ForecasterAutoreg¶
ForecasterAutoreg (ForecasterBase)
¶
This class turns any regressor compatible with the scikit-learn API into a
recursive autoregressive (multi-step) forecaster.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
regressor |
object |
An instance of a regressor or pipeline compatible with the scikit-learn API. |
required |
lags |
Union[int, numpy.ndarray, list] |
Lags used as predictors. Index starts at 1, so lag 1 is equal to t-1.
|
required |
transformer_y |
Optional[object] |
An instance of a transformer (preprocessor) compatible with the scikit-learn
preprocessing API with methods: fit, transform, fit_transform and inverse_transform.
ColumnTransformers are not allowed since they do not have inverse_transform method.
The transformation is applied to |
None |
transformer_exog |
Optional[object] |
An instance of a transformer (preprocessor) compatible with the scikit-learn
preprocessing API. The transformation is applied to |
None |
weight_func |
Optional[Callable] |
Function that defines the individual weights for each sample based on the
index. For example, a function that assigns a lower weight to certain dates.
Ignored if |
None |
fit_kwargs |
Optional[dict] |
Additional arguments to be passed to the |
None |
forecaster_id |
Union[str, int] |
Name used as an identifier of the forecaster. New in version 0.7.0 |
None |
Attributes:
| Name | Type | Description |
|---|---|---|
regressor |
regressor or pipeline compatible with the scikit-learn API |
An instance of a regressor or pipeline compatible with the scikit-learn API. |
lags |
numpy ndarray |
Lags used as predictors. |
transformer_y |
object transformer (preprocessor), default `None` |
An instance of a transformer (preprocessor) compatible with the scikit-learn
preprocessing API with methods: fit, transform, fit_transform and inverse_transform.
ColumnTransformers are not allowed since they do not have inverse_transform method.
The transformation is applied to |
transformer_exog |
object transformer (preprocessor), default `None` |
An instance of a transformer (preprocessor) compatible with the scikit-learn
preprocessing API. The transformation is applied to |
weight_func |
Callable |
Function that defines the individual weights for each sample based on the
index. For example, a function that assigns a lower weight to certain dates.
Ignored if |
source_code_weight_func |
str |
Source code of the custom function used to create weights. New in version 0.6.0 |
max_lag |
int |
Maximum value of lag included in |
window_size |
int |
Size of the window needed to create the predictors. It is equal to
|
last_window |
pandas Series |
Last window the forecaster has seen during training. It stores the
values needed to predict the next |
index_type |
type |
Type of index of the input used in training. |
index_freq |
str |
Frequency of Index of the input used in training. |
training_range |
pandas Index |
First and last values of index of the data used during training. |
included_exog |
bool |
If the forecaster has been trained using exogenous variable/s. |
exog_type |
type |
Type of exogenous data (pandas Series or DataFrame) used in training. |
exog_dtypes |
dict |
Type of each exogenous variable/s used in training. If |
exog_col_names |
list |
Names of columns of |
X_train_col_names |
list |
Names of columns of the matrix created internally for training. |
fit_kwargs |
dict |
Additional arguments to be passed to the |
in_sample_residuals |
numpy ndarray |
Residuals of the model when predicting training data. Only stored up to
1000 values. If |
out_sample_residuals |
numpy ndarray |
Residuals of the model when predicting non training data. Only stored
up to 1000 values. If |
fitted |
bool |
Tag to identify if the regressor has been fitted (trained). |
creation_date |
str |
Date of creation. |
fit_date |
str |
Date of last fit. |
skforcast_version |
str |
Version of skforecast library used to create the forecaster. |
python_version |
str |
Version of python used to create the forecaster. |
forecaster_id |
str, int default `None` |
Name used as an identifier of the forecaster. New in version 0.7.0 |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
class ForecasterAutoreg(ForecasterBase):
"""
This class turns any regressor compatible with the scikit-learn API into a
recursive autoregressive (multi-step) forecaster.
Parameters
----------
regressor : regressor or pipeline compatible with the scikit-learn API
An instance of a regressor or pipeline compatible with the scikit-learn API.
lags : int, list, 1d numpy ndarray, range
Lags used as predictors. Index starts at 1, so lag 1 is equal to t-1.
`int`: include lags from 1 to `lags` (included).
`list`, `numpy ndarray` or `range`: include only lags present in `lags`,
all elements must be int.
transformer_y : object transformer (preprocessor), default `None`
An instance of a transformer (preprocessor) compatible with the scikit-learn
preprocessing API with methods: fit, transform, fit_transform and inverse_transform.
ColumnTransformers are not allowed since they do not have inverse_transform method.
The transformation is applied to `y` before training the forecaster.
transformer_exog : object transformer (preprocessor), default `None`
An instance of a transformer (preprocessor) compatible with the scikit-learn
preprocessing API. The transformation is applied to `exog` before training the
forecaster. `inverse_transform` is not available when using ColumnTransformers.
weight_func : Callable, default `None`
Function that defines the individual weights for each sample based on the
index. For example, a function that assigns a lower weight to certain dates.
Ignored if `regressor` does not have the argument `sample_weight` in its `fit`
method. The resulting `sample_weight` cannot have negative values.
fit_kwargs : dict, default `None`
Additional arguments to be passed to the `fit` method of the regressor.
**New in version 0.8.0**
forecaster_id : str, int, default `None`
Name used as an identifier of the forecaster.
**New in version 0.7.0**
Attributes
----------
regressor : regressor or pipeline compatible with the scikit-learn API
An instance of a regressor or pipeline compatible with the scikit-learn API.
lags : numpy ndarray
Lags used as predictors.
transformer_y : object transformer (preprocessor), default `None`
An instance of a transformer (preprocessor) compatible with the scikit-learn
preprocessing API with methods: fit, transform, fit_transform and inverse_transform.
ColumnTransformers are not allowed since they do not have inverse_transform method.
The transformation is applied to `y` before training the forecaster.
transformer_exog : object transformer (preprocessor), default `None`
An instance of a transformer (preprocessor) compatible with the scikit-learn
preprocessing API. The transformation is applied to `exog` before training the
forecaster. `inverse_transform` is not available when using ColumnTransformers.
weight_func : Callable
Function that defines the individual weights for each sample based on the
index. For example, a function that assigns a lower weight to certain dates.
Ignored if `regressor` does not have the argument `sample_weight` in its `fit`
method.
**New in version 0.6.0**
source_code_weight_func : str
Source code of the custom function used to create weights.
**New in version 0.6.0**
max_lag : int
Maximum value of lag included in `lags`.
window_size : int
Size of the window needed to create the predictors. It is equal to
`max_lag`.
last_window : pandas Series
Last window the forecaster has seen during training. It stores the
values needed to predict the next `step` immediately after the training data.
index_type : type
Type of index of the input used in training.
index_freq : str
Frequency of Index of the input used in training.
training_range : pandas Index
First and last values of index of the data used during training.
included_exog : bool
If the forecaster has been trained using exogenous variable/s.
exog_type : type
Type of exogenous data (pandas Series or DataFrame) used in training.
exog_dtypes : dict
Type of each exogenous variable/s used in training. If `transformer_exog`
is used, the dtypes are calculated after the transformation.
exog_col_names : list
Names of columns of `exog` if `exog` used in training was a pandas
DataFrame.
X_train_col_names : list
Names of columns of the matrix created internally for training.
fit_kwargs : dict
Additional arguments to be passed to the `fit` method of the regressor.
**New in version 0.8.0**
in_sample_residuals : numpy ndarray
Residuals of the model when predicting training data. Only stored up to
1000 values. If `transformer_y` is not `None`, residuals are stored in the
transformed scale.
out_sample_residuals : numpy ndarray
Residuals of the model when predicting non training data. Only stored
up to 1000 values. If `transformer_y` is not `None`, residuals
are assumed to be in the transformed scale. Use `set_out_sample_residuals`
method to set values.
fitted : bool
Tag to identify if the regressor has been fitted (trained).
creation_date : str
Date of creation.
fit_date : str
Date of last fit.
skforcast_version : str
Version of skforecast library used to create the forecaster.
python_version : str
Version of python used to create the forecaster.
forecaster_id : str, int default `None`
Name used as an identifier of the forecaster.
