Source code for statsmodels.tsa.statespace.varmax

# -*- coding: utf-8 -*-
"""
Vector Autoregressive Moving Average with eXogenous regressors model

Author: Chad Fulton
License: Simplified-BSD
"""
from __future__ import division, absolute_import, print_function

from warnings import warn
from collections import OrderedDict

import pandas as pd
import numpy as np

from statsmodels.tools.tools import Bunch
from statsmodels.tools.data import _is_using_pandas
from statsmodels.tsa.vector_ar import var_model
import statsmodels.base.wrapper as wrap
from statsmodels.tools.sm_exceptions import EstimationWarning, ValueWarning

from .kalman_filter import INVERT_UNIVARIATE, SOLVE_LU
from .mlemodel import MLEModel, MLEResults, MLEResultsWrapper
from .tools import (
    is_invertible, prepare_exog,
    constrain_stationary_multivariate, unconstrain_stationary_multivariate,
    prepare_trend_spec, prepare_trend_data
)


[docs]class VARMAX(MLEModel): r""" Vector Autoregressive Moving Average with eXogenous regressors model Parameters ---------- endog : array_like The observed time-series process :math:`y`, , shaped nobs x k_endog. exog : array_like, optional Array of exogenous regressors, shaped nobs x k. 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 polynomial as in `numpy.poly1d`, where `[1,1,0,1]` would denote :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 : boolean, optional Whether or not to assume the endogenous observations `endog` were measured with error. Default is False. enforce_stationarity : boolean, optional Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. Default is True. enforce_invertibility : boolean, optional Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. Default is True. 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 ---------- 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 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 polynomial as in `numpy.poly1d`, where `[1,1,0,1]` would denote :math:`a + bt + ct^3`. 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 : boolean, optional Whether or not to assume the endogenous observations `endog` were measured with error. Default is False. enforce_stationarity : boolean, optional Whether or not to transform the AR parameters to enforce stationarity in the autoregressive component of the model. Default is True. enforce_invertibility : boolean, optional Whether or not to transform the MA parameters to enforce invertibility in the moving average component of the model. Default is True. 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] L├╝tkepohl, Helmut. 2007. New Introduction to Multiple Time Series Analysis. Berlin: Springer. """ def __init__(self, endog, exog=None, order=(1, 0), trend='c', error_cov_type='unstructured', measurement_error=False, enforce_stationarity=True, enforce_invertibility=True, **kwargs): # Model parameters self.error_cov_type = error_cov_type self.measurement_error = measurement_error self.enforce_stationarity = enforce_stationarity self.enforce_invertibility = enforce_invertibility # Save the given orders self.order = order self.trend = trend # Model orders self.k_ar = int(order[0]) self.k_ma = int(order[1]) # Check for valid model if error_cov_type not in ['diagonal', 'unstructured']: raise ValueError('Invalid error covariance matrix type' ' specification.') if self.k_ar == 0 and self.k_ma == 0: raise ValueError('Invalid VARMAX(p,q) specification; at least one' ' p,q must be greater than zero.') # Warn for VARMA model if self.k_ar > 0 and self.k_ma > 0: warn('Estimation of VARMA(p,q) models is not generically robust,' ' due especially to identification issues.', EstimationWarning) # Trend self.trend = trend self.polynomial_trend, self.k_trend = prepare_trend_spec(self.trend) self._trend_is_const = (self.polynomial_trend.size == 1 and self.polynomial_trend[0] == 1) # Exogenous data (self.k_exog, exog) = prepare_exog(exog) # Note: at some point in the future might add state regression, as in # SARIMAX. self.mle_regression = self.k_exog > 0 # We need to have an array or pandas at this point if not _is_using_pandas(endog, None): endog = np.asanyarray(endog) # Model order # Used internally in various places _min_k_ar = max(self.k_ar, 1) self._k_order = _min_k_ar + self.k_ma # Number of states k_endog = endog.shape[1] k_posdef = k_endog k_states = k_endog * self._k_order # By default, initialize as stationary kwargs.setdefault('initialization', 'stationary') # By default, use LU decomposition kwargs.setdefault('inversion_method', INVERT_UNIVARIATE | SOLVE_LU) # Initialize the state space model super(VARMAX, self).