auto.py

# -*- coding: utf-8 -*-
#
# Author: Taylor Smith <taylor.smith@alkaline-ml.com>
#
# Automatically find optimal parameters for an ARIMA

import numpy as np

from sklearn.linear_model import LinearRegression

import functools
import time
import warnings

from ..base import BaseARIMA
from . import _doc
from . import _validation as val
from .utils import ndiffs, is_constant, nsdiffs
from ..utils import diff, is_iterable, check_endog
from ..utils.metaestimators import if_has_delegate
from ._context import AbstractContext, ContextType

# Import as a namespace so we can mock
from . import _auto_solvers as solvers
from ..compat.numpy import DTYPE
from ..compat import statsmodels as sm_compat

__all__ = [
    'auto_arima',
    'AutoARIMA',
    'StepwiseContext'
]


def _warn_for_deprecations(**kwargs):
    # TODO: remove these warnings in the future
    for k in ('solver', 'transparams'):
        if kwargs.pop(k, None):
            warnings.warn('%s has been deprecated and will be removed in '
                          'a future version.' % k,
                          DeprecationWarning)
    return kwargs


class AutoARIMA(BaseARIMA):
    # Don't add the y, exog, etc. here since they are used in 'fit'
    __doc__ = _doc._AUTO_ARIMA_DOCSTR.format(
        y="",
        X="",
        fit_args="",
        return_valid_fits="",
        sarimax_kwargs=_doc._KWARGS_DOCSTR)

    # todo: someday store defaults somewhere else for single source of truth
    def __init__(
        self,
        start_p=2,
        d=None,
        start_q=2,
        max_p=5,
        max_d=2,
        max_q=5,
        start_P=1,
        D=None,
        start_Q=1,
        max_P=2,
        max_D=1,
        max_Q=2,
        max_order=5,
        m=1,
        seasonal=True,
        stationary=False,
        information_criterion='aic',
        alpha=0.05,
        test='kpss',
        seasonal_test='ocsb',
        stepwise=True,
        n_jobs=1,
        start_params=None,
        trend=None,
        method='lbfgs',
        maxiter=50,
        offset_test_args=None,
        seasonal_test_args=None,
        suppress_warnings=True,
        error_action='trace',
        trace=False,
        random=False,
        random_state=None,
        n_fits=10,
        out_of_sample_size=0,
        scoring='mse',
        scoring_args=None,
        with_intercept="auto",
        **kwargs,
    ):

        self.start_p = start_p
        self.d = d
        self.start_q = start_q
        self.max_p = max_p
        self.max_d = max_d
        self.max_q = max_q
        self.start_P = start_P
        self.D = D
        self.start_Q = start_Q
        self.max_P = max_P
        self.max_D = max_D
        self.max_Q = max_Q
        self.max_order = max_order
        self.m = m
        self.seasonal = seasonal
        self.stationary = stationary
        self.information_criterion = information_criterion
        self.alpha = alpha
        self.test = test
        self.seasonal_test = seasonal_test
        self.stepwise = stepwise
        self.n_jobs = n_jobs
        self.start_params = start_params
        self.trend = trend
        self.method = method
        self.maxiter = maxiter
        self.offset_test_args = offset_test_args
        self.seasonal_test_args = seasonal_test_args
        self.suppress_warnings = suppress_warnings
        self.error_action = error_action
        self.trace = trace
        self.random = random
        self.random_state = random_state
        self.n_fits = n_fits
        self.out_of_sample_size = out_of_sample_size
        self.scoring = scoring
        self.scoring_args = scoring_args
        self.with_intercept = with_intercept

        kwargs = _warn_for_deprecations(**kwargs)
        self.kwargs = kwargs

    def fit(self, y, X=None, **fit_args):
        """Fit the auto-arima estimator

        Fit an AutoARIMA to a vector, ``y``, of observations with an
        optional matrix of ``X`` variables.

        Parameters
        ----------
        y : array-like or iterable, shape=(n_samples,)
            The time-series to which to fit the ``ARIMA`` estimator. This may
            either be a Pandas ``Series`` object (statsmodels can internally
            use the dates in the index), or a numpy array. This should be a
            one-dimensional array of floats, and should not contain any
            ``np.nan`` or ``np.inf`` values.

