ForecasterEquivalentDate

skforecast.recursive._forecaster_equivalent_date.ForecasterEquivalentDate

ForecasterEquivalentDate(
    offset,
    n_offsets=1,
    agg_func=np.mean,
    binner_kwargs=None,
    forecaster_id=None,
)

This forecaster predicts future values based on the most recent equivalent date. It also allows to aggregate multiple past values of the equivalent date using a function (e.g. mean, median, max, min, etc.). The equivalent date is calculated by moving back in time a specified number of steps (offset). The offset can be defined as an integer or as a pandas DateOffset. This approach is useful as a baseline, but it is a simplistic method and may not capture complex underlying patterns.

Parameters:

Name	Type	Description	Default
offset	(int, DateOffset)	Number of steps to go back in time to find the most recent equivalent date to the target period. If offset is an integer, it represents the number of steps to go back in time. For example, if the frequency of the time series is daily, offset = 7 means that the most recent data similar to the target period is the value observed 7 days ago. Pandas DateOffsets can also be used to move forward a given number of valid dates. For example, Bday(2) can be used to move back two business days. If the date does not start on a valid date, it is first moved to a valid date. For example, if the date is a Saturday, it is moved to the previous Friday. Then, the offset is applied. If the result is a non-valid date, it is moved to the next valid date. For example, if the date is a Sunday, it is moved to the next Monday. For more information about offsets, see https://pandas.pydata.org/docs/reference/offset_frequency.html.	required
n_offsets	int	Number of equivalent dates (multiple of offset) used in the prediction. If n_offsets is greater than 1, the values at the equivalent dates are aggregated using the agg_func function. For example, if the frequency of the time series is daily, offset = 7, n_offsets = 2 and agg_func = np.mean, the predicted value will be the mean of the values observed 7 and 14 days ago.	1
agg_func	Callable	Function used to aggregate the values of the equivalent dates when the number of equivalent dates (n_offsets) is greater than 1.	np.mean
binner_kwargs	dict	Additional arguments to pass to the QuantileBinner used to discretize the residuals into k bins according to the predicted values associated with each residual. Available arguments are: n_bins, method, subsample, random_state and dtype. Argument method is passed internally to the function numpy.percentile. New in version 0.17.0	None
forecaster_id	(str, int)	Name used as an identifier of the forecaster.	None

Attributes:

Name	Type	Description
offset	(int, DateOffset)	Number of steps to go back in time to find the most recent equivalent date to the target period. If offset is an integer, it represents the number of steps to go back in time. For example, if the frequency of the time series is daily, offset = 7 means that the most recent data similar to the target period is the value observed 7 days ago. Pandas DateOffsets can also be used to move forward a given number of valid dates. For example, Bday(2) can be used to move back two business days. If the date does not start on a valid date, it is first moved to a valid date. For example, if the date is a Saturday, it is moved to the previous Friday. Then, the offset is applied. If the result is a non-valid date, it is moved to the next valid date. For example, if the date is a Sunday, it is moved to the next Monday. For more information about offsets, see https://pandas.pydata.org/docs/reference/offset_frequency.html.
n_offsets	int	Number of equivalent dates (multiple of offset) used in the prediction. If offset is greater than 1, the value at the equivalent dates is aggregated using the agg_func function. For example, if the frequency of the time series is daily, offset = 7, n_offsets = 2 and agg_func = np.mean, the predicted value will be the mean of the values observed 7 and 14 days ago.
agg_func	Callable	Function used to aggregate the values of the equivalent dates when the number of equivalent dates (n_offsets) is greater than 1.
window_size	int	Number of past values needed to include the last equivalent dates according to the offset and n_offsets.
last_window_	pandas Series	This window represents the most recent data observed by the predictor during its training phase. It contains the past values needed to include the last equivalent date according the offset and n_offsets.
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.
series_name_in_	str	Names of the series provided by the user during training.
in_sample_residuals_	numpy ndarray	Residuals of the model when predicting training data. Only stored up to 10_000 values. If transformer_y is not None, residuals are stored in the transformed scale. If differentiation is not None, residuals are stored after differentiation.
in_sample_residuals_by_bin_	dict	In sample residuals binned according to the predicted value each residual is associated with. The number of residuals stored per bin is limited to 10_000 // self.binner.n_bins_ in the form {bin: residuals}. If transformer_y is not None, residuals are stored in the transformed scale. If differentiation is not None, residuals are stored after differentiation.
out_sample_residuals_	numpy ndarray	Residuals of the model when predicting non-training data. Only stored up to 10_000 values. Use set_out_sample_residuals() method to set values. If transformer_y is not None, residuals are stored in the transformed scale. If differentiation is not None, residuals are stored after differentiation.
out_sample_residuals_by_bin_	dict	Out of sample residuals binned according to the predicted value each residual is associated with. The number of residuals stored per bin is limited to 10_000 // self.binner.n_bins_ in the form {bin: residuals}. If transformer_y is not None, residuals are stored in the transformed scale. If differentiation is not None, residuals are stored after differentiation.
binner	QuantileBinner	QuantileBinner used to discretize residuals into k bins according to the predicted values associated with each residual.
binner_intervals_	dict	Intervals used to discretize residuals into k bins according to the predicted values associated with each residual.
binner_kwargs	dict	Additional arguments to pass to the QuantileBinner.
creation_date	str	Date of creation.
is_fitted	bool	Tag to identify if the regressor has been fitted (trained).
fit_date	str	Date of last fit.
skforecast_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)	Name used as an identifier of the forecaster.
_probabilistic_mode	(str, bool)	Private attribute used to indicate whether the forecaster should perform some calculations during backtesting.
regressor	Ignored	Not used, present here for API consistency by convention.
differentiation	Ignored	Not used, present here for API consistency by convention.
differentiation_max	Ignored	Not used, present here for API consistency by convention.