**New in version 0.7.0**
"""
def __init__(
self,
regressor: object,
lags: Union[int, np.ndarray, list],
transformer_y: Optional[object]=None,
transformer_exog: Optional[object]=None,
weight_func: Optional[Callable]=None,
fit_kwargs: Optional[dict]=None,
forecaster_id: Optional[Union[str, int]]=None
) -> None:
self.regressor = regressor
self.transformer_y = transformer_y
self.transformer_exog = transformer_exog
self.weight_func = weight_func
self.source_code_weight_func = None
self.last_window = None
self.index_type = None
self.index_freq = None
self.training_range = None
self.included_exog = False
self.exog_type = None
self.exog_dtypes = None
self.exog_col_names = None
self.X_train_col_names = None
self.in_sample_residuals = None
self.out_sample_residuals = None
self.fitted = False
self.creation_date = pd.Timestamp.today().strftime('%Y-%m-%d %H:%M:%S')
self.fit_date = None
self.skforcast_version = skforecast.__version__
self.python_version = sys.version.split(" ")[0]
self.forecaster_id = forecaster_id
self.lags = initialize_lags(type(self).__name__, lags)
self.max_lag = max(self.lags)
self.window_size = self.max_lag
self.weight_func, self.source_code_weight_func, _ = initialize_weights(
forecaster_name = type(self).__name__,
regressor = regressor,
weight_func = weight_func,
series_weights = None
)
self.fit_kwargs = check_select_fit_kwargs(
regressor = regressor,
fit_kwargs = fit_kwargs
)
def __repr__(
self
) -> str:
"""
Information displayed when a ForecasterAutoreg object is printed.
"""
if isinstance(self.regressor, sklearn.pipeline.Pipeline):
name_pipe_steps = tuple(name + "__" for name in self.regressor.named_steps.keys())
params = {key : value for key, value in self.regressor.get_params().items() \
if key.startswith(name_pipe_steps)}
else:
params = self.regressor.get_params(deep=True)
info = (
f"{'=' * len(type(self).__name__)} \n"
f"{type(self).__name__} \n"
f"{'=' * len(type(self).__name__)} \n"
f"Regressor: {self.regressor} \n"
f"Lags: {self.lags} \n"
f"Transformer for y: {self.transformer_y} \n"
f"Transformer for exog: {self.transformer_exog} \n"
f"Window size: {self.window_size} \n"
f"Weight function included: {True if self.weight_func is not None else False} \n"
f"Exogenous included: {self.included_exog} \n"
f"Type of exogenous variable: {self.exog_type} \n"
f"Exogenous variables names: {self.exog_col_names} \n"
f"Training range: {self.training_range.to_list() if self.fitted else None} \n"
f"Training index type: {str(self.index_type).split('.')[-1][:-2] if self.fitted else None} \n"
f"Training index frequency: {self.index_freq if self.fitted else None} \n"
f"Regressor parameters: {params} \n"
f"fit_kwargs: {self.fit_kwargs} \n"
f"Creation date: {self.creation_date} \n"
f"Last fit date: {self.fit_date} \n"
f"Skforecast version: {self.skforcast_version} \n"
f"Python version: {self.python_version} \n"
f"Forecaster id: {self.forecaster_id} \n"
)
return info
def _create_lags(
self,
y: np.ndarray
) -> Tuple[np.ndarray, np.ndarray]:
"""
Transforms a 1d array into a 2d array (X) and a 1d array (y). Each row
in X is associated with a value of y and it represents the lags that
precede it.
Notice that, the returned matrix X_data, contains the lag 1 in the first
column, the lag 2 in the second column and so on.
Parameters
----------
y : 1d numpy ndarray
Training time series.
Returns
-------
X_data : 2d numpy ndarray, shape (samples - max(self.lags), len(self.lags))
2d numpy array with the lagged values (predictors).
y_data : 1d numpy ndarray, shape (samples - max(self.lags),)
Values of the time series related to each row of `X_data`.
"""
n_splits = len(y) - self.max_lag
if n_splits <= 0:
raise ValueError(
f"The maximum lag ({self.max_lag}) must be less than the length "
f"of the series ({len(y)})."
)
X_data = np.full(shape=(n_splits, len(self.lags)), fill_value=np.nan, dtype=float)
for i, lag in enumerate(self.lags):
X_data[:, i] = y[self.max_lag - lag: -lag]
y_data = y[self.max_lag:]
return X_data, y_data
def create_train_X_y(
self,
y: pd.Series,
exog: Optional[Union[pd.Series, pd.DataFrame]]=None
) -> Tuple[pd.DataFrame, pd.Series]:
"""
Create training matrices from univariate time series and exogenous
variables.
Parameters
----------
y : pandas Series
Training time series.
exog : pandas Series, pandas DataFrame, default `None`
Exogenous variable/s included as predictor/s. Must have the same
number of observations as `y` and their indexes must be aligned.
Returns
-------
X_train : pandas DataFrame, shape (len(y) - self.max_lag, len(self.lags))
Pandas DataFrame with the training values (predictors).
y_train : pandas Series, shape (len(y) - self.max_lag, )
Values (target) of the time series related to each row of `X_train`.
"""
check_y(y=y)
y = transform_series(
series = y,
transformer = self.transformer_y,
fit = True,
inverse_transform = False
)
y_values, y_index = preprocess_y(y=y)
if exog is not None:
if len(exog) != len(y):
raise ValueError(
(f'`exog` must have same number of samples as `y`. '
f'length `exog`: ({len(exog)}), length `y`: ({len(y)})')
)
check_exog(exog=exog, allow_nan=True)
if isinstance(exog, pd.Series):
exog = transform_series(
series = exog,
transformer = self.transformer_exog,
fit = True,
inverse_transform = False
)
else:
exog = transform_dataframe(
df = exog,
transformer = self.transformer_exog,
fit = True,
inverse_transform = False
)
check_exog(exog=exog, allow_nan=False)
check_exog_dtypes(exog)
self.exog_dtypes = get_exog_dtypes(exog=exog)
_, exog_index = preprocess_exog(exog=exog, return_values=False)
if not (exog_index[:len(y_index)] == y_index).all():
raise ValueError(
("Different index for `y` and `exog`. They must be equal "
"to ensure the correct alignment of values.")
)
X_train, y_train = self._create_lags(y=y_values)
X_train_col_names = [f"lag_{i}" for i in self.lags]
X_train = pd.DataFrame(
data = X_train,
columns = X_train_col_names,
index = y_index[self.max_lag: ]
)
if exog is not None:
# The first `self.max_lag` positions have to be removed from exog
# since they are not in X_train.
exog_to_train = exog.iloc[self.max_lag:, ]
X_train = pd.concat((X_train, exog_to_train), axis=1)
self.X_train_col_names = X_train.columns.to_list()
y_train = pd.Series(
data = y_train,
index = y_index[self.max_lag: ],
name = 'y'
)
return X_train, y_train
def create_sample_weights(
self,
X_train: pd.DataFrame,
)-> np.ndarray:
"""
Crate weights for each observation according to the forecaster's attribute
`weight_func`.
Parameters
----------
X_train : pandas DataFrame
Dataframe generated with the method `create_train_X_y`, first return.
Returns
-------
sample_weight : numpy ndarray
Weights to use in `fit` method.
"""
sample_weight = None
if self.weight_func is not None:
sample_weight = self.weight_func(X_train.index)
if sample_weight is not None:
if np.isnan(sample_weight).any():
raise ValueError(
"The resulting `sample_weight` cannot have NaN values."
)
if np.any(sample_weight < 0):
raise ValueError(
"The resulting `sample_weight` cannot have negative values."
)
if np.sum(sample_weight) == 0:
raise ValueError(
("The resulting `sample_weight` cannot be normalized because "
"the sum of the weights is zero.")
)
return sample_weight
def fit(
self,
y: pd.Series,
exog: Optional[Union[pd.Series, pd.DataFrame]]=None
) -> None:
"""
Training Forecaster.
Additional arguments to be passed to the `fit` method of the regressor
can be added with the `fit_kwargs` argument when initializing the forecaster.
Parameters
----------
y : pandas Series
Training time series.
exog : pandas Series, pandas DataFrame, default `None`
Exogenous variable/s included as predictor/s. Must have the same
number of observations as `y` and their indexes must be aligned so
that y[i] is regressed on exog[i].