__init__( endog, exog=exog, k_states=k_states, k_posdef=k_posdef, **kwargs ) # Set as time-varying model if we have time-trend or exog if self.k_exog > 0 or (self.k_trend > 0 and not self._trend_is_const): self.ssm._time_invariant = False # Initialize the parameters self.parameters = OrderedDict() self.parameters['trend'] = self.k_endog * self.k_trend self.parameters['ar'] = self.k_endog**2 * self.k_ar self.parameters['ma'] = self.k_endog**2 * self.k_ma self.parameters['regression'] = self.k_endog * self.k_exog if self.error_cov_type == 'diagonal': self.parameters['state_cov'] = self.k_endog # These parameters fill in a lower-triangular matrix which is then # dotted with itself to get a positive definite matrix. elif self.error_cov_type == 'unstructured': self.parameters['state_cov'] = ( int(self.k_endog * (self.k_endog + 1) / 2) ) self.parameters['obs_cov'] = self.k_endog * self.measurement_error self.k_params = sum(self.parameters.values()) # Initialize trend data self._trend_data = prepare_trend_data( self.polynomial_trend, self.k_trend, self.nobs, offset=1) # Initialize known elements of the state space matrices # If we have exog effects, then the state intercept needs to be # time-varying if (self.k_trend > 0 and not self._trend_is_const) or self.k_exog > 0: self.ssm['state_intercept'] = np.zeros((self.k_states, self.nobs)) # self.ssm['obs_intercept'] = np.zeros((self.k_endog, self.nobs)) # The design matrix is just an identity for the first k_endog states idx = np.diag_indices(self.k_endog) self.ssm[('design',) + idx] = 1 # The transition matrix is described in four blocks, where the upper # left block is in companion form with the autoregressive coefficient # matrices (so it is shaped k_endog * k_ar x k_endog * k_ar) ... if self.k_ar > 0: idx = np.diag_indices((self.k_ar - 1) * self.k_endog) idx = idx[0] + self.k_endog, idx[1] self.ssm[('transition',) + idx] = 1 # ... and the lower right block is in companion form with zeros as the # coefficient matrices (it is shaped k_endog * k_ma x k_endog * k_ma). idx = np.diag_indices((self.k_ma - 1) * self.k_endog) idx = (idx[0] + (_min_k_ar + 1) * self.k_endog, idx[1] + _min_k_ar * self.k_endog) self.ssm[('transition',) + idx] = 1 # The selection matrix is described in two blocks, where the upper # block selects the all k_posdef errors in the first k_endog rows # (the upper block is shaped k_endog * k_ar x k) and the lower block # also selects all k_posdef errors in the first k_endog rows (the lower # block is shaped k_endog * k_ma x k). idx = np.diag_indices(self.k_endog) self.ssm[('selection',) + idx] = 1 idx = idx[0] + _min_k_ar * self.k_endog, idx[1] if self.k_ma > 0: self.ssm[('selection',) + idx] = 1 # Cache some indices if self._trend_is_const and self.k_exog == 0: self._idx_state_intercept = np.s_['state_intercept', :k_endog, :] elif self.k_trend > 0 or self.k_exog > 0: self._idx_state_intercept = np.s_['state_intercept', :k_endog, :-1] if self.k_ar > 0: self._idx_transition = np.s_['transition', :k_endog, :] else: self._idx_transition = np.s_['transition', :k_endog, k_endog:] if self.error_cov_type == 'diagonal': self._idx_state_cov = ( ('state_cov',) + np.diag_indices(self.k_endog)) elif self.error_cov_type == 'unstructured': self._idx_lower_state_cov = np.tril_indices(self.k_endog) if self.measurement_error: self._idx_obs_cov = ('obs_cov',) + np.diag_indices(self.k_endog) # Cache some slices def _slice(key, offset): length = self.parameters[key] param_slice = np.s_[offset:offset + length] offset += length return param_slice, offset offset = 0 self._params_trend, offset = _slice('trend', offset) self._params_ar, offset = _slice('ar', offset) self._params_ma, offset = _slice('ma', offset) self._params_regression, offset = _slice('regression', offset) self._params_state_cov, offset = _slice('state_cov', offset) self._params_obs_cov, offset = _slice('obs_cov', offset) @property def _res_classes(self): return {'fit': (VARMAXResults, VARMAXResultsWrapper)} @property def start_params(self): params = np.zeros(self.k_params, dtype=np.float64) # A. Run a multivariate regression to get beta estimates endog = pd.DataFrame(self.endog.copy()) # Pandas < 0.13 didn't support the same type of DataFrame interpolation # TODO remove this now that we have dropped support for Pandas < 0.13 try: endog = endog.interpolate() except TypeError: pass endog = endog.fillna(method='backfill').values exog = None if self.k_trend > 0 and self.k_exog > 0: exog = np.c_[self._trend_data, self.exog] elif self.k_trend > 0: exog = self._trend_data elif self.k_exog > 0: exog = self.exog # Although the Kalman filter can deal with missing values in endog, # conditional sum of squares cannot if np.any(np.isnan(endog)): mask = ~np.any(np.isnan(endog), axis=1) endog = endog[mask] if exog is not None: exog = exog[mask] # Regression and trend effects via OLS trend_params = np.zeros(0) exog_params = np.zeros(0) if self.k_trend > 0 or self.k_exog > 0: trendexog_params = np.linalg.pinv(exog).dot(endog) endog -= np.dot(exog, trendexog_params) if self.k_trend > 0: trend_params = trendexog_params[:self.k_trend].T.ravel() if self.k_endog > 0: exog_params = trendexog_params[self.k_trend:].T.ravel() # B. Run a VAR model on endog to get trend, AR parameters ar_params = [] k_ar = self.k_ar if self.k_ar > 0 else 1 mod_ar = var_model.VAR(endog) res_ar = mod_ar.fit(maxlags=k_ar, ic=None, trend='nc') if self.k_ar > 0: ar_params = np.array(res_ar.params).T.ravel() endog = res_ar.resid # Test for stationarity if self.k_ar > 0 and self.enforce_stationarity: coefficient_matrices = ( ar_params.reshape( self.k_endog * self.k_ar, self.k_endog ).T ).reshape(self.k_endog, self.k_endog, self.k_ar).T stationary = is_invertible([1] + list(-coefficient_matrices)) if not stationary: warn('Non-stationary starting autoregressive parameters' ' found. Using zeros as starting parameters.') ar_params *= 0 # C. Run a VAR model on the residuals to get MA parameters ma_params = [] if self.k_ma > 0: mod_ma = var_model.VAR(endog) res_ma = mod_ma.fit(maxlags=self.k_ma, ic=None, trend='nc') ma_params = np.array(res_ma.params.T).ravel() # Test for invertibility if self.enforce_invertibility: coefficient_matrices = ( ma_params.reshape( self.k_endog * self.k_ma, self.k_endog ).T ).reshape(self.k_endog, self.k_endog, self.k_ma).T invertible = is_invertible([1] + list(-coefficient_matrices)) if not invertible: warn('Non-stationary starting moving-average parameters' ' found. Using zeros as starting parameters.') ma_params *= 0 # 1. Intercept terms if self.k_trend > 0: params[self._params_trend] = trend_params # 2. AR terms if self.k_ar > 0: params[self._params_ar] = ar_params # 3. MA terms if self.k_ma > 0: params[self._params_ma] = ma_params # 4. Regression terms if self.mle_regression: params[self._params_regression] = exog_params # 5. State covariance terms if self.error_cov_type == 'diagonal': params[self._params_state_cov] = res_ar.sigma_u.diagonal() elif self.error_cov_type == 'unstructured': cov_factor = np.linalg.cholesky(res_ar.sigma_u) params[self._params_state_cov] = ( cov_factor[self._idx_lower_state_cov].ravel()) # 5. Measurement error variance terms if self.measurement_error: if self.k_ma > 0: params[self._params_obs_cov] = res_ma.sigma_u.diagonal() else: params[self._params_obs_cov] = res_ar.sigma_u.diagonal() return params @property def param_names(self): param_names = [] # 1. Intercept terms if self.k_trend > 0: for i in self.polynomial_trend.nonzero()[0]: if i == 0: param_names += ['intercept.%s' % self.endog_names[j] for j in range(self.k_endog)] elif i == 1: param_names += ['drift.%s' % self.endog_names[j] for j in range(self.k_endog)] else: param_names += ['trend.%d.%s' % (i, self.endog_names[j]) for j in range(self.k_endog)] # 2. AR terms param_names += [ 'L%d.