an model-level simulation smoother objects, to use in
# simulating new time series.
self._simulators = {}
[docs]
def get_simulation_output(self, simulation_output=None,
simulate_state=None, simulate_disturbance=None,
simulate_all=None, **kwargs):
r"""
Get simulation output bitmask
Helper method to get final simulation output bitmask from a set of
optional arguments including the bitmask itself and possibly boolean
flags.
Parameters
----------
simulation_output : int, optional
Simulation output bitmask. If this is specified, it is simply
returned and the other arguments are ignored.
simulate_state : bool, optional
Whether or not to include the state in the simulation output.
simulate_disturbance : bool, optional
Whether or not to include the state and observation disturbances
in the simulation output.
simulate_all : bool, optional
Whether or not to include all simulation output.
\*\*kwargs
Additional keyword arguments. Present so that calls to this method
can use \*\*kwargs without clearing out additional arguments.
"""
# If we do not explicitly have simulation_output, try to get it from
# kwargs
if simulation_output is None:
simulation_output = 0
if simulate_state:
simulation_output |= SIMULATION_STATE
if simulate_disturbance:
simulation_output |= SIMULATION_DISTURBANCE
if simulate_all:
simulation_output |= SIMULATION_ALL
# Handle case of no information in kwargs
if simulation_output == 0:
# If some arguments were passed, but we still do not have any
# simulation output, raise an exception
argument_set = not all([
simulate_state is None, simulate_disturbance is None,
simulate_all is None
])
if argument_set:
raise ValueError("Invalid simulation output options:"
" given options would result in no"
" output.")
# Otherwise set simulation output to be the same as smoother
# output
simulation_output = self.smoother_output
return simulation_output
def _simulate(self, nsimulations, simulator=None, random_state=None,
return_simulator=False, **kwargs):
# Create the simulator, if necessary
if simulator is None:
simulator = self.simulator(nsimulations, random_state=random_state)
# Perform simulation smoothing
simulator.simulate(**kwargs)
# Retrieve and return the objects of interest
simulated_obs = np.array(simulator.generated_obs, copy=True)
simulated_state = np.array(simulator.generated_state, copy=True)
out = (simulated_obs.T[:nsimulations],
simulated_state.T[:nsimulations])
if return_simulator:
out = out + (simulator,)
return out
[docs]
def simulator(self, nsimulations, random_state=None):
return self.simulation_smoother(simulation_output=0, method='kfs',
nobs=nsimulations,
random_state=random_state)
[docs]
def simulation_smoother(self, simulation_output=None, method='kfs',
results_class=None, prefix=None, nobs=-1,
random_state=None, **kwargs):
r"""
Retrieve a simulation smoother for the statespace model.
Parameters
----------
simulation_output : int, optional
Determines which simulation smoother output is calculated.
Default is all (including state and disturbances).
method : {'kfs', 'cfa'}, optional
Method for simulation smoothing. If `method='kfs'`, then the
simulation smoother is based on Kalman filtering and smoothing
recursions. If `method='cfa'`, then the simulation smoother is
based on the Cholesky Factor Algorithm (CFA) approach. The CFA
approach is not applicable to all state space models, but can be
faster for the cases in which it is supported.
results_class : class, optional
Default results class to use to save output of simulation
smoothing. Default is `SimulationSmoothResults`. If specified,
class must extend from `SimulationSmoothResults`.
prefix : str
The prefix of the datatype. Usually only used internally.
nobs : int
The number of observations to simulate. If set to anything other
than -1, only simulation will be performed (i.e. simulation
smoothing will not be performed), so that only the `generated_obs`
and `generated_state` attributes will be available.
random_state : {None, int, Generator, RandomState}, optional
If `seed` is None (or `np.random`), the `numpy.random.RandomState`
singleton is used.
If `seed` is an int, a new ``numpy.random.RandomState`` instance
is used, seeded with `seed`.
If `seed` is already a ``numpy.random.Generator`` or
``numpy.random.RandomState`` instance then that instance is used.
**kwargs
Additional keyword arguments, used to set the simulation output.
