OverallWeightedAverage

class OverallWeightedAverage(sp=1, multioutput='uniform_average', multilevel='uniform_average', by_index=False, eps=None)[source]

Overall Weighted Average (OWA) metric as used in the M4 competition.

The OWA metric combines MASE and sMAPE, each normalized by the corresponding error of a Naive-2 benchmark forecaster:

\[\text{OWA} = 0.5 \left( \frac{\text{MASE}}{\text{MASE}_{\text{Naive2}}} + \frac{\text{sMAPE}}{\text{sMAPE}_{\text{Naive2}}} \right)\]

Lower values indicate better forecasting performance.

The Naive-2 benchmark is defined as:

Detect seasonality using SeasonalityACF
If seasonal (sp != 1), apply additive deseasonalization
Forecast using NaiveForecaster(strategy="last")

Parameters:

spint, default=1

Seasonal periodicity of the data.

multioutput‘uniform_average’ (default), 1D array-like, or ‘raw_values’

Whether and how to aggregate metric for multivariate (multioutput) data.

If 'uniform_average' (default), errors of all outputs are averaged with uniform weight.
If 1D array-like, errors are averaged across variables, with values used as averaging weights (same order).
If 'raw_values', does not average across variables (outputs), per-variable errors are returned.

multilevel{‘raw_values’, ‘uniform_average’, ‘uniform_average_time’}

How to aggregate the metric for hierarchical data (with levels).

If 'uniform_average' (default), errors are mean-averaged across levels.
If 'uniform_average_time', metric is applied to all data, ignoring level index.
If 'raw_values', does not average errors across levels, hierarchy is retained.

by_indexbool, default=False

Controls averaging over time points in direct call to metric object.

If False (default), direct call to the metric object averages over time points, equivalent to a call of the evaluate method.
If True, direct call to the metric object evaluates the metric at each time point, equivalent to a call of the evaluate_by_index method.

epsfloat, default=None

Numerical epsilon used in denominator to avoid division by zero. Absolute values smaller than eps are replaced by eps. If None, defaults to np.finfo(np.float64).eps

References

Makridakis, S., Spiliotis, E., & Assimakopoulos, V. (2020). The M4 Competition: 100,000 time series and 61 forecasting methods. International Journal of Forecasting, 36(1), 54-74. https://doi.org/10.1016/j.ijforecast.2019.04.014

Examples

>>> from sktime.performance_metrics.forecasting import OverallWeightedAverage
>>> import numpy as np
>>> y_true = np.array([100, 110, 105, 120])
>>> y_pred = np.array([102, 108, 107, 118])
>>> y_train = np.array([90, 95, 100, 110, 105, 100])
>>> metric = OverallWeightedAverage(sp=1)
>>> metric(y_true, y_pred, y_train=y_train)
np.float64(0.14512226890252225)

Methods

__call__(y_true, y_pred, **kwargs)

Calculate metric value using underlying metric function.

__call__(y_true, y_pred, **kwargs)[source]

Calculate metric value using underlying metric function.

Parameters:

y_truetime series in sktime compatible data container format.

Ground truth (correct) target values.

Individual data formats in sktime are so-called mtype specifications, each mtype implements an abstract scitype.

Series scitype = individual time series, vanilla forecasting. pd.DataFrame, pd.Series, or np.ndarray (1D or 2D)
Panel scitype = collection of time series, global/panel forecasting. pd.DataFrame with 2-level row MultiIndex (instance, time), 3D np.ndarray (instance, variable, time), list of Series typed pd.DataFrame
Hierarchical scitype = hierarchical collection, for hierarchical forecasting. pd.DataFrame with 3 or more level row MultiIndex (hierarchy_1, ..., hierarchy_n, time)

For further details on data format, see glossary on mtype. For usage, see forecasting tutorial examples/01_forecasting.ipynb

y_predtime series in sktime compatible data container format

Predicted values to evaluate against ground truth. Must be of same format as y_true, same indices and columns if indexed.

y_pred_benchmarkoptional, time series in sktime compatible data container format

Benchmark predictions to compare y_pred to, used for relative metrics. Required only if metric requires benchmark predictions, as indicated by tag requires-y-pred-benchmark. Otherwise, can be passed to ensure interface consistency, but is ignored. Must be of same format as y_true, same indices and columns if indexed.

y_trainoptional, time series in sktime compatible data container format

Training data used to normalize the error metric. Required only if metric requires training data, as indicated by tag requires-y-train. Otherwise, can be passed to ensure interface consistency, but is ignored. Must be of same format as y_true, same columns if indexed, but not necessarily same indices.

sample_weightoptional, 1D array-like, or callable, default=None

Sample weights for each time point.

If None, the time indices are considered equally weighted.
If an array, must be 1D. If y_true and y_pred``are a single time series, ``sample_weight must be of the same length as y_true. If the time series are panel or hierarchical, the length of all individual time series must be the same, and equal to the length of sample_weight, for all instances of time series passed.
If a callable, it must follow SampleWeightGenerator interface, or have one of the following signatures: y_true: pd.DataFrame -> 1D array-like, or y_true: pd.DataFrame x y_pred: pd.DataFrame -> 1D array-like.

Returns:

lossfloat, np.ndarray, or pd.DataFrame

Calculated metric, averaged or by variable. Weighted by sample_weight if provided.

float if multioutput="uniform_average" or array-like, and ``multilevel="uniform_average" or “uniform_average_time”``. Value is metric averaged over variables and levels (see class docstring)
np.ndarray of shape (y_true.columns,) if multioutput=”raw_values”` and multilevel="uniform_average" or "uniform_average_time". i-th entry is the, metric calculated for i-th variable
pd.DataFrame if multilevel="raw_values". of shape (n_levels, ), if multioutput="uniform_average"; of shape (n_levels, y_true.columns) if multioutput="raw_values". metric is applied per level, row averaging (yes/no) as in multioutput.