        X : array-like, shape=[n_obs, n_vars], optional (default=None)
            An optional 2-d array of exogenous variables. If provided, these
            variables are used as additional features in the regression
            operation. This should not include a constant or trend. Note that
            if an ``ARIMA`` is fit on exogenous features, it must be provided
            exogenous features for making predictions.

        **fit_args : dict or kwargs
            Any keyword arguments to pass to the auto-arima function.
        """
        sarimax_kwargs = {} if not self.kwargs else self.kwargs

        self.model_ = auto_arima(
            y,
            X=X,
            start_p=self.start_p,
            d=self.d,
            start_q=self.start_q,
            max_p=self.max_p,
            max_d=self.max_d,
            max_q=self.max_q,
            start_P=self.start_P,
            D=self.D,
            start_Q=self.start_Q,
            max_P=self.max_P,
            max_D=self.max_D,
            max_Q=self.max_Q,
            max_order=self.max_order,
            m=self.m,
            seasonal=self.seasonal,
            stationary=self.stationary,
            information_criterion=self.information_criterion,
            alpha=self.alpha,
            test=self.test,
            seasonal_test=self.seasonal_test,
            stepwise=self.stepwise,
            n_jobs=self.n_jobs,
            start_params=self.start_params,
            trend=self.trend,
            method=self.method,
            maxiter=self.maxiter,
            offset_test_args=self.offset_test_args,
            seasonal_test_args=self.seasonal_test_args,
            suppress_warnings=self.suppress_warnings,
            error_action=self.error_action,
            trace=self.trace,
            random=self.random,
            random_state=self.random_state,
            n_fits=self.n_fits,
            return_valid_fits=False,  # only return ONE
            out_of_sample_size=self.out_of_sample_size,
            scoring=self.scoring,
            scoring_args=self.scoring_args,
            with_intercept=self.with_intercept,
            sarimax_kwargs=sarimax_kwargs,
            **fit_args)

        return self

    @if_has_delegate("model_")
    def predict_in_sample(
        self,
        X=None,
        start=None,
        end=None,
        dynamic=False,
        return_conf_int=False,
        alpha=0.05,
        typ='levels',
    ):
        return self.model_.predict_in_sample(
            X=X,
            start=start,
            end=end,
            dynamic=dynamic,
            return_conf_int=return_conf_int,
            alpha=alpha,
            typ=typ,
        )

    @if_has_delegate("model_")
    def predict(
        self,
        n_periods=10,
        X=None,
        return_conf_int=False,
        alpha=0.05,
    ):
        return self.model_.predict(
            n_periods=n_periods,
            X=X,
            return_conf_int=return_conf_int,
            alpha=alpha,
        )

    @if_has_delegate("model_")
    def update(
        self,
        y,
        X=None,
        maxiter=None,
        **kwargs,
    ):
        return self.model_.update(
            y,
            X=X,
            maxiter=maxiter,
            **kwargs
        )

    @if_has_delegate('model_')
    def summary(self):
        """Get a summary of the ARIMA model"""
        return self.model_.summary()

    # TODO: decorator to automate all this composition + AIC, etc.


class StepwiseContext(AbstractContext):
    """Context manager to capture runtime context for stepwise mode.

    ``StepwiseContext`` allows one to call :func:`auto_arima` in the context
    of a runtime configuration that offers additional level of
    control required in certain scenarios. Use cases that are either
    sensitive to duration and/or the number of attempts to
    find the best fit can use ``StepwiseContext`` to control them.

    Parameters
    ----------
    max_steps : int, optional (default=100)
        The maximum number of steps to try to find a best fit. When
        the number of tries exceed this number, the stepwise process
        will stop and the best fit model at that time will be returned.

    max_dur : int, optional (default=None)
        The maximum duration in seconds to try to find a best fit.
        When the cumulative fit duration exceeds this number, the
        stepwise process will stop and the best fit model at that
        time will be returned. Please note that this is a soft limit.

    Notes
    -----
    Although the ``max_steps`` parameter is set to a default value of None
    here, the stepwise search is limited to 100 tries to find a best fit model.
    Defaulting the parameter to None here preserves the intention of the
    caller and properly handles the nested contexts, like:

    >>> with StepwiseContext(max_steps=10):
    ...     with StepwiseContext(max_dur=30):
    ...         auto_arima(sample, stepwise=True, ...)