See `set_simulation_output` for more details.
Returns
-------
SimulationSmoothResults
"""
method = method.lower()
# Short-circuit for CFA
if method == 'cfa':
if simulation_output not in [None, 1, -1]:
raise ValueError('Can only retrieve simulations of the state'
' vector using the CFA simulation smoother.')
return CFASimulationSmoother(self)
elif method != 'kfs':
raise ValueError('Invalid simulation smoother method "%s". Valid'
' methods are "kfs" or "cfa".' % method)
# Set the class to be the default results class, if None provided
if results_class is None:
results_class = self.simulation_smooth_results_class
# Instantiate a new results object
if not issubclass(results_class, SimulationSmoothResults):
raise ValueError('Invalid results class provided.')
# Make sure we have the required Statespace representation
prefix, dtype, create_smoother, create_filter, create_statespace = (
self._initialize_smoother())
# Simulation smoother parameters
simulation_output = self.get_simulation_output(simulation_output,
**kwargs)
# Kalman smoother parameters
smoother_output = kwargs.get('smoother_output', simulation_output)
# Kalman filter parameters
filter_method = kwargs.get('filter_method', self.filter_method)
inversion_method = kwargs.get('inversion_method',
self.inversion_method)
stability_method = kwargs.get('stability_method',
self.stability_method)
conserve_memory = kwargs.get('conserve_memory',
self.conserve_memory)
filter_timing = kwargs.get('filter_timing',
self.filter_timing)
loglikelihood_burn = kwargs.get('loglikelihood_burn',
self.loglikelihood_burn)
tolerance = kwargs.get('tolerance', self.tolerance)
# Create a new simulation smoother object
cls = self.prefix_simulation_smoother_map[prefix]
simulation_smoother = cls(
self._statespaces[prefix],
filter_method, inversion_method, stability_method, conserve_memory,
filter_timing, tolerance, loglikelihood_burn, smoother_output,
simulation_output, nobs
)
# Create results object
results = results_class(self, simulation_smoother,
random_state=random_state)
return results
[docs]
class SimulationSmoothResults:
r"""
Results from applying the Kalman smoother and/or filter to a state space
model.
Parameters
----------
model : Representation
A Statespace representation
simulation_smoother : {{prefix}}SimulationSmoother object
The Cython simulation smoother object with which to simulation smooth.
random_state : {None, int, Generator, RandomState}, optional
If `seed` is None (or `np.random`), the `numpy.random.RandomState`
singleton is used.
If `seed` is an int, a new ``numpy.random.RandomState`` instance
is used, seeded with `seed`.
If `seed` is already a ``numpy.random.Generator`` or
``numpy.random.RandomState`` instance then that instance is used.
Attributes
----------
model : Representation
A Statespace representation
dtype : dtype
Datatype of representation matrices
prefix : str
BLAS prefix of representation matrices
simulation_output : int
Bitmask controlling simulation output.
simulate_state : bool
Flag for if the state is included in simulation output.
simulate_disturbance : bool
Flag for if the state and observation disturbances are included in
simulation output.
simulate_all : bool
Flag for if simulation output should include everything.
generated_measurement_disturbance : ndarray
Measurement disturbance variates used to genereate the observation
vector.
generated_state_disturbance : ndarray
State disturbance variates used to genereate the state and
observation vectors.
generated_obs : ndarray
Generated observation vector produced as a byproduct of simulation
smoothing.
generated_state : ndarray
Generated state vector produced as a byproduct of simulation smoothing.
simulated_state : ndarray
Simulated state.
simulated_measurement_disturbance : ndarray
Simulated measurement disturbance.
simulated_state_disturbance : ndarray
Simulated state disturbance.