Methods:

Name	Description
fit	Training Forecaster.
predict	Predict n steps ahead.
predict_interval	Predict n steps ahead and estimate prediction intervals using conformal
set_in_sample_residuals	Set in-sample residuals in case they were not calculated during the
set_out_sample_residuals	Set new values to the attribute out_sample_residuals_. Out of sample
summary	Show forecaster information.

Source code in skforecast\recursive\_forecaster_equivalent_date.py

def __init__(
    self,
    offset: int | pd.tseries.offsets.DateOffset,
    n_offsets: int = 1,
    agg_func: Callable = np.mean,
    binner_kwargs: dict[str, object] | None = None,
    forecaster_id: str | int | None = None
) -> None:

    self.offset                       = offset
    self.n_offsets                    = n_offsets
    self.agg_func                     = agg_func
    self.last_window_                 = None
    self.index_type_                  = None
    self.index_freq_                  = None
    self.training_range_              = None
    self.series_name_in_              = None
    self.in_sample_residuals_         = None
    self.out_sample_residuals_        = None
    self.in_sample_residuals_by_bin_  = None
    self.out_sample_residuals_by_bin_ = None
    self.creation_date                = pd.Timestamp.today().strftime('%Y-%m-%d %H:%M:%S')
    self.is_fitted                    = False
    self.fit_date                     = None
    self.skforecast_version           = skforecast.__version__
    self.python_version               = sys.version.split(" ")[0]
    self.forecaster_id                = forecaster_id
    self._probabilistic_mode          = "binned"
    self.regressor                    = None
    self.differentiation              = None
    self.differentiation_max          = None

    if not isinstance(self.offset, (int, pd.tseries.offsets.DateOffset)):
        raise TypeError(
            "`offset` must be an integer greater than 0 or a "
            "pandas.tseries.offsets. Find more information about offsets in "
            "https://pandas.pydata.org/docs/reference/offset_frequency.html"
        )

    self.window_size = self.offset * self.n_offsets

    self.binner_kwargs = binner_kwargs
    if binner_kwargs is None:
        self.binner_kwargs = {
            'n_bins': 10, 'method': 'linear', 'subsample': 200000,
            'random_state': 789654, 'dtype': np.float64
        }
    self.binner = QuantileBinner(**self.binner_kwargs)
    self.binner_intervals_ = None

offset instance-attribute

offset = offset

n_offsets instance-attribute

n_offsets = n_offsets

agg_func instance-attribute

agg_func = agg_func

last_window_ instance-attribute

last_window_ = None

index_type_ instance-attribute

index_type_ = None

index_freq_ instance-attribute

index_freq_ = None

training_range_ instance-attribute

training_range_ = None

series_name_in_ instance-attribute

series_name_in_ = None

in_sample_residuals_ instance-attribute

in_sample_residuals_ = None

out_sample_residuals_ instance-attribute

out_sample_residuals_ = None

in_sample_residuals_by_bin_ instance-attribute

in_sample_residuals_by_bin_ = None

out_sample_residuals_by_bin_ instance-attribute

out_sample_residuals_by_bin_ = None

creation_date instance-attribute

creation_date = strftime('%Y-%m-%d %H:%M:%S')

is_fitted instance-attribute

is_fitted = False

fit_date instance-attribute

fit_date = None

skforecast_version instance-attribute

skforecast_version = __version__

python_version instance-attribute

python_version = split(' ')[0]

forecaster_id instance-attribute

forecaster_id = forecaster_id

_probabilistic_mode instance-attribute

_probabilistic_mode = 'binned'

regressor instance-attribute

regressor = None

differentiation instance-attribute

differentiation = None

differentiation_max instance-attribute

differentiation_max = None

window_size instance-attribute

window_size = offset * n_offsets

binner_kwargs instance-attribute

binner_kwargs = binner_kwargs

binner instance-attribute

binner = QuantileBinner(**(binner_kwargs))

binner_intervals_ instance-attribute

binner_intervals_ = None

_repr_html_

_repr_html_()

HTML representation of the object. The "General Information" section is expanded by default.

Source code in skforecast\recursive\_forecaster_equivalent_date.py

def _repr_html_(self):
    """
    HTML representation of the object.
    The "General Information" section is expanded by default.
    """

    style, unique_id = get_style_repr_html(self.is_fitted)

    content = f"""
    <div class="container-{unique_id}">
        <h2>{type(self).__name__}</h2>
        <details open>
            <summary>General Information</summary>
            <ul>
                <li><strong>Regressor:</strong> {type(self.regressor).__name__}</li>
                <li><strong>Offset:</strong> {self.offset}</li>
                <li><strong>Number of offsets:</strong> {self.n_offsets}</li>
                <li><strong>Aggregation function:</strong> {self.agg_func.__name__}</li>
                <li><strong>Window size:</strong> {self.window_size}</li>
                <li><strong>Creation date:</strong> {self.creation_date}</li>
                <li><strong>Last fit date:</strong> {self.fit_date}</li>
                <li><strong>Skforecast version:</strong> {self.skforecast_version}</li>
                <li><strong>Python version:</strong> {self.python_version}</li>
                <li><strong>Forecaster id:</strong> {self.forecaster_id}</li>
            </ul>
        </details>
        <details>
            <summary>Training Information</summary>
            <ul>
                <li><strong>Training range:</strong> {self.training_range_.to_list() if self.is_fitted else 'Not fitted'}</li>
                <li><strong>Training index type:</strong> {str(self.index_type_).split('.')[-1][:-2] if self.is_fitted else 'Not fitted'}</li>
                <li><strong>Training index frequency:</strong> {self.index_freq_ if self.is_fitted else 'Not fitted'}</li>
            </ul>
        </details>
        <p>
            <a href="https://skforecast.org/{skforecast.__version__}/api/forecasterequivalentdate.html">&#128712 <strong>API Reference</strong></a>
            &nbsp;&nbsp;
            <a href="https://skforecast.org/{skforecast.__version__}/user_guides/forecasting-baseline.html">&#128462 <strong>User Guide</strong></a>
        </p>
    </div>
    """

    return style + content

fit

fit(
    y,
    store_in_sample_residuals=False,
    random_state=123,
    exog=None,
)

Training Forecaster.