%s.%s' % (i+1, self.endog_names[k], self.endog_names[j]) for j in range(self.k_endog) for i in range(self.k_ar) for k in range(self.k_endog) ] # 3. MA terms param_names += [ 'L%d.e(%s).%s' % (i+1, self.endog_names[k], self.endog_names[j]) for j in range(self.k_endog) for i in range(self.k_ma) for k in range(self.k_endog) ] # 4. Regression terms param_names += [ 'beta.%s.%s' % (self.exog_names[j], self.endog_names[i]) for i in range(self.k_endog) for j in range(self.k_exog) ] # 5. State covariance terms if self.error_cov_type == 'diagonal': param_names += [ 'sigma2.%s' % self.endog_names[i] for i in range(self.k_endog) ] elif self.error_cov_type == 'unstructured': param_names += [ ('sqrt.var.%s' % self.endog_names[i] if i == j else 'sqrt.cov.%s.%s' % (self.endog_names[j], self.endog_names[i])) for i in range(self.k_endog) for j in range(i+1) ] # 5. Measurement error variance terms if self.measurement_error: param_names += [ 'measurement_variance.%s' % self.endog_names[i] for i in range(self.k_endog) ] return param_names
[docs] def transform_params(self, unconstrained): """ Transform unconstrained parameters used by the optimizer to constrained parameters used in likelihood evaluation Parameters ---------- unconstrained : array_like Array of unconstrained parameters used by the optimizer, to be transformed. Returns ------- constrained : array_like Array of constrained parameters which may be used in likelihood evalation. Notes ----- Constrains the factor transition to be stationary and variances to be positive. """ unconstrained = np.array(unconstrained, ndmin=1) constrained = np.zeros(unconstrained.shape, dtype=unconstrained.dtype) # 1. Intercept terms: nothing to do constrained[self._params_trend] = unconstrained[self._params_trend] # 2. AR terms: optionally force to be stationary if self.k_ar > 0 and self.enforce_stationarity: # Create the state covariance matrix if self.error_cov_type == 'diagonal': state_cov = np.diag(unconstrained[self._params_state_cov]**2) elif self.error_cov_type == 'unstructured': state_cov_lower = np.zeros(self.ssm['state_cov'].shape, dtype=unconstrained.dtype) state_cov_lower[self._idx_lower_state_cov] = ( unconstrained[self._params_state_cov]) state_cov = np.dot(state_cov_lower, state_cov_lower.T) # Transform the parameters coefficients = unconstrained[self._params_ar].reshape( self.k_endog, self.k_endog * self.k_ar) coefficient_matrices, variance = ( constrain_stationary_multivariate(coefficients, state_cov)) constrained[self._params_ar] = coefficient_matrices.ravel() else: constrained[self._params_ar] = unconstrained[self._params_ar] # 3. MA terms: optionally force to be invertible if self.k_ma > 0 and self.enforce_invertibility: # Transform the parameters, using an identity variance matrix state_cov = np.eye(self.k_endog, dtype=unconstrained.dtype) coefficients = unconstrained[self._params_ma].reshape( self.k_endog, self.k_endog * self.k_ma) coefficient_matrices, variance = ( constrain_stationary_multivariate(coefficients, state_cov)) constrained[self._params_ma] = coefficient_matrices.ravel() else: constrained[self._params_ma] = unconstrained[self._params_ma] # 4. Regression terms: nothing to do constrained[self._params_regression] = ( unconstrained[self._params_regression]) # 5. State covariance terms # If we have variances, force them to be positive if self.error_cov_type == 'diagonal': constrained[self._params_state_cov] = ( unconstrained[self._params_state_cov]**2) # Otherwise, nothing needs to be done elif self.error_cov_type == 'unstructured': constrained[self._params_state_cov] = ( unconstrained[self._params_state_cov]) # 5. Measurement error variance terms if self.measurement_error: # Force these to be positive constrained[self._params_obs_cov] = ( unconstrained[self._params_obs_cov]**2) return constrained