"""
def __init__(self, model, simulation_smoother, random_state=None):
self.model = model
self.prefix = model.prefix
self.dtype = model.dtype
self._simulation_smoother = simulation_smoother
self.random_state = check_random_state(random_state)
# Output
self._generated_measurement_disturbance = None
self._generated_state_disturbance = None
self._generated_obs = None
self._generated_state = None
self._simulated_state = None
self._simulated_measurement_disturbance = None
self._simulated_state_disturbance = None
@property
def simulation_output(self):
return self._simulation_smoother.simulation_output
@simulation_output.setter
def simulation_output(self, value):
self._simulation_smoother.simulation_output = value
@property
def simulate_state(self):
return bool(self.simulation_output & SIMULATION_STATE)
@simulate_state.setter
def simulate_state(self, value):
if bool(value):
self.simulation_output = self.simulation_output | SIMULATION_STATE
else:
self.simulation_output = self.simulation_output & ~SIMULATION_STATE
@property
def simulate_disturbance(self):
return bool(self.simulation_output & SIMULATION_DISTURBANCE)
@simulate_disturbance.setter
def simulate_disturbance(self, value):
if bool(value):
self.simulation_output = (
self.simulation_output | SIMULATION_DISTURBANCE)
else:
self.simulation_output = (
self.simulation_output & ~SIMULATION_DISTURBANCE)
@property
def simulate_all(self):
return bool(self.simulation_output & SIMULATION_ALL)
@simulate_all.setter
def simulate_all(self, value):
if bool(value):
self.simulation_output = self.simulation_output | SIMULATION_ALL
else:
self.simulation_output = self.simulation_output & ~SIMULATION_ALL
@property
def generated_measurement_disturbance(self):
r"""
Randomly drawn measurement disturbance variates
Used to construct `generated_obs`.
Notes
-----
.. math::
\varepsilon_t^+ ~ N(0, H_t)
If `disturbance_variates` were provided to the `simulate()` method,
then this returns those variates (which were N(0,1)) transformed to the
distribution above.
"""
if self._generated_measurement_disturbance is None:
self._generated_measurement_disturbance = np.array(
self._simulation_smoother.measurement_disturbance_variates,
copy=True).reshape(self.model.nobs, self.model.k_endog)
return self._generated_measurement_disturbance
@property
def generated_state_disturbance(self):
r"""
Randomly drawn state disturbance variates, used to construct
`generated_state` and `generated_obs`.
Notes
-----
.. math::
\eta_t^+ ~ N(0, Q_t)
If `disturbance_variates` were provided to the `simulate()` method,
then this returns those variates (which were N(0,1)) transformed to the
distribution above.
"""
if self._generated_state_disturbance is None:
self._generated_state_disturbance = np.array(
self._simulation_smoother.state_disturbance_variates,
copy=True).reshape(self.model.nobs, self.model.k_posdef)
return self._generated_state_disturbance
@property
def generated_obs(self):
r"""
Generated vector of observations by iterating on the observation and
transition equations, given a random initial state draw and random
disturbance draws.
Notes
-----
.. math::
y_t^+ = d_t + Z_t \alpha_t^+ + \varepsilon_t^+
"""
if self._generated_obs is None:
self._generated_obs = np.array(
self._simulation_smoother.generated_obs, copy=True
)
return self._generated_obs
@property
def generated_state(self):
r"""
Generated vector of states by iterating on the transition equation,
given a random initial state draw and random disturbance draws.
Notes
-----
.. math::
\alpha_{t+1}^+ = c_t + T_t \alpha_t^+ + \eta_t^+
"""
if self._generated_state is None:
self._generated_state = np.array(
self._simulation_smoother.generated_state, copy=True
)
return self._generated_state
@property
def simulated_state(self):
r"""
Random draw of the state vector from its conditional distribution.
Notes
-----
.. math::
\alpha ~ p(\alpha \mid Y_n)
"""
if self._simulated_state is None:
self._simulated_state = np.array(
self._simulation_smoother.simulated_state, copy=True
)
return self._simulated_state
@property
def simulated_measurement_disturbance(self):
r"""
Random draw of the measurement disturbance vector from its conditional
distribution.