Parameters:

Name	Type	Description	Default
y	pandas Series	Training time series.	required
store_in_sample_residuals	bool	If True, in-sample residuals will be stored in the forecaster object after fitting (in_sample_residuals_ and in_sample_residuals_by_bin_ attributes). If False, only the intervals of the bins are stored.	False
random_state	int	Set a seed for the random generator so that the stored sample residuals are always deterministic.	123
exog	Ignored	Not used, present here for API consistency by convention.	None

Returns:

Type	Description
None

Source code in skforecast\recursive\_forecaster_equivalent_date.py

def fit(
    self,
    y: pd.Series,
    store_in_sample_residuals: bool = False,
    random_state: int = 123,
    exog: Any = None
) -> None:
    """
    Training Forecaster.

    Parameters
    ----------
    y : pandas Series
        Training time series.
    store_in_sample_residuals : bool, default False
        If `True`, in-sample residuals will be stored in the forecaster object
        after fitting (`in_sample_residuals_` and `in_sample_residuals_by_bin_`
        attributes).
        If `False`, only the intervals of the bins are stored.
    random_state : int, default 123
        Set a seed for the random generator so that the stored sample 
        residuals are always deterministic.
    exog : Ignored
        Not used, present here for API consistency by convention.

    Returns
    -------
    None

    """

    if not isinstance(y, pd.Series):
        raise TypeError(
            f"`y` must be a pandas Series with a DatetimeIndex or a RangeIndex. "
            f"Found {type(y)}."
        )

    if isinstance(self.offset, pd.tseries.offsets.DateOffset):
        if not isinstance(y.index, pd.DatetimeIndex):
            raise TypeError(
                "If `offset` is a pandas DateOffset, the index of `y` must be a "
                "pandas DatetimeIndex with frequency."
            )
        elif y.index.freq is None:
            raise TypeError(
                "If `offset` is a pandas DateOffset, the index of `y` must be a "
                "pandas DatetimeIndex with frequency."
            )

    # Reset values in case the forecaster has already been fitted.
    self.last_window_    = None
    self.index_type_     = None
    self.index_freq_     = None
    self.training_range_ = None
    self.series_name_in_ = None
    self.is_fitted       = False

    _, y_index = check_extract_values_and_index(
        data=y, data_label='`y`', return_values=False
    )

    if isinstance(self.offset, pd.tseries.offsets.DateOffset):
        # Calculate the window_size in steps for compatibility with the
        # check_predict_input function. This is not a exact calculation
        # because the offset follows the calendar rules and the distance
        # between two dates may not be constant.
        first_valid_index = (y_index[-1] - self.offset * self.n_offsets)

        try:
            window_size_idx_start = y_index.get_loc(first_valid_index)
            window_size_idx_end = y_index.get_loc(y_index[-1])
            self.window_size = window_size_idx_end - window_size_idx_start
        except KeyError:
            raise ValueError(
                f"The length of `y` ({len(y)}), must be greater than or equal "
                f"to the window size ({self.window_size}). This is because  "
                f"the offset ({self.offset}) is larger than the available "
                f"data. Try to decrease the size of the offset ({self.offset}), "
                f"the number of `n_offsets` ({self.n_offsets}) or increase the "
                f"size of `y`."
            )
    else:
        if len(y) <= self.window_size:
            raise ValueError(
                f"Length of `y` must be greater than the maximum window size "
                f"needed by the forecaster. This is because  "
                f"the offset ({self.offset}) is larger than the available "
                f"data. Try to decrease the size of the offset ({self.offset}), "
                f"the number of `n_offsets` ({self.n_offsets}) or increase the "
                f"size of `y`.\n"
                f"    Length `y`: {len(y)}.\n"
                f"    Max window size: {self.window_size}.\n"
            )

    self.is_fitted = True
    self.series_name_in_ = y.name if y.name is not None else 'y'
    self.fit_date = pd.Timestamp.today().strftime('%Y-%m-%d %H:%M:%S')
    self.training_range_ = y_index[[0, -1]]
    self.index_type_ = type(y_index)
    self.index_freq_ = (
        y_index.freqstr if isinstance(y_index, pd.DatetimeIndex) else y_index.step
    )

    # NOTE: This is done to save time during fit in functions such as backtesting()
    if self._probabilistic_mode is not False:
        self._binning_in_sample_residuals(
            y                         = y,
            store_in_sample_residuals = store_in_sample_residuals,
            random_state              = random_state
        )

    # The last time window of training data is stored so that equivalent
    # dates are available when calling the `predict` method.
    # Store the whole series to avoid errors when the offset is larger 
    # than the data available.
    self.last_window_ = y.copy()

_binning_in_sample_residuals

_binning_in_sample_residuals(
    y, store_in_sample_residuals=False, random_state=123
)

Bin residuals according to the predicted value each residual is associated with. First a skforecast.preprocessing.QuantileBinner object is fitted to the predicted values. Then, residuals are binned according to the predicted value each residual is associated with. Residuals are stored in the forecaster object as in_sample_residuals_ and in_sample_residuals_by_bin_.