    In the above example, the stepwise search will be limited to either
    a maximum of 10 steps or a maximum duration of 30 seconds, whichever
    occurs first and the best fit model at that time will be returned
    """

    def __init__(self, max_steps=None, max_dur=None):
        # TODO: do we want an upper limit on this?
        if max_steps is not None and not 0 < max_steps <= 1000:
            raise ValueError('max_steps should be between 1 and 1000')

        if max_dur is not None and max_dur <= 0:
            raise ValueError('max_dur should be greater than zero')

        kwargs = {
            'max_steps': max_steps,
            'max_dur': max_dur
        }
        super(StepwiseContext, self).__init__(**kwargs)

    # override base class member
    def get_type(self):
        return ContextType.STEPWISE


def auto_arima(
    y,
    X=None,
    start_p=2,
    d=None,
    start_q=2,
    max_p=5,
    max_d=2,
    max_q=5,
    start_P=1,
    D=None,
    start_Q=1,
    max_P=2,
    max_D=1,
    max_Q=2,
    max_order=5,
    m=1,
    seasonal=True,
    stationary=False,
    information_criterion='aic',
    alpha=0.05,
    test='kpss',
    seasonal_test='ocsb',
    stepwise=True,
    n_jobs=1,
    start_params=None,
    trend=None,
    method='lbfgs',
    maxiter=50,
    offset_test_args=None,
    seasonal_test_args=None,
    suppress_warnings=True,
    error_action='trace',
    trace=False,
    random=False,
    random_state=None,
    n_fits=10,
    return_valid_fits=False,
    out_of_sample_size=0,
    scoring='mse',
    scoring_args=None,
    with_intercept="auto",
    sarimax_kwargs=None,
    **fit_args,
):

    # NOTE: Doc is assigned BELOW this function

    # pop out the deprecated kwargs
    fit_args = _warn_for_deprecations(**fit_args)

    # misc kwargs passed to various fit or test methods
    offset_test_args = val.check_kwargs(offset_test_args)
    seasonal_test_args = val.check_kwargs(seasonal_test_args)
    scoring_args = val.check_kwargs(scoring_args)
    sarimax_kwargs = val.check_kwargs(sarimax_kwargs)

    m = val.check_m(m, seasonal)
    trace = val.check_trace(trace)
    # can't have stepwise AND parallel
    n_jobs = val.check_n_jobs(stepwise, n_jobs)

    # validate start/max points
    start_p, max_p = val.check_start_max_values(start_p, max_p, "p")
    start_q, max_q = val.check_start_max_values(start_q, max_q, "q")
    start_P, max_P = val.check_start_max_values(start_P, max_P, "P")
    start_Q, max_Q = val.check_start_max_values(start_Q, max_Q, "Q")

    # validate d & D
    for _d, _max_d in ((d, max_d), (D, max_D)):
        if _max_d < 0:
            raise ValueError('max_d & max_D must be positive integers (>= 0)')
        if _d is not None:
            if _d < 0:
                raise ValueError('d & D must be None or a positive '
                                 'integer (>= 0)')

    # check on n_fits
    if random and n_fits < 0:
        raise ValueError('n_fits must be a positive integer '
                         'for a random search')

    # validate error action
    actions = {'warn', 'raise', 'ignore', 'trace', None}
    if error_action not in actions:
        raise ValueError('error_action must be one of %r, but got %r'
                         % (actions, error_action))

    # start the timer after the parameter validation
    start = time.time()

    # copy array
    y = check_endog(y, dtype=DTYPE, preserve_series=True)
    n_samples = y.shape[0]

    # the workhorse of the model fits
    fit_partial = functools.partial(
        solvers._fit_candidate_model,
        start_params=start_params,
        trend=trend,
        method=method,
        maxiter=maxiter,
        fit_params=fit_args,
        suppress_warnings=suppress_warnings,
        trace=trace,
        error_action=error_action,
        scoring=scoring,
        out_of_sample_size=out_of_sample_size,
        scoring_args=scoring_args,
        information_criterion=information_criterion,
    )

    # check for constant data
    if is_constant(y):
        warnings.warn('Input time-series is completely constant; '
                      'returning a (0, 0, 0) ARMA.')

        return _return_wrapper(
            solvers._sort_and_filter_fits(
                fit_partial(
                    y,
                    X=X,
                    order=(0, 0, 0),
                    seasonal_order=(0, 0, 0, 0),
                    with_intercept=val.auto_intercept(
                        with_intercept, False),  # False for the constant model
                    **sarimax_kwargs
                )
            ),
            return_valid_fits, start, trace)

    information_criterion = \
        val.check_information_criterion(information_criterion,
                                        out_of_sample_size)