Notes
-----
.. math::
\varepsilon ~ N(\hat \varepsilon, Var(\hat \varepsilon \mid Y_n))
"""
if self._simulated_measurement_disturbance is None:
self._simulated_measurement_disturbance = np.array(
self._simulation_smoother.simulated_measurement_disturbance,
copy=True
)
return self._simulated_measurement_disturbance
@property
def simulated_state_disturbance(self):
r"""
Random draw of the state disturbanc e vector from its conditional
distribution.
Notes
-----
.. math::
\eta ~ N(\hat \eta, Var(\hat \eta \mid Y_n))
"""
if self._simulated_state_disturbance is None:
self._simulated_state_disturbance = np.array(
self._simulation_smoother.simulated_state_disturbance,
copy=True
)
return self._simulated_state_disturbance
[docs]
def simulate(self, simulation_output=-1,
disturbance_variates=None,
measurement_disturbance_variates=None,
state_disturbance_variates=None,
initial_state_variates=None,
pretransformed=None,
pretransformed_measurement_disturbance_variates=None,
pretransformed_state_disturbance_variates=None,
pretransformed_initial_state_variates=False,
random_state=None):
r"""
Perform simulation smoothing
Does not return anything, but populates the object's `simulated_*`
attributes, as specified by simulation output.
Parameters
----------
simulation_output : int, optional
Bitmask controlling simulation output. Default is to use the
simulation output defined in object initialization.
measurement_disturbance_variates : array_like, optional
If specified, these are the shocks to the measurement equation,
:math:`\varepsilon_t`. If unspecified, these are automatically
generated using a pseudo-random number generator. If specified,
must be shaped `nsimulations` x `k_endog`, where `k_endog` is the
same as in the state space model.
state_disturbance_variates : array_like, optional
If specified, these are the shocks to the state equation,
:math:`\eta_t`. If unspecified, these are automatically
generated using a pseudo-random number generator. If specified,
must be shaped `nsimulations` x `k_posdef` where `k_posdef` is the
same as in the state space model.
initial_state_variates : array_like, optional
If specified, this is the state vector at time zero, which should
be shaped (`k_states` x 1), where `k_states` is the same as in the
state space model. If unspecified, but the model has been
initialized, then that initialization is used.
initial_state_variates : array_likes, optional
Random values to use as initial state variates. Usually only
specified if results are to be replicated (e.g. to enforce a seed)
or for testing. If not specified, random variates are drawn.
pretransformed_measurement_disturbance_variates : bool, optional
If `measurement_disturbance_variates` is provided, this flag
indicates whether it should be directly used as the shocks. If
False, then it is assumed to contain draws from the standard Normal
distribution that must be transformed using the `obs_cov`
covariance matrix. Default is False.
pretransformed_state_disturbance_variates : bool, optional
If `state_disturbance_variates` is provided, this flag indicates
whether it should be directly used as the shocks. If False, then it
is assumed to contain draws from the standard Normal distribution
that must be transformed using the `state_cov` covariance matrix.
Default is False.
pretransformed_initial_state_variates : bool, optional
If `initial_state_variates` is provided, this flag indicates
whether it should be directly used as the initial_state. If False,
then it is assumed to contain draws from the standard Normal
distribution that must be transformed using the `initial_state_cov`
covariance matrix. Default is False.
random_state : {None, int, Generator, RandomState}, optional
If `seed` is None (or `np.random`), the `numpy.random.RandomState`
singleton is used.
If `seed` is an int, a new ``numpy.random.RandomState`` instance
is used, seeded with `seed`.
If `seed` is already a ``numpy.random.Generator`` or
``numpy.random.RandomState`` instance then that instance is used.
disturbance_variates : bool, optional
Deprecated, please use pretransformed_measurement_shocks and
pretransformed_state_shocks instead.
.. deprecated:: 0.14.0
Use ``measurement_disturbance_variates`` and
``state_disturbance_variates`` as replacements.
pretransformed : bool, optional
Deprecated, please use pretransformed_measurement_shocks and
pretransformed_state_shocks instead.
.. deprecated:: 0.14.0
Use ``pretransformed_measurement_disturbance_variates`` and
``pretransformed_state_disturbance_variates`` as replacements.