The number of residuals stored per bin is limited to 10_000 // self.binner.n_bins_. The total number of residuals stored is 10_000. New in version 0.17.0

Parameters:

Name	Type	Description	Default
y	pandas Series	Training time series.	required
store_in_sample_residuals	bool	If True, in-sample residuals will be stored in the forecaster object after fitting (in_sample_residuals_ and in_sample_residuals_by_bin_ attributes). If False, only the intervals of the bins are stored.	False
random_state	int	Set a seed for the random generator so that the stored sample residuals are always deterministic.	123

Returns:

Type	Description
None

Source code in skforecast\recursive\_forecaster_equivalent_date.py

def _binning_in_sample_residuals(
    self,
    y: pd.Series,
    store_in_sample_residuals: bool = False,
    random_state: int = 123
) -> None:
    """
    Bin residuals according to the predicted value each residual is
    associated with. First a `skforecast.preprocessing.QuantileBinner` object
    is fitted to the predicted values. Then, residuals are binned according
    to the predicted value each residual is associated with. Residuals are
    stored in the forecaster object as `in_sample_residuals_` and
    `in_sample_residuals_by_bin_`.

    The number of residuals stored per bin is limited to 
    `10_000 // self.binner.n_bins_`. The total number of residuals stored is
    `10_000`.
    **New in version 0.17.0**

    Parameters
    ----------
    y : pandas Series
        Training time series.
    store_in_sample_residuals : bool, default False
        If `True`, in-sample residuals will be stored in the forecaster object
        after fitting (`in_sample_residuals_` and `in_sample_residuals_by_bin_`
        attributes).
        If `False`, only the intervals of the bins are stored.
    random_state : int, default 123
        Set a seed for the random generator so that the stored sample 
        residuals are always deterministic.

    Returns
    -------
    None

    """

    if isinstance(self.offset, pd.tseries.offsets.DateOffset):
        y_preds = []
        for n_off in range(1, self.n_offsets + 1):
            idx = y.index - self.offset * n_off
            mask = idx >= y.index[0]
            y_pred = y.loc[idx[mask]]
            y_pred.index = y.index[-mask.sum():]
            y_preds.append(y_pred)

        y_preds = pd.concat(y_preds, axis=1).to_numpy()
        y_true = y.to_numpy()[-len(y_preds):]

    else:
        y_preds = [
            y.shift(self.offset * n_off)[self.window_size:]
            for n_off in range(1, self.n_offsets + 1)
        ]
        y_preds = np.column_stack(y_preds)
        y_true = y.to_numpy()[self.window_size:]

    y_pred = np.apply_along_axis(
                 self.agg_func,
                 axis = 1,
                 arr  = y_preds
             )

    residuals = y_true - y_pred

    if self._probabilistic_mode == "binned":
        data = pd.DataFrame(
            {'prediction': y_pred, 'residuals': residuals}
        ).dropna()
        y_pred = data['prediction'].to_numpy()
        residuals = data['residuals'].to_numpy()

        self.binner.fit(y_pred)
        self.binner_intervals_ = self.binner.intervals_

    if store_in_sample_residuals:
        rng = np.random.default_rng(seed=random_state)
        if self._probabilistic_mode == "binned":
            data['bin'] = self.binner.transform(y_pred).astype(int)
            self.in_sample_residuals_by_bin_ = (
                data.groupby('bin')['residuals'].apply(np.array).to_dict()
            )

            max_sample = 10_000 // self.binner.n_bins_
            for k, v in self.in_sample_residuals_by_bin_.items():
                if len(v) > max_sample:
                    sample = v[rng.integers(low=0, high=len(v), size=max_sample)]
                    self.in_sample_residuals_by_bin_[k] = sample

            for k in self.binner_intervals_.keys():
                if k not in self.in_sample_residuals_by_bin_:
                    self.in_sample_residuals_by_bin_[k] = np.array([])

            empty_bins = [
                k for k, v in self.in_sample_residuals_by_bin_.items() 
                if v.size == 0
            ]
            if empty_bins:
                empty_bin_size = min(max_sample, len(residuals))
                for k in empty_bins:
                    self.in_sample_residuals_by_bin_[k] = rng.choice(
                        a       = residuals,
                        size    = empty_bin_size,
                        replace = False
                    )

        if len(residuals) > 10_000:
            residuals = residuals[
                rng.integers(low=0, high=len(residuals), size=10_000)
            ]

        self.in_sample_residuals_ = residuals

predict

predict(
    steps, last_window=None, check_inputs=True, exog=None
)

Predict n steps ahead.

Parameters:

Name	Type	Description	Default
steps	int	Number of steps to predict.	required
last_window	pandas Series	Past values needed to select the last equivalent dates according to the offset. If last_window = None, the values stored in self.last_window_ are used and the predictions start immediately after the training data.	None
check_inputs	bool	If True, the input is checked for possible warnings and errors with the check_predict_input function. This argument is created for internal use and is not recommended to be changed.	True
exog	Ignored	Not used, present here for API consistency by convention.	None

Returns:

Name	Type	Description
predictions	pandas Series	Predicted values.

Source code in skforecast\recursive\_forecaster_equivalent_date.py

def predict(
    self,
    steps: int,
    last_window: pd.Series | None = None,
    check_inputs: bool = True,
    exog: Any = None
) -> pd.Series:
    """
    Predict n steps ahead.

    Parameters
    ----------
    steps : int
        Number of steps to predict. 
    last_window : pandas Series, default None
        Past values needed to select the last equivalent dates according to 
        the offset. If `last_window = None`, the values stored in 
        `self.last_window_` are used and the predictions start immediately 
        after the training data.
    check_inputs : bool, default True
        If `True`, the input is checked for possible warnings and errors 
        with the `check_predict_input` function. This argument is created 
        for internal use and is not recommended to be changed.
    exog : Ignored
        Not used, present here for API consistency by convention.

    Returns
    -------
    predictions : pandas Series
        Predicted values.