Returns
-------
None
"""
# Reset values in case the forecaster has already been fitted.
self.index_type = None
self.index_freq = None
self.last_window = None
self.included_exog = False
self.exog_type = None
self.exog_dtypes = None
self.exog_col_names = None
self.X_train_col_names = None
self.in_sample_residuals = None
self.fitted = False
self.training_range = None
if exog is not None:
self.included_exog = True
self.exog_type = type(exog)
self.exog_col_names = \
exog.columns.to_list() if isinstance(exog, pd.DataFrame) else exog.name
X_train, y_train = self.create_train_X_y(y=y, exog=exog)
sample_weight = self.create_sample_weights(X_train=X_train)
if sample_weight is not None:
self.regressor.fit(X=X_train, y=y_train, sample_weight=sample_weight,
**self.fit_kwargs)
else:
self.regressor.fit(X=X_train, y=y_train, **self.fit_kwargs)
self.fitted = True
self.fit_date = pd.Timestamp.today().strftime('%Y-%m-%d %H:%M:%S')
self.training_range = preprocess_y(y=y, return_values=False)[1][[0, -1]]
self.index_type = type(X_train.index)
if isinstance(X_train.index, pd.DatetimeIndex):
self.index_freq = X_train.index.freqstr
else:
self.index_freq = X_train.index.step
residuals = (y_train - self.regressor.predict(X_train)).to_numpy()
if len(residuals) > 1000:
# Only up to 1000 residuals are stored
rng = np.random.default_rng(seed=123)
residuals = rng.choice(
a = residuals,
size = 1000,
replace = False
)
self.in_sample_residuals = residuals
# The last time window of training data is stored so that lags needed as
# predictors in the first iteration of `predict()` can be calculated.
self.last_window = y.iloc[-self.max_lag:].copy()
def _recursive_predict(
self,
steps: int,
last_window: np.ndarray,
exog: Optional[np.ndarray]=None
) -> np.ndarray:
"""
Predict n steps ahead. It is an iterative process in which, each prediction,
is used as a predictor for the next step.
Parameters
----------
steps : int
Number of future steps predicted.
last_window : numpy ndarray
Series values used to create the predictors (lags) needed in the
first iteration of the prediction (t + 1).
exog : numpy ndarray, default `None`
Exogenous variable/s included as predictor/s.
Returns
-------
predictions : numpy ndarray
Predicted values.
"""
predictions = np.full(shape=steps, fill_value=np.nan)
for i in range(steps):
X = last_window[-self.lags].reshape(1, -1)
if exog is not None:
X = np.column_stack((X, exog[i, ].reshape(1, -1)))
with warnings.catch_warnings():
# Suppress scikit-learn warning: "X does not have valid feature names,
# but NoOpTransformer was fitted with feature names".
warnings.simplefilter("ignore")
prediction = self.regressor.predict(X)
predictions[i] = prediction.ravel()[0]
# Update `last_window` values. The first position is discarded and
# the new prediction is added at the end.
last_window = np.append(last_window[1:], prediction)
return predictions
def predict(
self,
steps: int,
last_window: Optional[pd.Series]=None,
exog: Optional[Union[pd.Series, pd.DataFrame]]=None
) -> pd.Series:
"""
Predict n steps ahead. It is an recursive process in which, each prediction,
is used as a predictor for the next step.
Parameters
----------
steps : int
Number of future steps predicted.
last_window : pandas Series, default `None`
Series values used to create the predictors (lags) needed in the
first iteration of the prediction (t + 1).
If `last_window = None`, the values stored in `self.last_window` are
used to calculate the initial predictors, and the predictions start
right after training data.
exog : pandas Series, pandas DataFrame, default `None`
Exogenous variable/s included as predictor/s.
Returns
-------
predictions : pandas Series
Predicted values.
"""
if last_window is None:
last_window = copy(self.last_window)
check_predict_input(
forecaster_name = type(self).__name__,
steps = steps,
fitted = self.fitted,
included_exog = self.included_exog,
index_type = self.index_type,
index_freq = self.index_freq,
window_size = self.window_size,
last_window = last_window,
last_window_exog = None,
exog = exog,
exog_type = self.exog_type,
exog_col_names = self.exog_col_names,
interval = None,
alpha = None,
max_steps = None,
levels = None,
series_col_names = None
)
if exog is not None:
if isinstance(exog, pd.DataFrame):
exog = transform_dataframe(
df = exog,
transformer = self.transformer_exog,
fit = False,
inverse_transform = False
)
else:
exog = transform_series(
series = exog,
transformer = self.transformer_exog,
fit = False,
inverse_transform = False
)
check_exog_dtypes(exog=exog)
exog_values = exog.iloc[:steps, ].to_numpy()
else:
exog_values = None
last_window = transform_series(
series = last_window,
transformer = self.transformer_y,
fit = False,
inverse_transform = False
)
last_window_values, last_window_index = preprocess_last_window(
last_window = last_window
)
predictions = self._recursive_predict(
steps = steps,
last_window = copy(last_window_values),
exog = copy(exog_values)
)
predictions = pd.Series(
data = predictions,
index = expand_index(
index = last_window_index,
steps = steps
),
name = 'pred'
)
predictions = transform_series(
series = predictions,
transformer = self.transformer_y,
fit = False,
inverse_transform = True
)
return predictions
def predict_bootstrapping(
self,
steps: int,
last_window: Optional[pd.Series]=None,
exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
n_boot: int=500,
random_state: int=123,
in_sample_residuals: bool=True
) -> pd.DataFrame:
"""
Generate multiple forecasting predictions using a bootstrapping process.
By sampling from a collection of past observed errors (the residuals),
each iteration of bootstrapping generates a different set of predictions.
See the Notes section for more information.
Parameters
----------
steps : int
Number of future steps predicted.
last_window : pandas Series, default `None`
Series values used to create the predictors (lags) needed in the
first iteration of the prediction (t + 1).
If `last_window = None`, the values stored in `self.last_window` are
used to calculate the initial predictors, and the predictions start
right after training data.
exog : pandas Series, pandas DataFrame, default `None`
Exogenous variable/s included as predictor/s.
n_boot : int, default `500`
Number of bootstrapping iterations used to estimate prediction
intervals.
random_state : int, default `123`
Sets a seed to the random generator, so that boot intervals are always
deterministic.
in_sample_residuals : bool, default `True`
If `True`, residuals from the training data are used as proxy of
prediction error to create prediction intervals. If `False`, out of
sample residuals are used. In the latter case, the user should have
calculated and stored the residuals within the forecaster (see
`set_out_sample_residuals()`).
Returns
-------
boot_predictions : pandas DataFrame, shape (steps, n_boot)
Predictions generated by bootstrapping.
Notes
-----
More information about prediction intervals in forecasting:
https://otexts.com/fpp3/prediction-intervals.html#prediction-intervals-from-bootstrapped-residuals
Forecasting: Principles and Practice (3nd ed) Rob J Hyndman and George Athanasopoulos.
"""
if not in_sample_residuals and self.out_sample_residuals is None:
raise ValueError(
('`forecaster.out_sample_residuals` is `None`. Use '
'`in_sample_residuals=True` or method `set_out_sample_residuals()` '
'before `predict_interval()`, `predict_bootstrapping()` or '
'`predict_dist()`.')
)
if last_window is None:
last_window = copy(self.last_window)
check_predict_input(
forecaster_name = type(self).__name__,
steps = steps,
fitted = self.fitted,
included_exog = self.included_exog,
index_type = self.index_type,
index_freq = self.index_freq,
window_size = self.window_size,
last_window = last_window,
last_window_exog = None,
exog = exog,
exog_type = self.exog_type,
exog_col_names = self.exog_col_names,
interval = None,
alpha = None,
max_steps = None,
levels = None,
series_col_names = None
)
if exog is not None:
if isinstance(exog, pd.DataFrame):
exog = transform_dataframe(
df = exog,
transformer = self.transformer_exog,
fit = False,
inverse_transform = False
)
else:
exog = transform_series(
series = exog,
transformer = self.transformer_exog,
fit = False,
inverse_transform = False
)
exog_values = exog.iloc[:steps, ].to_numpy()
else:
exog_values = None
last_window = transform_series(
series = last_window,
transformer = self.transformer_y,
fit = False,
inverse_transform = False
)
last_window_values, last_window_index = preprocess_last_window(
last_window = last_window
)
boot_predictions = np.full(
shape = (steps, n_boot),
fill_value = np.nan,
dtype = float
)
rng = np.random.default_rng(seed=random_state)
seeds = rng.integers(low=0, high=10000, size=n_boot)
if in_sample_residuals:
residuals = self.in_sample_residuals
else:
residuals = self.out_sample_residuals
for i in range(n_boot):
# In each bootstraping iteration the initial last_window and exog
# need to be restored.
last_window_boot = last_window_values.copy()
exog_boot = exog_values.copy() if exog is not None else None
rng = np.random.default_rng(seed=seeds[i])
sample_residuals = rng.choice(
a = residuals,
size = steps,
replace = True
)
for step in range(steps):
prediction = self._recursive_predict(
steps = 1,
last_window = last_window_boot,
exog = exog_boot
)
prediction_with_residual = prediction + sample_residuals[step]
boot_predictions[step, i] = prediction_with_residual
last_window_boot = np.append(
last_window_boot[1:],
prediction_with_residual
)
if exog is not None:
exog_boot = exog_boot[1:]
boot_predictions = pd.DataFrame(
data = boot_predictions,
index = expand_index(last_window_index, steps=steps),
columns = [f"pred_boot_{i}" for i in range(n_boot)]
)
if self.transformer_y:
for col in boot_predictions.columns:
boot_predictions[col] = transform_series(
series = boot_predictions[col],
transformer = self.transformer_y,
fit = False,
inverse_transform = True
)
return boot_predictions
def predict_interval(
self,
steps: int,
last_window: Optional[pd.Series]=None,
exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
interval: list=[5, 95],
n_boot: int=500,
random_state: int=123,
in_sample_residuals: bool=True
) -> pd.DataFrame:
"""
Iterative process in which each prediction is used as a predictor
for the next step, and bootstrapping is used to estimate prediction
intervals. Both predictions and intervals are returned.