[docs] def untransform_params(self, constrained): """ Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer. Parameters ---------- constrained : array_like Array of constrained parameters used in likelihood evalution, to be transformed. Returns ------- unconstrained : array_like Array of unconstrained parameters used by the optimizer. """ constrained = np.array(constrained, ndmin=1) unconstrained = np.zeros(constrained.shape, dtype=constrained.dtype) # 1. Intercept terms: nothing to do unconstrained[self._params_trend] = constrained[self._params_trend] # 2. AR terms: optionally were forced to be stationary if self.k_ar > 0 and self.enforce_stationarity: # Create the state covariance matrix if self.error_cov_type == 'diagonal': state_cov = np.diag(constrained[self._params_state_cov]) elif self.error_cov_type == 'unstructured': state_cov_lower = np.zeros(self.ssm['state_cov'].shape, dtype=constrained.dtype) state_cov_lower[self._idx_lower_state_cov] = ( constrained[self._params_state_cov]) state_cov = np.dot(state_cov_lower, state_cov_lower.T) # Transform the parameters coefficients = constrained[self._params_ar].reshape( self.k_endog, self.k_endog * self.k_ar) unconstrained_matrices, variance = ( unconstrain_stationary_multivariate(coefficients, state_cov)) unconstrained[self._params_ar] = unconstrained_matrices.ravel() else: unconstrained[self._params_ar] = constrained[self._params_ar] # 3. MA terms: optionally were forced to be invertible if self.k_ma > 0 and self.enforce_invertibility: # Transform the parameters, using an identity variance matrix state_cov = np.eye(self.k_endog, dtype=constrained.dtype) coefficients = constrained[self._params_ma].reshape( self.k_endog, self.k_endog * self.k_ma) unconstrained_matrices, variance = ( unconstrain_stationary_multivariate(coefficients, state_cov)) unconstrained[self._params_ma] = unconstrained_matrices.ravel() else: unconstrained[self._params_ma] = constrained[self._params_ma] # 4. Regression terms: nothing to do unconstrained[self._params_regression] = ( constrained[self._params_regression]) # 5. State covariance terms # If we have variances, then these were forced to be positive if self.error_cov_type == 'diagonal': unconstrained[self._params_state_cov] = ( constrained[self._params_state_cov]**0.5) # Otherwise, nothing needs to be done elif self.error_cov_type == 'unstructured': unconstrained[self._params_state_cov] = ( constrained[self._params_state_cov]) # 5. Measurement error variance terms if self.measurement_error: # These were forced to be positive unconstrained[self._params_obs_cov] = ( constrained[self._params_obs_cov]**0.5) return unconstrained
[docs] def update(self, params, **kwargs): params = super(VARMAX, self).update(params, **kwargs) # 1. State intercept # - Exog if self.mle_regression: exog_params = params[self._params_regression].reshape( self.k_endog, self.k_exog).T intercept = np.dot(self.exog[1:], exog_params) self.ssm[self._idx_state_intercept] = intercept.T # - Trend if self.k_trend > 0: # If we didn't set the intercept above, zero it out so we can # just += later if not self.mle_regression: zero = np.array(0, dtype=params.dtype) self.ssm[self._idx_state_intercept] = zero trend_params = params[self._params_trend].reshape( self.k_endog, self.k_trend).T if self._trend_is_const: intercept = trend_params else: intercept = np.dot(self._trend_data[1:], trend_params) self.ssm[self._idx_state_intercept] += intercept.T # Need to set the last state intercept to np.nan (with appropriate # dtype) if self.mle_regression: nan = np.array(np.nan, dtype=params.dtype) self.ssm['state_intercept', :self.k_endog, -1] = nan # 2. Transition ar = params[self._params_ar].reshape( self.k_endog, self.k_endog * self.k_ar) ma = params[self._params_ma].reshape( self.k_endog, self.k_endog * self.k_ma) self.ssm[self._idx_transition] = np.c_[ar, ma] # 3. State covariance if self.error_cov_type == 'diagonal': self.ssm[self._idx_state_cov] = ( params[self._params_state_cov] ) elif self.error_cov_type == 'unstructured': state_cov_lower = np.zeros(self.ssm['state_cov'].shape, dtype=params.dtype) state_cov_lower[self._idx_lower_state_cov] = ( params[self._params_state_cov]) self.ssm['state_cov'] = np.dot(state_cov_lower, state_cov_lower.T) # 4. Observation covariance if self.measurement_error: self.ssm[self._idx_obs_cov] = params[self._params_obs_cov]