    """

    if last_window is None:
        last_window = self.last_window_

    if check_inputs:
        check_predict_input(
            forecaster_name = type(self).__name__,
            steps           = steps,
            is_fitted       = self.is_fitted,
            exog_in_        = False,
            index_type_     = self.index_type_,
            index_freq_     = self.index_freq_,
            window_size     = self.window_size,
            last_window     = last_window
        )

    prediction_index = expand_index(index=last_window.index, steps=steps)

    if isinstance(self.offset, int):

        last_window_values = last_window.to_numpy(copy=True).ravel()
        equivalent_indexes = np.tile(
                                 np.arange(-self.offset, 0),
                                 int(np.ceil(steps / self.offset))
                             )
        equivalent_indexes = equivalent_indexes[:steps]

        if self.n_offsets == 1:
            equivalent_values = last_window_values[equivalent_indexes]
            predictions = equivalent_values.ravel()

        if self.n_offsets > 1:
            equivalent_indexes = [
                equivalent_indexes - n * self.offset 
                for n in np.arange(self.n_offsets)
            ]
            equivalent_indexes = np.vstack(equivalent_indexes)
            equivalent_values = last_window_values[equivalent_indexes]
            predictions = np.apply_along_axis(
                              self.agg_func,
                              axis = 0,
                              arr  = equivalent_values
                          )

        predictions = pd.Series(
                          data  = predictions,
                          index = prediction_index,
                          name  = 'pred'
                      )

    if isinstance(self.offset, pd.tseries.offsets.DateOffset):

        last_window = last_window.copy()
        max_allowed_date = last_window.index[-1]

        # For every date in prediction_index, calculate the n offsets
        offset_dates = []
        for date in prediction_index:
            selected_offsets = []
            while len(selected_offsets) < self.n_offsets:
                offset_date = date - self.offset
                if offset_date <= max_allowed_date:
                    selected_offsets.append(offset_date)
                date = offset_date
            offset_dates.append(selected_offsets)

        offset_dates = np.array(offset_dates)

        # Select the values of the time series corresponding to the each
        # offset date. If the offset date is not in the time series, the
        # value is set to NaN.
        equivalent_values = (
            last_window.
            reindex(offset_dates.ravel())
            .to_numpy()
            .reshape(-1, self.n_offsets)
        )
        equivalent_values = pd.DataFrame(
                                data    = equivalent_values,
                                index   = prediction_index,
                                columns = [f'offset_{i}' for i in range(self.n_offsets)]
                            )

        # Error if all values are missing
        if equivalent_values.isnull().all().all():
            raise ValueError(
                f"All equivalent values are missing. This is caused by using "
                f"an offset ({self.offset}) larger than the available data. "
                f"Try to decrease the size of the offset ({self.offset}), "
                f"the number of `n_offsets` ({self.n_offsets}) or increase the "
                f"size of `last_window`. In backtesting, this error may be "
                f"caused by using an `initial_train_size` too small."
            )

        # Warning if equivalent values are missing
        incomplete_offsets = equivalent_values.isnull().any(axis=1)
        incomplete_offsets = incomplete_offsets[incomplete_offsets].index
        if not incomplete_offsets.empty:
            warnings.warn(
                f"Steps: {incomplete_offsets.strftime('%Y-%m-%d').to_list()} "
                f"are calculated with less than {self.n_offsets} `n_offsets`. "
                f"To avoid this, increase the `last_window` size or decrease "
                f"the number of `n_offsets`. The current configuration requires " 
                f"a total offset of {self.offset * self.n_offsets}.",
                MissingValuesWarning
            )

        aggregate_values = equivalent_values.apply(self.agg_func, axis=1)
        predictions = aggregate_values.rename('pred')

    return predictions

predict_interval

predict_interval(
    steps,
    last_window=None,
    method="conformal",
    interval=[5, 95],
    use_in_sample_residuals=True,
    use_binned_residuals=True,
    random_state=None,
    exog=None,
    n_boot=None,
)

Predict n steps ahead and estimate prediction intervals using conformal prediction method. Refer to the References section for additional details on this method.

Parameters:

Name	Type	Description	Default
steps	int	Number of steps to predict.	required
last_window	pandas Series	Past values needed to select the last equivalent dates according to the offset. If last_window = None, the values stored in self.last_window_ are used and the predictions start immediately after the training data.	None
method	str	Technique used to estimate prediction intervals. Available options: 'conformal': Employs the conformal prediction split method for interval estimation [1]_.	'conformal'
interval	(float, list, tuple)	Confidence level of the prediction interval. Interpretation depends on the method used: If float, represents the nominal (expected) coverage (between 0 and 1). For instance, interval=0.95 corresponds to [2.5, 97.5] percentiles. If list or tuple, defines the exact percentiles to compute, which must be between 0 and 100 inclusive. For example, interval of 95% should be as interval = [2.5, 97.5]. When using method='conformal', the interval must be a float or a list/tuple defining a symmetric interval.	[5, 95]
use_in_sample_residuals	bool	If True, residuals from the training data are used as proxy of prediction error to create predictions. If False, out of sample residuals (calibration) are used. Out-of-sample residuals must be precomputed using Forecaster's set_out_sample_residuals() method.	True
use_binned_residuals	bool	If True, residuals are selected based on the predicted values (binned selection). If False, residuals are selected randomly.	True
random_state	Ignored	Not used, present here for API consistency by convention.	None
exog	Ignored	Not used, present here for API consistency by convention.	None
n_boot	Ignored	Not used, present here for API consistency by convention.	None

Returns:

Name	Type	Description
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 of the interval.

References

.. [1] MAPIE - Model Agnostic Prediction Interval Estimator. https://mapie.readthedocs.io/en/stable/theoretical_description_regression.html#the-split-method

Source code in skforecast\recursive\_forecaster_equivalent_date.py

def predict_interval(
    self,
    steps: int,
    last_window: pd.Series | None = None,
    method: str = 'conformal',
    interval: float | list[float] | tuple[float] = [5, 95],
    use_in_sample_residuals: bool = True,
    use_binned_residuals: bool = True,
    random_state: Any = None,
    exog: Any = None,
    n_boot: Any = None
) -> pd.DataFrame:
    """
    Predict n steps ahead and estimate prediction intervals using conformal 
    prediction method. Refer to the References section for additional 
    details on this method.