Parameters
----------
steps : int
Number of future steps predicted.
last_window : pandas Series, default `None`
Series values used to create the predictors (lags) needed in the
first iteration of the prediction (t + 1).
If `last_window = None`, the values stored in` self.last_window` are
used to calculate the initial predictors, and the predictions start
right after training data.
exog : pandas Series, pandas DataFrame, default `None`
Exogenous variable/s included as predictor/s.
interval : list, default `[5, 95]`
Confidence of the prediction interval estimated. Sequence of
percentiles to compute, which must be between 0 and 100 inclusive.
For example, interval of 95% should be as `interval = [2.5, 97.5]`.
n_boot : int, default `500`
Number of bootstrapping iterations used to estimate prediction
intervals.
random_state : int, default `123`
Sets a seed to the random generator, so that boot intervals are always
deterministic.
in_sample_residuals : bool, default `True`
If `True`, residuals from the training data are used as proxy of
prediction error to create prediction intervals. If `False`, out of
sample residuals are used. In the latter case, the user should have
calculated and stored the residuals within the forecaster (see
`set_out_sample_residuals()`).
Returns
-------
predictions : pandas DataFrame
Values predicted by the forecaster and their estimated interval:
- pred: predictions.
- lower_bound: lower bound of the interval.
- upper_bound: upper bound interval of the interval.
Notes
-----
More information about prediction intervals in forecasting:
https://otexts.com/fpp2/prediction-intervals.html
Forecasting: Principles and Practice (2nd ed) Rob J Hyndman and
George Athanasopoulos.
"""
check_interval(interval=interval)
predictions = self.predict(
steps = steps,
last_window = last_window,
exog = exog
)
boot_predictions = self.predict_bootstrapping(
steps = steps,
last_window = last_window,
exog = exog,
n_boot = n_boot,
random_state = random_state,
in_sample_residuals = in_sample_residuals
)
interval = np.array(interval)/100
predictions_interval = boot_predictions.quantile(q=interval, axis=1).transpose()
predictions_interval.columns = ['lower_bound', 'upper_bound']
predictions = pd.concat((predictions, predictions_interval), axis=1)
return predictions
def predict_dist(
self,
steps: int,
distribution: object,
last_window: Optional[pd.Series]=None,
exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
n_boot: int=500,
random_state: int=123,
in_sample_residuals: bool=True
) -> pd.DataFrame:
"""
Fit a given probability distribution for each step. After generating
multiple forecasting predictions through a bootstrapping process, each
step is fitted to the given distribution.
Parameters
----------
steps : int
Number of future steps predicted.
distribution : Object
A distribution object from scipy.stats.
last_window : pandas Series, default `None`
Series values used to create the predictors (lags) needed in the
first iteration of the prediction (t + 1).
If `last_window = None`, the values stored in` self.last_window` are
used to calculate the initial predictors, and the predictions start
right after training data.
exog : pandas Series, pandas DataFrame, default `None`
Exogenous variable/s included as predictor/s.
n_boot : int, default `500`
Number of bootstrapping iterations used to estimate prediction
intervals.
random_state : int, default `123`
Sets a seed to the random generator, so that boot intervals are always
deterministic.
in_sample_residuals : bool, default `True`
If `True`, residuals from the training data are used as proxy of
prediction error to create prediction intervals. If `False`, out of
sample residuals are used. In the latter case, the user should have
calculated and stored the residuals within the forecaster (see
`set_out_sample_residuals()`).
Returns
-------
predictions : pandas DataFrame
Distribution parameters estimated for each step.
"""
boot_samples = self.predict_bootstrapping(
steps = steps,
last_window = last_window,
exog = exog,
n_boot = n_boot,
random_state = random_state,
in_sample_residuals = in_sample_residuals
)
param_names = [p for p in inspect.signature(distribution._pdf).parameters if not p=='x'] + ["loc","scale"]
param_values = np.apply_along_axis(lambda x: distribution.fit(x), axis=1, arr=boot_samples)
predictions = pd.DataFrame(
data = param_values,
columns = param_names,
index = boot_samples.index
)
return predictions
def set_params(
self,
params: dict
) -> None:
"""
Set new values to the parameters of the scikit learn model stored in the
forecaster.
Parameters
----------
params : dict
Parameters values.
Returns
-------
self
"""
self.regressor = clone(self.regressor)
self.regressor.set_params(**params)
def set_fit_kwargs(
self,
fit_kwargs: dict
) -> None:
"""
Set new values for the additional keyword arguments passed to the `fit`
method of the regressor.
Parameters
----------
fit_kwargs : dict
Dict of the form {"argument": new_value}.
Returns
-------
None
"""
self.fit_kwargs = check_select_fit_kwargs(self.regressor, fit_kwargs=fit_kwargs)
def set_lags(
self,
lags: Union[int, list, np.ndarray, range]
) -> None:
"""
Set new value to the attribute `lags`.
Attributes `max_lag` and `window_size` are also updated.
Parameters
----------
lags : int, list, 1D np.ndarray, range
Lags used as predictors. Index starts at 1, so lag 1 is equal to t-1.
`int`: include lags from 1 to `lags`.
`list` or `np.ndarray`: include only lags present in `lags`.
Returns
-------
None
"""
self.lags = initialize_lags(type(self).__name__, lags)
self.max_lag = max(self.lags)
self.window_size = max(self.lags)
def set_out_sample_residuals(
self,
residuals: np.ndarray,
append: bool=True,
transform: bool=True,
random_state: int=123
)-> None:
"""
Set new values to the attribute `out_sample_residuals`. Out of sample
residuals are meant to be calculated using observations that did not
participate in the training process.
Parameters
----------
residuals : numpy ndarray
Values of residuals. If len(residuals) > 1000, only a random sample
of 1000 values are stored.
append : bool, default `True`
If `True`, new residuals are added to the once already stored in the
attribute `out_sample_residuals`. Once the limit of 1000 values is
reached, no more values are appended. If False, `out_sample_residuals`
is overwritten with the new residuals.
transform : bool, default `True`
If `True`, new residuals are transformed using self.transformer_y.
random_state : int, default `123`
Sets a seed to the random sampling for reproducible output.
Returns
-------
self
"""
if not isinstance(residuals, np.ndarray):
raise TypeError(
f"`residuals` argument must be `numpy ndarray`. Got {type(residuals)}."
)
if not transform and self.transformer_y is not None:
warnings.warn(
(f"Argument `transform` is set to `False` but forecaster was trained "
f"using a transformer {self.transformer_y}. Ensure that the new residuals "
f"are already transformed or set `transform=True`.")
)
if transform and self.transformer_y is not None:
warnings.warn(
(f"Residuals will be transformed using the same transformer used "
f"when training the forecaster ({self.transformer_y}). Ensure that the "
f"new residuals are on the same scale as the original time series.")
)
residuals = transform_series(
series = pd.Series(residuals, name='residuals'),
transformer = self.transformer_y,
fit = False,
inverse_transform = False
).to_numpy()
if len(residuals) > 1000:
rng = np.random.default_rng(seed=random_state)
residuals = rng.choice(a=residuals, size=1000, replace=False)
if append and self.out_sample_residuals is not None:
free_space = max(0, 1000 - len(self.out_sample_residuals))
if len(residuals) < free_space:
residuals = np.hstack((
self.out_sample_residuals,
residuals
))
else:
residuals = np.hstack((
self.out_sample_residuals,
residuals[:free_space]
))
self.out_sample_residuals = residuals
def get_feature_importances(
self
) -> pd.DataFrame:
"""
Return feature importances of the regressor stored in the
forecaster. Only valid when regressor stores internally the feature
importances in the attribute `feature_importances_` or `coef_`.
Parameters
----------
self
Returns
-------
feature_importances : pandas DataFrame
Feature importances associated with each predictor.
"""
if not self.fitted:
raise sklearn.exceptions.NotFittedError(
("This forecaster is not fitted yet. Call `fit` with appropriate "
"arguments before using `get_feature_importances()`.")
