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# -*- 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