[docs]class VARMAXResults(MLEResults): """ Class to hold results from fitting an VARMAX model. Parameters ---------- model : VARMAX instance The fitted model instance Attributes ---------- specification : dictionary Dictionary including all attributes from the VARMAX model instance. coefficient_matrices_var : array Array containing autoregressive lag polynomial coefficient matrices, ordered from lowest degree to highest. coefficient_matrices_vma : array Array containing moving average lag polynomial coefficients, ordered from lowest degree to highest. See Also -------- statsmodels.tsa.statespace.kalman_filter.FilterResults statsmodels.tsa.statespace.mlemodel.MLEResults """ def __init__(self, model, params, filter_results, cov_type='opg', cov_kwds=None, **kwargs): super(VARMAXResults, self).__init__(model, params, filter_results, cov_type, cov_kwds, **kwargs) self.specification = Bunch(**{ # Set additional model parameters 'error_cov_type': self.model.error_cov_type, 'measurement_error': self.model.measurement_error, 'enforce_stationarity': self.model.enforce_stationarity, 'enforce_invertibility': self.model.enforce_invertibility, 'order': self.model.order, # Model order 'k_ar': self.model.k_ar, 'k_ma': self.model.k_ma, # Trend / Regression 'trend': self.model.trend, 'k_trend': self.model.k_trend, 'k_exog': self.model.k_exog, }) # Polynomials / coefficient matrices self.coefficient_matrices_var = None self.coefficient_matrices_vma = None if self.model.k_ar > 0: ar_params = np.array(self.params[self.model._params_ar]) k_endog = self.model.k_endog k_ar = self.model.k_ar self.coefficient_matrices_var = ( ar_params.reshape(k_endog * k_ar, k_endog).T ).reshape(k_endog, k_endog, k_ar).T if self.model.k_ma > 0: ma_params = np.array(self.params[self.model._params_ma]) k_endog = self.model.k_endog k_ma = self.model.k_ma self.coefficient_matrices_vma = ( ma_params.reshape(k_endog * k_ma, k_endog).T ).reshape(k_endog, k_endog, k_ma).T
[docs] def get_prediction(self, start=None, end=None, dynamic=False, index=None, exog=None, **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 first forecast is start. 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. exog : array_like, optional If the model includes exogenous regressors, you must provide exactly enough out-of-sample values for the exogenous variables if end is beyond 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. 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 = self.model._index[0] # Handle end (e.g. date) _start, _end, _out_of_sample, prediction_index = ( self.model._get_prediction_index(start, end, index, silent=True)) # Handle exogenous parameters last_intercept = None if _out_of_sample and (self.model.k_exog + self.model.k_trend > 0): # Create a new faux VARMAX model for the extended dataset nobs = self.model.data.orig_endog.shape[0] + _out_of_sample endog = np.zeros((nobs, self.model.k_endog)) if self.model.k_exog > 0: if exog is None: raise ValueError('Out-of-sample forecasting in a model' ' with a regression component requires' ' additional exogenous values via the' ' `exog` argument.') exog = np.array(exog) required_exog_shape = (_out_of_sample, self.model.k_exog) if not exog.shape == required_exog_shape: raise ValueError('Provided exogenous values are not of the' ' appropriate shape. Required %s, got %s.' % (str(required_exog_shape), str(exog.shape))) exog = np.c_[self.model.data.orig_exog.T, exog.T].T # TODO replace with init_kwds or specification or similar model = VARMAX( endog, exog=exog, order=self.model.order, trend=self.model.trend, error_cov_type=self.model.error_cov_type, measurement_error=self.model.measurement_error, enforce_stationarity=self.model.enforce_stationarity, enforce_invertibility=self.model.enforce_invertibility ) model.update(self.params) if model['state_intercept'].ndim > 1: last_intercept = model['state_intercept', :, self.nobs - 1] else: last_intercept = model['state_intercept', :, 0] # Set the kwargs with the update time-varying state space # representation matrices for name in self.filter_results.shapes.keys(): if name == 'obs': continue mat = getattr(model.ssm, name) if mat.shape[-1] > 1: if