DynamicFactor

Dynamic Factor Forecaster.

Quickstart

from sktime.forecasting.dynamic_factor import DynamicFactor

estimator = DynamicFactor(k_factors=1, factor_order=1, error_cov_type='diagonal', error_order=0, error_var=False, enforce_stationarity=True, start_params=None, transformed=True, includes_fixed=False, cov_type=None, cov_kwds=None, method='lbfgs', maxiter=50, full_output=False, disp=False, callback=None, return_params=False, optim_score=None, optim_complex_step=None, optim_hessian=None, flags=None, low_memory=False)

Parameters(21)

k_factorsint

The number of unobserved factors.

factor_orderint

The order of vector autoregression followed by factors.

error_cov_type{‘scalar’,’diagonal’,’unstructured’},default = ‘diagonal’

The structure of the covariance matrix of the observation error term, where “unstructured” puts no restrictions on the matrix, “diagonal” requires it to be any diagonal matrix (uncorrelated errors), and “scalar” requires it to be a scalar times the identity matrix.

error_orderint, default = 0

The order of the vector autoregression followed by the observation error component. Default is None, corresponding to white noise errors.

error_varbool, default = False, optional

Whether or not to model the errors jointly via a vector autoregression, rather than as individual autoregression.

enforce_stationaritybool default = True

Whether or not to model the AR parameters to enforce stationarity in the autoregressive component of the model.

start_params:array_like,default = None

Initial guess of the solution for the loglikelihood maximization.

transformedbool, default = True

Whether or not start_params is already transformed.

includes_fixedbool, default = False

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.

cov_type{‘opg’,’oim’,’approx’,’robust’,’robust_approx’,’none’},default = ‘opg’

‘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.

cov_kwds:dict or None, default = None

‘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.

methodstr, ‘lbfgs’

‘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

maxiterint, optional,default = 50

The maximum number of iterations to perform.

full_outputbool, default = 1

Set to True to have all available output in the Results object’s mle_retvals attribute. The output is dependent on the solver.

dispbool, default = 5

Set to True to print convergence messages.

callbackcallable callback(xk), default = None

Called after each iteration, as callback(xk), where xk is the current parameter vector.

return_paramsbool,default = False

Whether or not to return only the array of maximizing parameters.

optim_score{‘harvey’,’approx’}, default = None

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.

optim_complex_stepbool, default = True

Whether or not to use complex step differentiation when approximating the score; if False, finite difference approximation is used.

optim_hessian{‘opg’,’oim’,’approx’}, default = None

‘opg’ uses outer product of gradients, ‘oim’ uses the information matrix formula from Harvey (1989), and ‘approx’ uses numerical approximation.

low_memorybool, default = False

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.

Examples

>>> from sktime.utils._testing.series import _make_series
>>> from sktime.forecasting.dynamic_factor import DynamicFactor
>>> y = _make_series (n_columns = 4)
>>> forecaster = DynamicFactor ()
>>> forecaster. fit (y) DynamicFactor(
... )
>>> y_pred = forecaster. predict (fh = [1, 2, 3 ])

References

1. [1 ] Lütkepohl, Helmut. 2007. New Introduction to Multiple Time Series Analysis. Berlin: Springer.