    Parameters
    ----------
    steps : int
        Number of steps to predict.
    last_window : pandas Series, default None
        Past values needed to select the last equivalent dates according to 
        the offset. If `last_window = None`, the values stored in 
        `self.last_window_` are used and the predictions start immediately 
        after the training data.
    method : str, default 'conformal'
        Technique used to estimate prediction intervals. Available options:

        - 'conformal': Employs the conformal prediction split method for 
        interval estimation [1]_.
    interval : float, list, tuple, default [5, 95]
        Confidence level of the prediction interval. Interpretation depends 
        on the method used:

        - If `float`, represents the nominal (expected) coverage (between 0 
        and 1). For instance, `interval=0.95` corresponds to `[2.5, 97.5]` 
        percentiles.
        - If `list` or `tuple`, defines the exact percentiles to compute, which 
        must be between 0 and 100 inclusive. For example, interval 
        of 95% should be as `interval = [2.5, 97.5]`.
        - When using `method='conformal'`, the interval must be a float or 
        a list/tuple defining a symmetric interval.
    use_in_sample_residuals : bool, default True
        If `True`, residuals from the training data are used as proxy of
        prediction error to create predictions. 
        If `False`, out of sample residuals (calibration) are used. 
        Out-of-sample residuals must be precomputed using Forecaster's
        `set_out_sample_residuals()` method.
    use_binned_residuals : bool, default True
        If `True`, residuals are selected based on the predicted values 
        (binned selection).
        If `False`, residuals are selected randomly.
    random_state : Ignored
        Not used, present here for API consistency by convention.
    exog : Ignored
        Not used, present here for API consistency by convention.
    n_boot : Ignored
        Not used, present here for API consistency by convention.

    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 of the interval.

    References
    ----------        
    .. [1] MAPIE - Model Agnostic Prediction Interval Estimator.
           https://mapie.readthedocs.io/en/stable/theoretical_description_regression.html#the-split-method

    """

    if method != 'conformal':
        raise ValueError(
            f"Method '{method}' is not supported. Only 'conformal' is available."
        )

    if last_window is None:
        last_window = self.last_window_

    check_predict_input(
        forecaster_name = type(self).__name__,
        steps           = steps,
        is_fitted       = self.is_fitted,
        exog_in_        = False,
        index_type_     = self.index_type_,
        index_freq_     = self.index_freq_,
        window_size     = self.window_size,
        last_window     = last_window
    )

    check_residuals_input(
        forecaster_name              = type(self).__name__,
        use_in_sample_residuals      = use_in_sample_residuals,
        in_sample_residuals_         = self.in_sample_residuals_,
        out_sample_residuals_        = self.out_sample_residuals_,
        use_binned_residuals         = use_binned_residuals,
        in_sample_residuals_by_bin_  = self.in_sample_residuals_by_bin_,
        out_sample_residuals_by_bin_ = self.out_sample_residuals_by_bin_
    )

    if isinstance(interval, (list, tuple)):
        check_interval(interval=interval, ensure_symmetric_intervals=True)
        nominal_coverage = (interval[1] - interval[0]) / 100
    else:
        check_interval(alpha=interval, alpha_literal='interval')
        nominal_coverage = interval

    if use_in_sample_residuals:
        residuals = self.in_sample_residuals_
        residuals_by_bin = self.in_sample_residuals_by_bin_
    else:
        residuals = self.out_sample_residuals_
        residuals_by_bin = self.out_sample_residuals_by_bin_

    prediction_index = expand_index(index=last_window.index, steps=steps)

    if isinstance(self.offset, int):

        last_window_values = last_window.to_numpy(copy=True).ravel()
        equivalent_indexes = np.tile(
                                 np.arange(-self.offset, 0),
                                 int(np.ceil(steps / self.offset))
                             )
        equivalent_indexes = equivalent_indexes[:steps]

        if self.n_offsets == 1:
            equivalent_values = last_window_values[equivalent_indexes]
            predictions = equivalent_values.ravel()

        if self.n_offsets > 1:
            equivalent_indexes = [
                equivalent_indexes - n * self.offset 
                for n in np.arange(self.n_offsets)
            ]
            equivalent_indexes = np.vstack(equivalent_indexes)
            equivalent_values = last_window_values[equivalent_indexes]
            predictions = np.apply_along_axis(
                              self.agg_func,
                              axis = 0,
                              arr  = equivalent_values
                          )

    if isinstance(self.offset, pd.tseries.offsets.DateOffset):

        last_window = last_window.copy()
        max_allowed_date = last_window.index[-1]

        # For every date in prediction_index, calculate the n offsets
        offset_dates = []
        for date in prediction_index:
            selected_offsets = []
            while len(selected_offsets) < self.n_offsets:
                offset_date = date - self.offset
                if offset_date <= max_allowed_date:
                    selected_offsets.append(offset_date)
                date = offset_date
            offset_dates.append(selected_offsets)

        offset_dates = np.array(offset_dates)

        # Select the values of the time series corresponding to the each
        # offset date. If the offset date is not in the time series, the
        # value is set to NaN.
        equivalent_values = (
            last_window.
            reindex(offset_dates.ravel())
            .to_numpy()
            .reshape(-1, self.n_offsets)
        )
        equivalent_values = pd.DataFrame(
                                data    = equivalent_values,
                                index   = prediction_index,
                                columns = [f'offset_{i}' for i in range(self.n_offsets)]
                            )

        # Error if all values are missing
        if equivalent_values.isnull().all().all():
            raise ValueError(
                f"All equivalent values are missing. This is caused by using "
                f"an offset ({self.offset}) larger than the available data. "
                f"Try to decrease the size of the offset ({self.offset}), "
                f"the number of `n_offsets` ({self.n_offsets}) or increase the "
                f"size of `last_window`. In backtesting, this error may be "
                f"caused by using an `initial_train_size` too small."
            )