)
if isinstance(self.regressor, sklearn.pipeline.Pipeline):
estimator = self.regressor[-1]
else:
estimator = self.regressor
if hasattr(estimator, 'feature_importances_'):
feature_importances = estimator.feature_importances_
elif hasattr(estimator, 'coef_'):
feature_importances = estimator.coef_
else:
warnings.warn(
(f"Impossible to access feature importances for regressor of type "
f"{type(estimator)}. This method is only valid when the "
f"regressor stores internally the feature importances in the "
f"attribute `feature_importances_` or `coef_`.")
)
feature_importances = None
if feature_importances is not None:
feature_importances = pd.DataFrame({
'feature': self.X_train_col_names,
'importance': feature_importances
})
return feature_importances
def get_feature_importance(
self
) -> pd.DataFrame:
"""
This method has been replaced by `get_feature_importances()`.
Return feature importances of the regressor stored in the
forecaster. Only valid when regressor stores internally the feature
importances in the attribute `feature_importances_` or `coef_`.
Parameters
----------
self
Returns
-------
feature_importances : pandas DataFrame
Feature importances associated with each predictor.
"""
warnings.warn(
("get_feature_importance() method has been renamed to get_feature_importances(). "
"This method will be removed in skforecast 0.9.0.")
)
return self.get_feature_importances()
create_sample_weights(self, X_train)
¶
Crate weights for each observation according to the forecaster's attribute
weight_func.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
X_train |
DataFrame |
Dataframe generated with the method |
required |
Returns:
| Type | Description |
|---|---|
ndarray |
Weights to use in |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def create_sample_weights(
self,
X_train: pd.DataFrame,
)-> np.ndarray:
"""
Crate weights for each observation according to the forecaster's attribute
`weight_func`.
Parameters
----------
X_train : pandas DataFrame
Dataframe generated with the method `create_train_X_y`, first return.
Returns
-------
sample_weight : numpy ndarray
Weights to use in `fit` method.
"""
sample_weight = None
if self.weight_func is not None:
sample_weight = self.weight_func(X_train.index)
if sample_weight is not None:
if np.isnan(sample_weight).any():
raise ValueError(
"The resulting `sample_weight` cannot have NaN values."
)
if np.any(sample_weight < 0):
raise ValueError(
"The resulting `sample_weight` cannot have negative values."
)
if np.sum(sample_weight) == 0:
raise ValueError(
("The resulting `sample_weight` cannot be normalized because "
"the sum of the weights is zero.")
)
return sample_weight
create_train_X_y(self, y, exog=None)
¶
Create training matrices from univariate time series and exogenous
variables.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
y |
Series |
Training time series. |
required |
exog |
Union[pandas.core.series.Series, pandas.core.frame.DataFrame] |
Exogenous variable/s included as predictor/s. Must have the same
number of observations as |
None |
Returns:
| Type | Description |
|---|---|
Tuple[pandas.core.frame.DataFrame, pandas.core.series.Series] |
Pandas DataFrame with the training values (predictors). |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def create_train_X_y(
self,
y: pd.Series,
exog: Optional[Union[pd.Series, pd.DataFrame]]=None
) -> Tuple[pd.DataFrame, pd.Series]:
"""
Create training matrices from univariate time series and exogenous
variables.
Parameters
----------
y : pandas Series
Training time series.
exog : pandas Series, pandas DataFrame, default `None`
Exogenous variable/s included as predictor/s. Must have the same
number of observations as `y` and their indexes must be aligned.
Returns
-------
X_train : pandas DataFrame, shape (len(y) - self.max_lag, len(self.lags))
Pandas DataFrame with the training values (predictors).
y_train : pandas Series, shape (len(y) - self.max_lag, )
Values (target) of the time series related to each row of `X_train`.
"""
check_y(y=y)
y = transform_series(
series = y,
transformer = self.transformer_y,
fit = True,
inverse_transform = False
)
y_values, y_index = preprocess_y(y=y)
if exog is not None:
if len(exog) != len(y):
raise ValueError(
(f'`exog` must have same number of samples as `y`. '
f'length `exog`: ({len(exog)}), length `y`: ({len(y)})')
)
check_exog(exog=exog, allow_nan=True)
if isinstance(exog, pd.Series):
exog = transform_series(
series = exog,
transformer = self.transformer_exog,
fit = True,
inverse_transform = False
)
else:
exog = transform_dataframe(
df = exog,
transformer = self.transformer_exog,
fit = True,
inverse_transform = False
)
check_exog(exog=exog, allow_nan=False)
check_exog_dtypes(exog)
self.exog_dtypes = get_exog_dtypes(exog=exog)
_, exog_index = preprocess_exog(exog=exog, return_values=False)
if not (exog_index[:len(y_index)] == y_index).all():
raise ValueError(
("Different index for `y` and `exog`. They must be equal "
"to ensure the correct alignment of values.")
)
X_train, y_train = self._create_lags(y=y_values)
X_train_col_names = [f"lag_{i}" for i in self.lags]
X_train = pd.DataFrame(
data = X_train,
columns = X_train_col_names,
index = y_index[self.max_lag: ]
)
if exog is not None:
# The first `self.max_lag` positions have to be removed from exog
# since they are not in X_train.
exog_to_train = exog.iloc[self.max_lag:, ]
X_train = pd.concat((X_train, exog_to_train), axis=1)
self.X_train_col_names = X_train.columns.to_list()
y_train = pd.Series(
data = y_train,
index = y_index[self.max_lag: ],
name = 'y'
)
return X_train, y_train
fit(self, y, exog=None)
¶
Training Forecaster.
Additional arguments to be passed to the fit method of the regressor
can be added with the fit_kwargs argument when initializing the forecaster.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
y |
Series |
Training time series. |
required |
exog |
Union[pandas.core.series.Series, pandas.core.frame.DataFrame] |
Exogenous variable/s included as predictor/s. Must have the same
number of observations as |
None |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def fit(
self,
y: pd.Series,
exog: Optional[Union[pd.Series, pd.DataFrame]]=None
) -> None:
"""
Training Forecaster.
Additional arguments to be passed to the `fit` method of the regressor
can be added with the `fit_kwargs` argument when initializing the forecaster.
Parameters
----------
y : pandas Series
Training time series.
exog : pandas Series, pandas DataFrame, default `None`
Exogenous variable/s included as predictor/s. Must have the same
number of observations as `y` and their indexes must be aligned so
that y[i] is regressed on exog[i].
Returns
-------
None
"""
# Reset values in case the forecaster has already been fitted.
self.index_type = None
self.index_freq = None
self.last_window = None
self.included_exog = False
self.exog_type = None
self.exog_dtypes = None
self.exog_col_names = None
self.X_train_col_names = None
self.in_sample_residuals = None
self.fitted = False
self.training_range = None
if exog is not None:
self.included_exog = True
self.exog_type = type(exog)
self.exog_col_names = \
exog.columns.to_list() if isinstance(exog, pd.DataFrame) else exog.name
X_train, y_train = self.create_train_X_y(y=y, exog=exog)
sample_weight = self.create_sample_weights(X_train=X_train)
if sample_weight is not None:
self.regressor.fit(X=X_train, y=y_train, sample_weight=sample_weight,
**self.fit_kwargs)
else:
self.regressor.fit(X=X_train, y=y_train, **self.fit_kwargs)
self.fitted = True
self.fit_date = pd.Timestamp.today().strftime('%Y-%m-%d %H:%M:%S')
self.training_range = preprocess_y(y=y, return_values=False)[1][[0, -1]]
self.index_type = type(X_train.index)
if isinstance(X_train.index, pd.DatetimeIndex):
self.index_freq = X_train.index.freqstr
else:
self.index_freq = X_train.index.step
residuals = (y_train - self.regressor.predict(X_train)).to_numpy()
if len(residuals) > 1000:
# Only up to 1000 residuals are stored
rng = np.random.default_rng(seed=123)
residuals = rng.choice(
a = residuals,
size = 1000,
replace = False
)
self.in_sample_residuals = residuals
# The last time window of training data is stored so that lags needed as
# predictors in the first iteration of `predict()` can be calculated.
self.last_window = y.iloc[-self.max_lag:].copy()
get_feature_importance(self)
¶
This method has been replaced by get_feature_importances().
Return feature importances of the regressor stored in the
forecaster. Only valid when regressor stores internally the feature
importances in the attribute feature_importances_ or coef_.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
self |
None |
required |
Returns:
| Type | Description |
|---|---|
DataFrame |
Feature importances associated with each predictor. |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def get_feature_importance(
self
) -> pd.DataFrame:
"""
This method has been replaced by `get_feature_importances()`.
Return feature importances of the regressor stored in the
forecaster. Only valid when regressor stores internally the feature
importances in the attribute `feature_importances_` or `coef_`.
Parameters
----------
self
Returns
-------
feature_importances : pandas DataFrame
Feature importances associated with each predictor.
"""
warnings.warn(
("get_feature_importance() method has been renamed to get_feature_importances(). "
"This method will be removed in skforecast 0.9.0.")