"""
# Handle deprecated argumennts
if disturbance_variates is not None:
msg = ('`disturbance_variates` keyword is deprecated, use'
' `measurement_disturbance_variates` and'
' `state_disturbance_variates` instead.')
warnings.warn(msg, FutureWarning)
if (measurement_disturbance_variates is not None
or state_disturbance_variates is not None):
raise ValueError('Cannot use `disturbance_variates` in'
' combination with '
' `measurement_disturbance_variates` or'
' `state_disturbance_variates`.')
if disturbance_variates is not None:
disturbance_variates = disturbance_variates.ravel()
n_mds = self.model.nobs * self.model.k_endog
measurement_disturbance_variates = disturbance_variates[:n_mds]
state_disturbance_variates = disturbance_variates[n_mds:]
if pretransformed is not None:
msg = ('`pretransformed` keyword is deprecated, use'
' `pretransformed_measurement_disturbance_variates` and'
' `pretransformed_state_disturbance_variates` instead.')
warnings.warn(msg, FutureWarning)
if (pretransformed_measurement_disturbance_variates is not None
or pretransformed_state_disturbance_variates is not None):
raise ValueError(
'Cannot use `pretransformed` in combination with '
' `pretransformed_measurement_disturbance_variates` or'
' `pretransformed_state_disturbance_variates`.')
if pretransformed is not None:
pretransformed_measurement_disturbance_variates = (
pretransformed)
pretransformed_state_disturbance_variates = pretransformed
if pretransformed_measurement_disturbance_variates is None:
pretransformed_measurement_disturbance_variates = False
if pretransformed_state_disturbance_variates is None:
pretransformed_state_disturbance_variates = False
# Clear any previous output
self._generated_measurement_disturbance = None
self._generated_state_disturbance = None
self._generated_state = None
self._generated_obs = None
self._generated_state = None
self._simulated_state = None
self._simulated_measurement_disturbance = None
self._simulated_state_disturbance = None
# Handle the random state
if random_state is None:
random_state = self.random_state
else:
random_state = check_random_state(random_state)
# Re-initialize the _statespace representation
prefix, dtype, create_smoother, create_filter, create_statespace = (
self.model._initialize_smoother())
if create_statespace:
raise ValueError('The simulation smoother currently cannot replace'
' the underlying _{{prefix}}Representation model'
' object if it changes (which happens e.g. if the'
' dimensions of some system matrices change.')
# Initialize the state
self.model._initialize_state(prefix=prefix)
# Draw the (independent) random variates for disturbances in the
# simulation
if measurement_disturbance_variates is not None:
self._simulation_smoother.set_measurement_disturbance_variates(
np.array(measurement_disturbance_variates,
dtype=self.dtype).ravel(),
pretransformed=pretransformed_measurement_disturbance_variates
)
else:
self._simulation_smoother.draw_measurement_disturbance_variates(
random_state)
# Draw the (independent) random variates for disturbances in the
# simulation
if state_disturbance_variates is not None:
self._simulation_smoother.set_state_disturbance_variates(
np.array(state_disturbance_variates, dtype=self.dtype).ravel(),
pretransformed=pretransformed_state_disturbance_variates
)
else:
self._simulation_smoother.draw_state_disturbance_variates(
random_state)
# Draw the (independent) random variates for the initial states in the
# simulation
if initial_state_variates is not None:
if pretransformed_initial_state_variates:
self._simulation_smoother.set_initial_state(
np.array(initial_state_variates, dtype=self.dtype)
)
else:
self._simulation_smoother.set_initial_state_variates(
np.array(initial_state_variates, dtype=self.dtype),
pretransformed=False
)
# Note: there is a third option, which is to set the initial state
# variates with pretransformed = True. However, this option simply
# eliminates the multiplication by the Cholesky factor of the
# initial state cov, but still adds the initial state mean. It's
# not clear when this would be useful...
else:
self._simulation_smoother.draw_initial_state_variates(
random_state)
# Perform simulation smoothing
self._simulation_smoother.simulate(simulation_output)
Last update:
Nov 14, 2024