"""
ARIMA
-----
Models for ARIMA (Autoregressive integrated moving average) [1]_.
The implementations is wrapped around `statsmodels <https://github.com/statsmodels/statsmodels>`_.
References
----------
.. [1] https://wikipedia.org/wiki/Autoregressive_integrated_moving_average
"""
import sys
from collections.abc import Sequence
from typing import Literal, Optional, Union
if sys.version_info >= (3, 10):
from typing import TypeAlias
else:
from typing_extensions import TypeAlias
from sklearn.utils import check_random_state
from statsmodels.tsa.arima.model import ARIMA as staARIMA
from darts import TimeSeries
from darts.logging import get_logger
from darts.models.forecasting.forecasting_model import (
TransferableFutureCovariatesLocalForecastingModel,
)
from darts.utils.utils import random_method
logger = get_logger(__name__)
IntOrIntSequence: TypeAlias = Union[int, Sequence[int]]
[docs]class ARIMA(TransferableFutureCovariatesLocalForecastingModel):
@random_method
def __init__(
self,
p: IntOrIntSequence = 12,
d: int = 1,
q: IntOrIntSequence = 0,
seasonal_order: tuple[int, IntOrIntSequence, IntOrIntSequence, int] = (
0,
0,
0,
0,
),
trend: Optional[Union[Literal["n", "c", "t", "ct"], list[int]]] = None,
random_state: Optional[int] = None,
add_encoders: Optional[dict] = None,
):
"""ARIMA
ARIMA-type models extensible with exogenous variables (future covariates)
and seasonal components.
Parameters
----------
p : int | Sequence[int]
Order (number of time lags) of the autoregressive model (AR).
If a sequence of integers, specifies the exact lags to include.
d : int
The order of differentiation; i.e., the number of times the data
have had past values subtracted (I).
q : int | Sequence[int]
The size of the moving average window (MA).
If a sequence of integers, specifies the exact lags to include in the window.
seasonal_order: Tuple[int | Sequence[int], int, int | Sequence[int], int]
The (P,D,Q,s) order of the seasonal component for the AR parameters (P),
differences (D), MA parameters (Q) and periodicity (s). D and s are always integers,
while P and Q may either be integers or sequence of positive integers
specifying exactly which lag orders are included.
trend: Literal['n', 'c', 't', 'ct'] | list[int], optional
Parameter controlling the deterministic trend. Either a string or list of integers.
If a string, can be 'n' for no trend, 'c' for a constant term, 't' for a linear trend in time,
and 'ct' for a constant term and linear trend.
If a list of integers, defines a polynomial according to `numpy.poly1d` [1]_. E.g., `[1,1,0,1]` would
translate to :math:`a + bt + ct^3`.
Trend term of lower order than `d + D` cannot be as they would be eliminated due to the differencing
operation.
Default is 'c' for models without integration, and 'n' for models with integration.
add_encoders
A large number of future covariates can be automatically generated with `add_encoders`.
This can be done by adding multiple pre-defined index encoders and/or custom user-made functions that
will be used as index encoders. Additionally, a transformer such as Darts' :class:`Scaler` can be added to
transform the generated covariates. This happens all under one hood and only needs to be specified at
model creation.
Read :meth:`SequentialEncoder <darts.dataprocessing.encoders.SequentialEncoder>` to find out more about
``add_encoders``. Default: ``None``. An example showing some of ``add_encoders`` features:
.. highlight:: python
.. code-block:: python
def encode_year(idx):
return (idx.year - 1950) / 50
add_encoders={
'cyclic': {'future': ['month']},
'datetime_attribute': {'future': ['hour', 'dayofweek']},
'position': {'future': ['relative']},
'custom': {'future': [encode_year]},
'transformer': Scaler(),
'tz': 'CET'
}
..
random_state: int or None
Controls the randomness for reproducible forecasting.
Examples
--------
>>> from darts.datasets import AirPassengersDataset
>>> from darts.models import ARIMA
>>> from darts.utils.timeseries_generation import datetime_attribute_timeseries
>>> series = AirPassengersDataset().load()
>>> # optionally, use some future covariates; e.g. the value of the month encoded as a sine and cosine series
>>> future_cov = datetime_attribute_timeseries(series, "month", cyclic=True, add_length=6)
>>> # define ARIMA parameters
>>> model = ARIMA(p=12, d=1, q=2)
>>> model.fit(series, future_covariates=future_cov)
>>> pred = model.predict(6, future_covariates=future_cov)
>>> pred.values()
array([[451.36489334],
[416.88972829],
[443.10520391],
[481.07892911],
[502.11286509],
[555.50153984]])
References
----------
.. [1] https://numpy.org/doc/stable/reference/generated/numpy.poly1d.html
"""
super().__init__(add_encoders=add_encoders)
self.order = p, d, q
self.seasonal_order = seasonal_order
self.trend = trend
self.model = None
@property
def supports_multivariate(self) -> bool:
return False
def _fit(self, series: TimeSeries, future_covariates: Optional[TimeSeries] = None):
super()._fit(series, future_covariates)
self._assert_univariate(series)
# storing to restore the statsmodels model results object
self.training_historic_future_covariates = future_covariates
m = staARIMA(
series.values(copy=False),
exog=future_covariates.values(copy=False) if future_covariates else None,
order=self.order,
seasonal_order=self.seasonal_order,
trend=self.trend,
)
self.model = m.fit()
return self
@random_method
def _predict(
self,
n: int,
series: Optional[TimeSeries] = None,
historic_future_covariates: Optional[TimeSeries] = None,
future_covariates: Optional[TimeSeries] = None,
num_samples: int = 1,
predict_likelihood_parameters: bool = False,
verbose: bool = False,
random_state: Optional[int] = None,
) -> TimeSeries:
if num_samples > 1 and self.trend:
logger.warning(
"Trends are not well supported yet for getting probabilistic forecasts with ARIMA."
"If you run into issues, try calling fit() with num_samples=1 or removing the trend from"
"your model."
)
super()._predict(
n,
series,
historic_future_covariates,
future_covariates,
num_samples,
random_state=random_state,
)
# updating statsmodels results object state with the new ts and covariates
if series is not None:
self.model = self.model.apply(
series.values(copy=False),
exog=(
historic_future_covariates.values(copy=False)
if historic_future_covariates
else None
),
)
if num_samples == 1:
forecast = self.model.forecast(
steps=n,
exog=(
future_covariates.values(copy=False) if future_covariates else None
),
)
else:
rng = check_random_state(random_state)
forecast = self.model.simulate(
nsimulations=n,
repetitions=num_samples,
initial_state=self.model.states.predicted[-1, :],
random_state=rng,
anchor="end",
exog=(
future_covariates.values(copy=False) if future_covariates else None
),
)
# restoring statsmodels results object state
if series is not None:
self.model = self.model.apply(
self._orig_training_series.values(copy=False),
exog=(
self.training_historic_future_covariates.values(copy=False)
if self.training_historic_future_covariates
else None
),
)
return self._build_forecast_series(forecast)
@property
def supports_probabilistic_prediction(self) -> bool:
return True
@property
def min_train_series_length(self) -> int:
return 30