)
return self.get_feature_importances()
get_feature_importances(self)
¶
Return feature importances of the regressor stored in the
forecaster. Only valid when regressor stores internally the feature
importances in the attribute feature_importances_ or coef_.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
self |
None |
required |
Returns:
| Type | Description |
|---|---|
DataFrame |
Feature importances associated with each predictor. |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def get_feature_importances(
self
) -> pd.DataFrame:
"""
Return feature importances of the regressor stored in the
forecaster. Only valid when regressor stores internally the feature
importances in the attribute `feature_importances_` or `coef_`.
Parameters
----------
self
Returns
-------
feature_importances : pandas DataFrame
Feature importances associated with each predictor.
"""
if not self.fitted:
raise sklearn.exceptions.NotFittedError(
("This forecaster is not fitted yet. Call `fit` with appropriate "
"arguments before using `get_feature_importances()`.")
)
if isinstance(self.regressor, sklearn.pipeline.Pipeline):
estimator = self.regressor[-1]
else:
estimator = self.regressor
if hasattr(estimator, 'feature_importances_'):
feature_importances = estimator.feature_importances_
elif hasattr(estimator, 'coef_'):
feature_importances = estimator.coef_
else:
warnings.warn(
(f"Impossible to access feature importances for regressor of type "
f"{type(estimator)}. This method is only valid when the "
f"regressor stores internally the feature importances in the "
f"attribute `feature_importances_` or `coef_`.")
)
feature_importances = None
if feature_importances is not None:
feature_importances = pd.DataFrame({
'feature': self.X_train_col_names,
'importance': feature_importances
})
return feature_importances
predict(self, steps, last_window=None, exog=None)
¶
Predict n steps ahead. It is an recursive process in which, each prediction,
is used as a predictor for the next step.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
steps |
int |
Number of future steps predicted. |
required |
last_window |
Optional[pandas.core.series.Series] |
Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If |
None |
exog |
Union[pandas.core.series.Series, pandas.core.frame.DataFrame] |
Exogenous variable/s included as predictor/s. |
None |
Returns:
| Type | Description |
|---|---|
Series |
Predicted values. |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def predict(
self,
steps: int,
last_window: Optional[pd.Series]=None,
exog: Optional[Union[pd.Series, pd.DataFrame]]=None
) -> pd.Series:
"""
Predict n steps ahead. It is an recursive process in which, each prediction,
is used as a predictor for the next step.
Parameters
----------
steps : int
Number of future steps predicted.
last_window : pandas Series, default `None`
Series values used to create the predictors (lags) needed in the
first iteration of the prediction (t + 1).
If `last_window = None`, the values stored in `self.last_window` are
used to calculate the initial predictors, and the predictions start
right after training data.
exog : pandas Series, pandas DataFrame, default `None`
Exogenous variable/s included as predictor/s.
Returns
-------
predictions : pandas Series
Predicted values.
"""
if last_window is None:
last_window = copy(self.last_window)
check_predict_input(
forecaster_name = type(self).__name__,
steps = steps,
fitted = self.fitted,
included_exog = self.included_exog,
index_type = self.index_type,
index_freq = self.index_freq,
window_size = self.window_size,
last_window = last_window,
last_window_exog = None,
exog = exog,
exog_type = self.exog_type,
exog_col_names = self.exog_col_names,
interval = None,
alpha = None,
max_steps = None,
levels = None,
series_col_names = None
)
if exog is not None:
if isinstance(exog, pd.DataFrame):
exog = transform_dataframe(
df = exog,
transformer = self.transformer_exog,
fit = False,
inverse_transform = False
)
else:
exog = transform_series(
series = exog,
transformer = self.transformer_exog,
fit = False,
inverse_transform = False
)
check_exog_dtypes(exog=exog)
exog_values = exog.iloc[:steps, ].to_numpy()
else:
exog_values = None
last_window = transform_series(
series = last_window,
transformer = self.transformer_y,
fit = False,
inverse_transform = False
)
last_window_values, last_window_index = preprocess_last_window(
last_window = last_window
)
predictions = self._recursive_predict(
steps = steps,
last_window = copy(last_window_values),
exog = copy(exog_values)
)
predictions = pd.Series(
data = predictions,
index = expand_index(
index = last_window_index,
steps = steps
),
name = 'pred'
)
predictions = transform_series(
series = predictions,
transformer = self.transformer_y,
fit = False,
inverse_transform = True
)
return predictions
predict_bootstrapping(self, steps, last_window=None, exog=None, n_boot=500, random_state=123, in_sample_residuals=True)
¶
Generate multiple forecasting predictions using a bootstrapping process.
By sampling from a collection of past observed errors (the residuals), each iteration of bootstrapping generates a different set of predictions. See the Notes section for more information.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
steps |
int |
Number of future steps predicted. |
required |
last_window |
Optional[pandas.core.series.Series] |
Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If |
None |
exog |
Union[pandas.core.series.Series, pandas.core.frame.DataFrame] |
Exogenous variable/s included as predictor/s. |
None |
n_boot |
int |
Number of bootstrapping iterations used to estimate prediction intervals. |
500 |
random_state |
int |
Sets a seed to the random generator, so that boot intervals are always deterministic. |
123 |
in_sample_residuals |
bool |
If |
True |
Returns:
| Type | Description |
|---|---|
DataFrame |
Predictions generated by bootstrapping. |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def predict_bootstrapping(
self,
steps: int,
last_window: Optional[pd.Series]=None,
exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
n_boot: int=500,
random_state: int=123,
in_sample_residuals: bool=True
) -> pd.DataFrame:
"""
Generate multiple forecasting predictions using a bootstrapping process.
By sampling from a collection of past observed errors (the residuals),
each iteration of bootstrapping generates a different set of predictions.
See the Notes section for more information.
Parameters
----------
steps : int
Number of future steps predicted.
last_window : pandas Series, default `None`
Series values used to create the predictors (lags) needed in the
first iteration of the prediction (t + 1).
If `last_window = None`, the values stored in `self.last_window` are
used to calculate the initial predictors, and the predictions start
right after training data.
exog : pandas Series, pandas DataFrame, default `None`
Exogenous variable/s included as predictor/s.
n_boot : int, default `500`
Number of bootstrapping iterations used to estimate prediction
intervals.
random_state : int, default `123`
Sets a seed to the random generator, so that boot intervals are always
deterministic.
in_sample_residuals : bool, default `True`
If `True`, residuals from the training data are used as proxy of
prediction error to create prediction intervals. If `False`, out of
sample residuals are used. In the latter case, the user should have
calculated and stored the residuals within the forecaster (see
`set_out_sample_residuals()`).
Returns
-------
boot_predictions : pandas DataFrame, shape (steps, n_boot)
Predictions generated by bootstrapping.
Notes
-----
More information about prediction intervals in forecasting:
https://otexts.com/fpp3/prediction-intervals.html#prediction-intervals-from-bootstrapped-residuals
Forecasting: Principles and Practice (3nd ed) Rob J Hyndman and George Athanasopoulos.
"""
if not in_sample_residuals and self.out_sample_residuals is None:
raise ValueError(
('`forecaster.out_sample_residuals` is `None`. Use '
'`in_sample_residuals=True` or method `set_out_sample_residuals()` '
'before `predict_interval()`, `predict_bootstrapping()` or '
'`predict_dist()`.')
)
if last_window is None:
last_window = copy(self.last_window)
check_predict_input(
forecaster_name = type(self).__name__,
steps = steps,
fitted = self.fitted,
included_exog = self.included_exog,
index_type = self.index_type,
index_freq = self.index_freq,
window_size = self.window_size,
last_window = last_window,
last_window_exog = None,
exog = exog,
exog_type = self.exog_type,
exog_col_names = self.exog_col_names,
interval = None,
alpha = None,
max_steps = None,
levels = None,
series_col_names = None
)
if exog is not None:
if isinstance(exog, pd.DataFrame):
exog = transform_dataframe(
df = exog,
transformer = self.transformer_exog,
fit = False,
inverse_transform = False
)
else:
exog = transform_series(
series = exog,
transformer = self.transformer_exog,
fit = False,
inverse_transform = False
)
exog_values = exog.iloc[:steps, ].to_numpy()
else:
exog_values = None
last_window = transform_series(
series = last_window,
transformer = self.transformer_y,
fit = False,
inverse_transform = False
)
last_window_values, last_window_index = preprocess_last_window(
last_window = last_window
)
boot_predictions = np.full(
shape = (steps, n_boot),
fill_value = np.nan,
dtype = float
)
rng = np.random.default_rng(seed=random_state)
seeds = rng.integers(low=0, high=10000, size=n_boot)
if in_sample_residuals:
residuals = self.in_sample_residuals
else:
residuals = self.out_sample_residuals
for i in range(n_boot):