        # Warning if equivalent values are missing
        incomplete_offsets = equivalent_values.isnull().any(axis=1)
        incomplete_offsets = incomplete_offsets[incomplete_offsets].index
        if not incomplete_offsets.empty:
            warnings.warn(
                f"Steps: {incomplete_offsets.strftime('%Y-%m-%d').to_list()} "
                f"are calculated with less than {self.n_offsets} `n_offsets`. "
                f"To avoid this, increase the `last_window` size or decrease "
                f"the number of `n_offsets`. The current configuration requires " 
                f"a total offset of {self.offset * self.n_offsets}.",
                MissingValuesWarning
            )

        aggregate_values = equivalent_values.apply(self.agg_func, axis=1)
        predictions = aggregate_values.to_numpy()

    if use_binned_residuals:
        correction_factor_by_bin = {
            k: np.quantile(np.abs(v), nominal_coverage)
            for k, v in residuals_by_bin.items()
        }
        replace_func = np.vectorize(lambda x: correction_factor_by_bin[x])
        predictions_bin = self.binner.transform(predictions)
        correction_factor = replace_func(predictions_bin)
    else:
        correction_factor = np.quantile(np.abs(residuals), nominal_coverage)

    lower_bound = predictions - correction_factor
    upper_bound = predictions + correction_factor
    predictions = np.column_stack([predictions, lower_bound, upper_bound])

    predictions = pd.DataFrame(
                      data    = predictions,
                      index   = prediction_index,
                      columns = ["pred", "lower_bound", "upper_bound"]
                  )

    return predictions

set_in_sample_residuals

set_in_sample_residuals(y, random_state=123, exog=None)

Set in-sample residuals in case they were not calculated during the training process.

In-sample residuals are calculated as the difference between the true values and the predictions made by the forecaster using the training data. The following internal attributes are updated:

• in_sample_residuals_: residuals stored in a numpy ndarray.
• binner_intervals_: intervals used to bin the residuals are calculated using the quantiles of the predicted values.
• in_sample_residuals_by_bin_: residuals are binned according to the predicted value they are associated with and stored in a dictionary, where the keys are the intervals of the predicted values and the values are the residuals associated with that range.

A total of 10_000 residuals are stored in the attribute in_sample_residuals_. If the number of residuals is greater than 10_000, a random sample of 10_000 residuals is stored. The number of residuals stored per bin is limited to 10_000 // self.binner.n_bins_.

Parameters:

Name	Type	Description	Default
y	pandas Series	Training time series.	required
random_state	int	Sets a seed to the random sampling for reproducible output.	123
exog	Ignored	Not used, present here for API consistency by convention.	None

Returns:

Type	Description
None

Source code in skforecast\recursive\_forecaster_equivalent_date.py

def set_in_sample_residuals(
    self,
    y: pd.Series,
    random_state: int = 123,
    exog: Any = None
) -> None:
    """
    Set in-sample residuals in case they were not calculated during the
    training process. 

    In-sample residuals are calculated as the difference between the true 
    values and the predictions made by the forecaster using the training 
    data. The following internal attributes are updated:

    + `in_sample_residuals_`: residuals stored in a numpy ndarray.
    + `binner_intervals_`: intervals used to bin the residuals are calculated
    using the quantiles of the predicted values.
    + `in_sample_residuals_by_bin_`: residuals are binned according to the
    predicted value they are associated with and stored in a dictionary, where
    the keys are the intervals of the predicted values and the values are
    the residuals associated with that range. 

    A total of 10_000 residuals are stored in the attribute `in_sample_residuals_`.
    If the number of residuals is greater than 10_000, a random sample of
    10_000 residuals is stored. The number of residuals stored per bin is
    limited to `10_000 // self.binner.n_bins_`.

    Parameters
    ----------
    y : pandas Series
        Training time series.
    random_state : int, default 123
        Sets a seed to the random sampling for reproducible output.
    exog : Ignored
        Not used, present here for API consistency by convention.

    Returns
    -------
    None

    """

    if not self.is_fitted:
        raise NotFittedError(
            "This forecaster is not fitted yet. Call `fit` with appropriate "
            "arguments before using `set_in_sample_residuals()`."
        )

    check_y(y=y)
    y_index_range = check_extract_values_and_index(
        data=y, data_label='`y`', return_values=False
    )[1][[0, -1]]
    if not y_index_range.equals(self.training_range_):
        raise IndexError(
            f"The index range of `y` does not match the range "
            f"used during training. Please ensure the index is aligned "
            f"with the training data.\n"
            f"    Expected : {self.training_range_}\n"
            f"    Received : {y_index_range}"
        )

    self._binning_in_sample_residuals(
        y                         = y,
        store_in_sample_residuals = True,
        random_state              = random_state
    )

set_out_sample_residuals

set_out_sample_residuals(
    y_true, y_pred, append=False, 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. Two internal attributes are updated:

• out_sample_residuals_: residuals stored in a numpy ndarray.
• out_sample_residuals_by_bin_: residuals are binned according to the predicted value they are associated with and stored in a dictionary, where the keys are the intervals of the predicted values and the values are the residuals associated with that range. If a bin binning is empty, it is filled with a random sample of residuals from other bins. This is done to ensure that all bins have at least one residual and can be used in the prediction process.

A total of 10_000 residuals are stored in the attribute out_sample_residuals_. If the number of residuals is greater than 10_000, a random sample of 10_000 residuals is stored. The number of residuals stored per bin is limited to 10_000 // self.binner.n_bins_.