    # the R code handles this, but I don't think statsmodels
    # will even fit a model this small...
    # if n_samples <= 3:
    #     if information_criterion != 'aic':
    #         warnings.warn('n_samples (%i) <= 3 '
    #                       'necessitates using AIC' % n_samples)
    #     information_criterion = 'aic'

    # adjust max p, q -- R code:
    # max.p <- min(max.p, floor(serieslength/3))
    # max.q <- min(max.q, floor(serieslength/3))
    max_p = int(min(max_p, np.floor(n_samples / 3)))
    max_q = int(min(max_q, np.floor(n_samples / 3)))

    # this is not in the R code and poses a risk that R did not consider...
    # if max_p|q has now dropped below start_p|q, correct it.
    start_p = min(start_p, max_p)
    start_q = min(start_q, max_q)

    # if it's not seasonal, we can avoid multiple 'if not is None' comparisons
    # later by just using this shortcut (hack):
    # TODO: can we remove this hack now?
    if not seasonal:
        D = m = -1

    # TODO: check rank deficiency, check for constant Xs, regress if necessary
    xx = y.copy()
    if X is not None:
        lm = LinearRegression().fit(X, y)
        xx = y - lm.predict(X)

    # choose the order of differencing
    # is the TS stationary?
    if stationary:
        d = D = 0

    # todo: or not seasonal ?
    if m == 1:
        D = max_P = max_Q = 0
    # m must be > 1 for nsdiffs
    elif D is None:  # we don't have a D yet and we need one (seasonal)
        D = nsdiffs(xx, m=m, test=seasonal_test, max_D=max_D,
                    **seasonal_test_args)

        if D > 0 and X is not None:
            diffxreg = diff(X, differences=D, lag=m)
            # check for constance on any column
            if np.apply_along_axis(is_constant, arr=diffxreg, axis=0).any():
                D -= 1

    # D might still be None if not seasonal
    if D > 0:
        dx = diff(xx, differences=D, lag=m)
    else:
        dx = xx

    # If D was too big, we might have gotten rid of x altogether!
    if dx.shape[0] == 0:
        raise ValueError("The seasonal differencing order, D=%i, was too "
                         "large for your time series, and after differencing, "
                         "there are no samples remaining in your data. "
                         "Try a smaller value for D, or if you didn't set D "
                         "to begin with, try setting it explicitly. This can "
                         "also occur in seasonal settings when m is too large."
                         % D)

    # difference the exogenous matrix
    if X is not None:
        if D > 0:
            diffxreg = diff(X, differences=D, lag=m)
        else:
            diffxreg = X
    else:
        # here's the thing... we're only going to use diffxreg if exogenous
        # was not None in the first place. However, PyCharm doesn't know that
        # and it thinks we might use it before assigning it. Therefore, assign
        # it to None as a default value and it won't raise the warning anymore.
        diffxreg = None

    # determine/set the order of differencing by estimating the number of
    # orders it would take in order to make the TS stationary.
    if d is None:
        d = ndiffs(
            dx,
            test=test,
            alpha=alpha,
            max_d=max_d,
            **offset_test_args,
        )

        if d > 0 and X is not None:
            diffxreg = diff(diffxreg, differences=d, lag=1)

            # if any columns are constant, subtract one order of differencing
            if np.apply_along_axis(is_constant, arr=diffxreg, axis=0).any():
                d -= 1

    # check differences (do we want to warn?...)
    if not suppress_warnings:  # TODO: context manager for entire block  # noqa: E501
        val.warn_for_D(d=d, D=D)

    if d > 0:
        dx = diff(dx, differences=d, lag=1)

    # check for constant
    if is_constant(dx):
        ssn = (0, 0, 0, 0) if not seasonal \
            else sm_compat.check_seasonal_order((0, D, 0, m))

        # Include the benign `ifs`, because R's auto.arima does. R has some
        # more options to control that we don't, but this is more readable
        # with a single `else` clause than a complex `elif`.
        if D > 0 and d == 0:
            with_intercept = val.auto_intercept(with_intercept, True)
            # TODO: if ever implemented in sm
            # fixed=mean(dx/m, na.rm = TRUE)
        elif D > 0 and d > 0:
            pass
        elif d == 2:
            pass
        elif d < 2:
            with_intercept = val.auto_intercept(with_intercept, True)
            # TODO: if ever implemented in sm
            # fixed=mean(dx, na.rm = TRUE)
        else:
            raise ValueError('data follow a simple polynomial and are not '
                             'suitable for ARIMA modeling')