# In each bootstraping iteration the initial last_window and exog
# need to be restored.
last_window_boot = last_window_values.copy()
exog_boot = exog_values.copy() if exog is not None else None
rng = np.random.default_rng(seed=seeds[i])
sample_residuals = rng.choice(
a = residuals,
size = steps,
replace = True
)
for step in range(steps):
prediction = self._recursive_predict(
steps = 1,
last_window = last_window_boot,
exog = exog_boot
)
prediction_with_residual = prediction + sample_residuals[step]
boot_predictions[step, i] = prediction_with_residual
last_window_boot = np.append(
last_window_boot[1:],
prediction_with_residual
)
if exog is not None:
exog_boot = exog_boot[1:]
boot_predictions = pd.DataFrame(
data = boot_predictions,
index = expand_index(last_window_index, steps=steps),
columns = [f"pred_boot_{i}" for i in range(n_boot)]
)
if self.transformer_y:
for col in boot_predictions.columns:
boot_predictions[col] = transform_series(
series = boot_predictions[col],
transformer = self.transformer_y,
fit = False,
inverse_transform = True
)
return boot_predictions
predict_dist(self, steps, distribution, last_window=None, exog=None, n_boot=500, random_state=123, in_sample_residuals=True)
¶
Fit a given probability distribution for each step. After generating
multiple forecasting predictions through a bootstrapping process, each step is fitted to the given distribution.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
steps |
int |
Number of future steps predicted. |
required |
distribution |
object |
A distribution object from scipy.stats. |
required |
last_window |
Optional[pandas.core.series.Series] |
Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If |
None |
exog |
Union[pandas.core.series.Series, pandas.core.frame.DataFrame] |
Exogenous variable/s included as predictor/s. |
None |
n_boot |
int |
Number of bootstrapping iterations used to estimate prediction intervals. |
500 |
random_state |
int |
Sets a seed to the random generator, so that boot intervals are always deterministic. |
123 |
in_sample_residuals |
bool |
If |
True |
Returns:
| Type | Description |
|---|---|
DataFrame |
Distribution parameters estimated for each step. |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def predict_dist(
self,
steps: int,
distribution: object,
last_window: Optional[pd.Series]=None,
exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
n_boot: int=500,
random_state: int=123,
in_sample_residuals: bool=True
) -> pd.DataFrame:
"""
Fit a given probability distribution for each step. After generating
multiple forecasting predictions through a bootstrapping process, each
step is fitted to the given distribution.
Parameters
----------
steps : int
Number of future steps predicted.
distribution : Object
A distribution object from scipy.stats.
last_window : pandas Series, default `None`
Series values used to create the predictors (lags) needed in the
first iteration of the prediction (t + 1).
If `last_window = None`, the values stored in` self.last_window` are
used to calculate the initial predictors, and the predictions start
right after training data.
exog : pandas Series, pandas DataFrame, default `None`
Exogenous variable/s included as predictor/s.
n_boot : int, default `500`
Number of bootstrapping iterations used to estimate prediction
intervals.
random_state : int, default `123`
Sets a seed to the random generator, so that boot intervals are always
deterministic.
in_sample_residuals : bool, default `True`
If `True`, residuals from the training data are used as proxy of
prediction error to create prediction intervals. If `False`, out of
sample residuals are used. In the latter case, the user should have
calculated and stored the residuals within the forecaster (see
`set_out_sample_residuals()`).
Returns
-------
predictions : pandas DataFrame
Distribution parameters estimated for each step.
"""
boot_samples = self.predict_bootstrapping(
steps = steps,
last_window = last_window,
exog = exog,
n_boot = n_boot,
random_state = random_state,
in_sample_residuals = in_sample_residuals
)
param_names = [p for p in inspect.signature(distribution._pdf).parameters if not p=='x'] + ["loc","scale"]
param_values = np.apply_along_axis(lambda x: distribution.fit(x), axis=1, arr=boot_samples)
predictions = pd.DataFrame(
data = param_values,
columns = param_names,
index = boot_samples.index
)
return predictions
predict_interval(self, steps, last_window=None, exog=None, interval=[5, 95], n_boot=500, random_state=123, in_sample_residuals=True)
¶
Iterative process in which each prediction is used as a predictor
for the next step, and bootstrapping is used to estimate prediction intervals. Both predictions and intervals are returned.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
steps |
int |
Number of future steps predicted. |
required |
last_window |
Optional[pandas.core.series.Series] |
Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). If |
None |
exog |
Union[pandas.core.series.Series, pandas.core.frame.DataFrame] |
Exogenous variable/s included as predictor/s. |
None |
interval |
list |
Confidence of the prediction interval estimated. Sequence of
percentiles to compute, which must be between 0 and 100 inclusive.
For example, interval of 95% should be as |
[5, 95] |
n_boot |
int |
Number of bootstrapping iterations used to estimate prediction intervals. |
500 |
random_state |
int |
Sets a seed to the random generator, so that boot intervals are always deterministic. |
123 |
in_sample_residuals |
bool |
If |
True |
Returns:
| Type | Description |
|---|---|
DataFrame |
Values predicted by the forecaster and their estimated interval:
|
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def predict_interval(
self,
steps: int,
last_window: Optional[pd.Series]=None,
exog: Optional[Union[pd.Series, pd.DataFrame]]=None,
interval: list=[5, 95],
n_boot: int=500,
random_state: int=123,
in_sample_residuals: bool=True
) -> pd.DataFrame:
"""
Iterative process in which each prediction is used as a predictor
for the next step, and bootstrapping is used to estimate prediction
intervals. Both predictions and intervals are returned.
Parameters
----------
steps : int
Number of future steps predicted.
last_window : pandas Series, default `None`
Series values used to create the predictors (lags) needed in the
first iteration of the prediction (t + 1).
If `last_window = None`, the values stored in` self.last_window` are
used to calculate the initial predictors, and the predictions start
right after training data.
exog : pandas Series, pandas DataFrame, default `None`
Exogenous variable/s included as predictor/s.
interval : list, default `[5, 95]`
Confidence of the prediction interval estimated. Sequence of
percentiles to compute, which must be between 0 and 100 inclusive.
For example, interval of 95% should be as `interval = [2.5, 97.5]`.
n_boot : int, default `500`
Number of bootstrapping iterations used to estimate prediction
intervals.
random_state : int, default `123`
Sets a seed to the random generator, so that boot intervals are always
deterministic.
in_sample_residuals : bool, default `True`
If `True`, residuals from the training data are used as proxy of
prediction error to create prediction intervals. If `False`, out of
sample residuals are used. In the latter case, the user should have
calculated and stored the residuals within the forecaster (see
`set_out_sample_residuals()`).
Returns
-------
predictions : pandas DataFrame
Values predicted by the forecaster and their estimated interval:
- pred: predictions.
- lower_bound: lower bound of the interval.
- upper_bound: upper bound interval of the interval.
Notes
-----
More information about prediction intervals in forecasting:
https://otexts.com/fpp2/prediction-intervals.html
Forecasting: Principles and Practice (2nd ed) Rob J Hyndman and
George Athanasopoulos.
"""
check_interval(interval=interval)
predictions = self.predict(
steps = steps,
last_window = last_window,
exog = exog
)
boot_predictions = self.predict_bootstrapping(
steps = steps,
last_window = last_window,
exog = exog,
n_boot = n_boot,
random_state = random_state,
in_sample_residuals = in_sample_residuals
)
interval = np.array(interval)/100
predictions_interval = boot_predictions.quantile(q=interval, axis=1).transpose()
predictions_interval.columns = ['lower_bound', 'upper_bound']
predictions = pd.concat((predictions, predictions_interval), axis=1)
return predictions
set_fit_kwargs(self, fit_kwargs)
¶
Set new values for the additional keyword arguments passed to the fit
method of the regressor.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
fit_kwargs |
dict |
Dict of the form {"argument": new_value}. |
required |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def set_fit_kwargs(
self,
fit_kwargs: dict
) -> None:
"""
Set new values for the additional keyword arguments passed to the `fit`
method of the regressor.
Parameters
----------
fit_kwargs : dict
Dict of the form {"argument": new_value}.
Returns
-------
None
"""
self.fit_kwargs = check_select_fit_kwargs(self.regressor, fit_kwargs=fit_kwargs)
set_lags(self, lags)
¶
Set new value to the attribute lags.
Attributes max_lag and window_size are also updated.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
lags |
Union[int, list, numpy.ndarray, range] |
Lags used as predictors. Index starts at 1, so lag 1 is equal to t-1.
|
required |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def set_lags(
self,
lags: Union[int, list, np.ndarray, range]
) -> None:
"""
Set new value to the attribute `lags`.
Attributes `max_lag` and `window_size` are also updated.