Parameters:

Name	Type	Description	Default
y_true	numpy ndarray, pandas Series	True values of the time series from which the residuals have been calculated.	required
y_pred	numpy ndarray, pandas Series	Predicted values of the time series.	required
append	bool	If True, new residuals are added to the once already stored in the forecaster. If after appending the new residuals, the limit of 10_000 // self.binner.n_bins_ values per bin is reached, a random sample of residuals is stored.	False
random_state	int	Sets a seed to the random sampling for reproducible output.	123

Returns:

Type	Description
None

Source code in skforecast\recursive\_forecaster_equivalent_date.py

def set_out_sample_residuals(
    self,
    y_true: np.ndarray | pd.Series,
    y_pred: np.ndarray | pd.Series,
    append: bool = False,
    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. Two internal attributes are updated:

    + `out_sample_residuals_`: residuals stored in a numpy ndarray.
    + `out_sample_residuals_by_bin_`: residuals are binned according to the
    predicted value they are associated with and stored in a dictionary, where
    the keys are the  intervals of the predicted values and the values are
    the residuals associated with that range. If a bin binning is empty, it
    is filled with a random sample of residuals from other bins. This is done
    to ensure that all bins have at least one residual and can be used in the
    prediction process.

    A total of 10_000 residuals are stored in the attribute `out_sample_residuals_`.
    If the number of residuals is greater than 10_000, a random sample of
    10_000 residuals is stored. The number of residuals stored per bin is
    limited to `10_000 // self.binner.n_bins_`.

    Parameters
    ----------
    y_true : numpy ndarray, pandas Series
        True values of the time series from which the residuals have been
        calculated.
    y_pred : numpy ndarray, pandas Series
        Predicted values of the time series.
    append : bool, default False
        If `True`, new residuals are added to the once already stored in the
        forecaster. If after appending the new residuals, the limit of
        `10_000 // self.binner.n_bins_` values per bin is reached, a random
        sample of residuals is stored.
    random_state : int, default 123
        Sets a seed to the random sampling for reproducible output.

    Returns
    -------
    None

    """

    if not self.is_fitted:
        raise NotFittedError(
            "This forecaster is not fitted yet. Call `fit` with appropriate "
            "arguments before using `set_out_sample_residuals()`."
        )

    if not isinstance(y_true, (np.ndarray, pd.Series)):
        raise TypeError(
            f"`y_true` argument must be `numpy ndarray` or `pandas Series`. "
            f"Got {type(y_true)}."
        )

    if not isinstance(y_pred, (np.ndarray, pd.Series)):
        raise TypeError(
            f"`y_pred` argument must be `numpy ndarray` or `pandas Series`. "
            f"Got {type(y_pred)}."
        )

    if len(y_true) != len(y_pred):
        raise ValueError(
            f"`y_true` and `y_pred` must have the same length. "
            f"Got {len(y_true)} and {len(y_pred)}."
        )

    if isinstance(y_true, pd.Series) and isinstance(y_pred, pd.Series):
        if not y_true.index.equals(y_pred.index):
            raise ValueError(
                "`y_true` and `y_pred` must have the same index."
            )

    if not isinstance(y_pred, np.ndarray):
        y_pred = y_pred.to_numpy()
    if not isinstance(y_true, np.ndarray):
        y_true = y_true.to_numpy()

    data = pd.DataFrame(
        {'prediction': y_pred, 'residuals': y_true - y_pred}
    ).dropna()
    y_pred = data['prediction'].to_numpy()
    residuals = data['residuals'].to_numpy()

    data['bin'] = self.binner.transform(y_pred).astype(int)
    residuals_by_bin = data.groupby('bin')['residuals'].apply(np.array).to_dict()

    out_sample_residuals = (
        np.array([]) 
        if self.out_sample_residuals_ is None
        else self.out_sample_residuals_
    )
    out_sample_residuals_by_bin = (
        {} 
        if self.out_sample_residuals_by_bin_ is None
        else self.out_sample_residuals_by_bin_
    )
    if append:
        out_sample_residuals = np.concatenate([out_sample_residuals, residuals])
        for k, v in residuals_by_bin.items():
            if k in out_sample_residuals_by_bin:
                out_sample_residuals_by_bin[k] = np.concatenate(
                    (out_sample_residuals_by_bin[k], v)
                )
            else:
                out_sample_residuals_by_bin[k] = v
    else:
        out_sample_residuals = residuals
        out_sample_residuals_by_bin = residuals_by_bin

    max_samples = 10_000 // self.binner.n_bins_
    rng = np.random.default_rng(seed=random_state)
    for k, v in out_sample_residuals_by_bin.items():
        if len(v) > max_samples:
            sample = rng.choice(a=v, size=max_samples, replace=False)
            out_sample_residuals_by_bin[k] = sample

    bin_keys = (
        []
        if self.binner_intervals_ is None
        else self.binner_intervals_.keys()
    )
    for k in bin_keys:
        if k not in out_sample_residuals_by_bin:
            out_sample_residuals_by_bin[k] = np.array([])

    empty_bins = [
        k for k, v in out_sample_residuals_by_bin.items() 
        if v.size == 0
    ]
    if empty_bins:
        warnings.warn(
            f"The following bins have no out of sample residuals: {empty_bins}. "
            f"No predicted values fall in the interval "
            f"{[self.binner_intervals_[bin] for bin in empty_bins]}. "
            f"Empty bins will be filled with a random sample of residuals.",
            ResidualsUsageWarning
        )
        empty_bin_size = min(max_samples, len(out_sample_residuals))
        for k in empty_bins:
            out_sample_residuals_by_bin[k] = rng.choice(
                a       = out_sample_residuals,
                size    = empty_bin_size,
                replace = False
            )

    if len(out_sample_residuals) > 10_000:
        out_sample_residuals = rng.choice(
            a       = out_sample_residuals, 
            size    = 10_000, 
            replace = False
        )

    self.out_sample_residuals_ = out_sample_residuals
    self.out_sample_residuals_by_bin_ = out_sample_residuals_by_bin

summary

summary()

Show forecaster information.

Parameters:

Name	Type	Description	Default
self			required

Returns:

Type	Description
None

Source code in skforecast\recursive\_forecaster_equivalent_date.py

def summary(self) -> None:
    """
    Show forecaster information.

    Parameters
    ----------
    self

    Returns
    -------
    None

    """

    print(self)