        # perfect regression
        return _return_wrapper(
            solvers._sort_and_filter_fits(
                fit_partial(
                    y,
                    X=X,
                    order=(0, d, 0),
                    seasonal_order=ssn,
                    with_intercept=with_intercept,
                    **sarimax_kwargs
                )
            ),
            return_valid_fits, start, trace
        )

    # seasonality issues
    if m > 1:
        if max_P > 0:
            max_p = min(max_p, m - 1)
        if max_Q > 0:
            max_q = min(max_q, m - 1)

    # TODO: if approximation
    #   . we need method='css' or something similar for this

    # R determines whether to use a constant like this:
    #   allowdrift <- allowdrift & (d + D) == 1
    #   allowmean <- allowmean & (d + D) == 0
    #   constant <- allowdrift | allowmean
    # but we don't have `allowdrift` or `allowmean` so use just d and D
    if with_intercept == 'auto':
        with_intercept = (d + D) in (0, 1)

    if not stepwise:

        # validate max_order
        if max_order is None:
            max_order = np.inf
        elif max_order < 0:
            raise ValueError('max_order must be None or a positive '
                             'integer (>= 0)')

        search = solvers._RandomFitWrapper(
            y=y,
            X=X,
            fit_partial=fit_partial,
            d=d,
            D=D,
            m=m,
            max_order=max_order,
            max_p=max_p,
            max_q=max_q,
            max_P=max_P,
            max_Q=max_Q,
            random=random,
            random_state=random_state,
            n_fits=n_fits,
            n_jobs=n_jobs,
            seasonal=seasonal,
            trace=trace,
            with_intercept=with_intercept,
            sarimax_kwargs=sarimax_kwargs,
        )

    else:
        if n_samples < 10:
            start_p = min(start_p, 1)
            start_q = min(start_q, 1)
            start_P = start_Q = 0

        # seed p, q, P, Q vals
        p = min(start_p, max_p)
        q = min(start_q, max_q)
        P = min(start_P, max_P)
        Q = min(start_Q, max_Q)

        # init the stepwise model wrapper
        search = solvers._StepwiseFitWrapper(
            y,
            X=X,
            start_params=start_params,
            trend=trend,
            method=method,
            maxiter=maxiter,
            fit_params=fit_args,
            suppress_warnings=suppress_warnings,
            trace=trace,
            error_action=error_action,
            out_of_sample_size=out_of_sample_size,
            scoring=scoring,
            scoring_args=scoring_args,
            p=p,
            d=d,
            q=q,
            P=P,
            D=D,
            Q=Q,
            m=m,
            max_p=max_p,
            max_q=max_q,
            max_P=max_P,
            max_Q=max_Q,
            seasonal=seasonal,
            information_criterion=information_criterion,
            with_intercept=with_intercept,
            **sarimax_kwargs,
        )

    sorted_res = search.solve()
    return _return_wrapper(sorted_res, return_valid_fits, start, trace)


# Assign the doc to the auto_arima func
auto_arima.__doc__ = _doc._AUTO_ARIMA_DOCSTR.format(
    y=_doc._Y_DOCSTR,
    X=_doc._EXOG_DOCSTR,
    fit_args=_doc._FIT_ARGS_DOCSTR,
    sarimax_kwargs=_doc._SARIMAX_ARGS_DOCSTR,
    return_valid_fits=_doc._VALID_FITS_DOCSTR
)


def _return_wrapper(fits, return_all, start, trace):
    """If the user wants to get all of the models back, this will
    return a list of the ARIMA models, otherwise it will just return
    the model. If this is called from the end of the function, ``fits``
    will already be a list.

    We *know* that if a function call makes it here, ``fits`` is NOT None
    or it would have thrown an exception in :func:`_post_ppc_arima`.

    Parameters
    ----------
    fits : iterable or ARIMA
        The ARIMA(s)

    return_all : bool
        Whether to return all.
    """
    # make sure it's an iterable
    if not is_iterable(fits):
        fits = [fits]

    # whether to print the final runtime
    if trace:
        print('Total fit time: %.3f seconds' % (time.time() - start))

    # which to return? if not all, then first index (assume sorted)
    if not return_all:
        return fits[0]
    return fits