Parameters
----------
lags : int, list, 1D np.ndarray, range
Lags used as predictors. Index starts at 1, so lag 1 is equal to t-1.
`int`: include lags from 1 to `lags`.
`list` or `np.ndarray`: include only lags present in `lags`.
Returns
-------
None
"""
self.lags = initialize_lags(type(self).__name__, lags)
self.max_lag = max(self.lags)
self.window_size = max(self.lags)
set_out_sample_residuals(self, residuals, append=True, transform=True, random_state=123)
¶
Set new values to the attribute out_sample_residuals. Out of sample
residuals are meant to be calculated using observations that did not participate in the training process.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
residuals |
ndarray |
Values of residuals. If len(residuals) > 1000, only a random sample of 1000 values are stored. |
required |
append |
bool |
If |
True |
transform |
bool |
If |
True |
random_state |
int |
Sets a seed to the random sampling for reproducible output. |
123 |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def set_out_sample_residuals(
self,
residuals: np.ndarray,
append: bool=True,
transform: bool=True,
random_state: int=123
)-> None:
"""
Set new values to the attribute `out_sample_residuals`. Out of sample
residuals are meant to be calculated using observations that did not
participate in the training process.
Parameters
----------
residuals : numpy ndarray
Values of residuals. If len(residuals) > 1000, only a random sample
of 1000 values are stored.
append : bool, default `True`
If `True`, new residuals are added to the once already stored in the
attribute `out_sample_residuals`. Once the limit of 1000 values is
reached, no more values are appended. If False, `out_sample_residuals`
is overwritten with the new residuals.
transform : bool, default `True`
If `True`, new residuals are transformed using self.transformer_y.
random_state : int, default `123`
Sets a seed to the random sampling for reproducible output.
Returns
-------
self
"""
if not isinstance(residuals, np.ndarray):
raise TypeError(
f"`residuals` argument must be `numpy ndarray`. Got {type(residuals)}."
)
if not transform and self.transformer_y is not None:
warnings.warn(
(f"Argument `transform` is set to `False` but forecaster was trained "
f"using a transformer {self.transformer_y}. Ensure that the new residuals "
f"are already transformed or set `transform=True`.")
)
if transform and self.transformer_y is not None:
warnings.warn(
(f"Residuals will be transformed using the same transformer used "
f"when training the forecaster ({self.transformer_y}). Ensure that the "
f"new residuals are on the same scale as the original time series.")
)
residuals = transform_series(
series = pd.Series(residuals, name='residuals'),
transformer = self.transformer_y,
fit = False,
inverse_transform = False
).to_numpy()
if len(residuals) > 1000:
rng = np.random.default_rng(seed=random_state)
residuals = rng.choice(a=residuals, size=1000, replace=False)
if append and self.out_sample_residuals is not None:
free_space = max(0, 1000 - len(self.out_sample_residuals))
if len(residuals) < free_space:
residuals = np.hstack((
self.out_sample_residuals,
residuals
))
else:
residuals = np.hstack((
self.out_sample_residuals,
residuals[:free_space]
))
self.out_sample_residuals = residuals
set_params(self, params)
¶
Set new values to the parameters of the scikit learn model stored in the
forecaster.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
params |
dict |
Parameters values. |
required |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def set_params(
self,
params: dict
) -> None:
"""
Set new values to the parameters of the scikit learn model stored in the
forecaster.
Parameters
----------
params : dict
Parameters values.
Returns
-------
self
"""
self.regressor = clone(self.regressor)
self.regressor.set_params(**params)
_create_lags(self, y)
private
¶
Transforms a 1d array into a 2d array (X) and a 1d array (y). Each row
in X is associated with a value of y and it represents the lags that precede it.
Notice that, the returned matrix X_data, contains the lag 1 in the first column, the lag 2 in the second column and so on.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
y |
ndarray |
Training time series. |
required |
Returns:
| Type | Description |
|---|---|
Tuple[numpy.ndarray, numpy.ndarray] |
2d numpy array with the lagged values (predictors). |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def _create_lags(
self,
y: np.ndarray
) -> Tuple[np.ndarray, np.ndarray]:
"""
Transforms a 1d array into a 2d array (X) and a 1d array (y). Each row
in X is associated with a value of y and it represents the lags that
precede it.
Notice that, the returned matrix X_data, contains the lag 1 in the first
column, the lag 2 in the second column and so on.
Parameters
----------
y : 1d numpy ndarray
Training time series.
Returns
-------
X_data : 2d numpy ndarray, shape (samples - max(self.lags), len(self.lags))
2d numpy array with the lagged values (predictors).
y_data : 1d numpy ndarray, shape (samples - max(self.lags),)
Values of the time series related to each row of `X_data`.
"""
n_splits = len(y) - self.max_lag
if n_splits <= 0:
raise ValueError(
f"The maximum lag ({self.max_lag}) must be less than the length "
f"of the series ({len(y)})."
)
X_data = np.full(shape=(n_splits, len(self.lags)), fill_value=np.nan, dtype=float)
for i, lag in enumerate(self.lags):
X_data[:, i] = y[self.max_lag - lag: -lag]
y_data = y[self.max_lag:]
return X_data, y_data
_recursive_predict(self, steps, last_window, exog=None)
private
¶
Predict n steps ahead. It is an iterative process in which, each prediction,
is used as a predictor for the next step.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
steps |
int |
Number of future steps predicted. |
required |
last_window |
ndarray |
Series values used to create the predictors (lags) needed in the first iteration of the prediction (t + 1). |
required |
exog |
Optional[numpy.ndarray] |
Exogenous variable/s included as predictor/s. |
None |
Returns:
| Type | Description |
|---|---|
ndarray |
Predicted values. |
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def _recursive_predict(
self,
steps: int,
last_window: np.ndarray,
exog: Optional[np.ndarray]=None
) -> np.ndarray:
"""
Predict n steps ahead. It is an iterative process in which, each prediction,
is used as a predictor for the next step.
Parameters
----------
steps : int
Number of future steps predicted.
last_window : numpy ndarray
Series values used to create the predictors (lags) needed in the
first iteration of the prediction (t + 1).
exog : numpy ndarray, default `None`
Exogenous variable/s included as predictor/s.
Returns
-------
predictions : numpy ndarray
Predicted values.
"""
predictions = np.full(shape=steps, fill_value=np.nan)
for i in range(steps):
X = last_window[-self.lags].reshape(1, -1)
if exog is not None:
X = np.column_stack((X, exog[i, ].reshape(1, -1)))
with warnings.catch_warnings():
# Suppress scikit-learn warning: "X does not have valid feature names,
# but NoOpTransformer was fitted with feature names".
warnings.simplefilter("ignore")
prediction = self.regressor.predict(X)
predictions[i] = prediction.ravel()[0]
# Update `last_window` values. The first position is discarded and
# the new prediction is added at the end.
last_window = np.append(last_window[1:], prediction)
return predictions
__repr__(self)
special
¶
Information displayed when a ForecasterAutoreg object is printed.
Source code in skforecast/ForecasterAutoreg/ForecasterAutoreg.py
def __repr__(
self
) -> str:
"""
Information displayed when a ForecasterAutoreg object is printed.
"""
if isinstance(self.regressor, sklearn.pipeline.Pipeline):
name_pipe_steps = tuple(name + "__" for name in self.regressor.named_steps.keys())
params = {key : value for key, value in self.regressor.get_params().items() \
if key.startswith(name_pipe_steps)}
else:
params = self.regressor.get_params(deep=True)
info = (
f"{'=' * len(type(self).__name__)} \n"
f"{type(self).__name__} \n"
f"{'=' * len(type(self).__name__)} \n"
f"Regressor: {self.regressor} \n"
f"Lags: {self.lags} \n"
f"Transformer for y: {self.transformer_y} \n"
f"Transformer for exog: {self.transformer_exog} \n"
f"Window size: {self.window_size} \n"
f"Weight function included: {True if self.weight_func is not None else False} \n"
f"Exogenous included: {self.included_exog} \n"
f"Type of exogenous variable: {self.exog_type} \n"
f"Exogenous variables names: {self.exog_col_names} \n"
f"Training range: {self.training_range.to_list() if self.fitted else None} \n"
f"Training index type: {str(self.index_type).split('.')[-1][:-2] if self.fitted else None} \n"
f"Training index frequency: {self.index_freq if self.fitted else None} \n"
f"Regressor parameters: {params} \n"
f"fit_kwargs: {self.fit_kwargs} \n"
f"Creation date: {self.creation_date} \n"
f"Last fit date: {self.fit_date} \n"
f"Skforecast version: {self.skforcast_version} \n"
f"Python version: {self.python_version} \n"
f"Forecaster id: {self.forecaster_id} \n"
)
return info