len(mat.shape) == 2: kwargs[name] = mat[:, -_out_of_sample:] else: kwargs[name] = mat[:, :, -_out_of_sample:] elif self.model.k_exog == 0 and exog is not None: warn('Exogenous array provided to predict, but additional data not' ' required. `exog` argument ignored.', ValueWarning) # If we had exog, then the last predicted_state has been set to NaN # since we didn't have the appropriate exog to create it. Then, if # we are forecasting, we now have new exog that we need to put into # the existing state_intercept array (and we will take it out, below) if last_intercept is not None: self.filter_results.state_intercept[:, -1] = last_intercept res = super(VARMAXResults, self).get_prediction( start=start, end=end, dynamic=dynamic, index=index, exog=exog, **kwargs) if last_intercept is not None: self.filter_results.state_intercept[:, -1] = np.nan return res
[docs] def summary(self, alpha=.05, start=None, separate_params=True): from statsmodels.iolib.summary import summary_params # Create the model name spec = self.specification if spec.k_ar > 0 and spec.k_ma > 0: model_name = 'VARMA' order = '(%s,%s)' % (spec.k_ar, spec.k_ma) elif spec.k_ar > 0: model_name = 'VAR' order = '(%s)' % (spec.k_ar) else: model_name = 'VMA' order = '(%s)' % (spec.k_ma) if spec.k_exog > 0: model_name += 'X' model_name = [model_name + order] if spec.k_trend > 0: model_name.append('intercept') if spec.measurement_error: model_name.append('measurement error') summary = super(VARMAXResults, self).summary( alpha=alpha, start=start, model_name=model_name, display_params=not separate_params ) if separate_params: indices = np.arange(len(self.params)) def make_table(self, mask, title, strip_end=True): res = (self, self.params[mask], self.bse[mask], self.zvalues[mask], self.pvalues[mask], self.conf_int(alpha)[mask]) param_names = [ '.'.join(name.split('.')[:-1]) if strip_end else name for name in np.array(self.data.param_names)[mask].tolist() ] return summary_params(res, yname=None, xname=param_names, alpha=alpha, use_t=False, title=title) # Add parameter tables for each endogenous variable k_endog = self.model.k_endog k_ar = self.model.k_ar k_ma = self.model.k_ma k_trend = self.model.k_trend k_exog = self.model.k_exog endog_masks = [] for i in range(k_endog): masks = [] offset = 0 # 1. Intercept terms if k_trend > 0: masks.append(np.arange(i, i + k_endog * k_trend, k_endog)) offset += k_endog * k_trend # 2. AR terms if k_ar > 0: start = i * k_endog * k_ar end = (i + 1) * k_endog * k_ar masks.append( offset + np.arange(start, end)) offset += k_ar * k_endog**2 # 3. MA terms if k_ma > 0: start = i * k_endog * k_ma end = (i + 1) * k_endog * k_ma masks.append( offset + np.arange(start, end)) offset += k_ma * k_endog**2 # 4. Regression terms if k_exog > 0: masks.append( offset + np.arange(i * k_exog, (i + 1) * k_exog)) offset += k_endog * k_exog # 5. Measurement error variance terms if self.model.measurement_error: masks.append( np.array(self.model.k_params - i - 1, ndmin=1)) # Create the table mask = np.concatenate(masks) endog_masks.append(mask) title = "Results for equation %s" % self.model.endog_names[i] table = make_table(self, mask, title) summary.tables.append(table) # State covariance terms state_cov_mask = ( np.arange(len(self.params))[self.model._params_state_cov]) table = make_table(self, state_cov_mask, "Error covariance matrix", strip_end=False) summary.tables.append(table) # Add a table for all other parameters masks = [] for m in (endog_masks, [state_cov_mask]): m = np.array(m).flatten() if len(m) > 0: masks.append(m) masks = np.concatenate(masks) inverse_mask = np.array(list(set(indices).difference(set(masks)))) if len(inverse_mask) > 0: table = make_table(self, inverse_mask, "Other parameters", strip_end=False) summary.tables.append(table) return summary
summary.__doc__ = MLEResults.summary.__doc__
class VARMAXResultsWrapper(MLEResultsWrapper): _attrs = {} _wrap_attrs = wrap.union_dicts(MLEResultsWrapper._wrap_attrs, _attrs) _methods = {} _wrap_methods = wrap.union_dicts(MLEResultsWrapper._wrap_methods, _methods) wrap.populate_wrapper(VARMAXResultsWrapper, VARMAXResults) # noqa:E305