# Copyright 2018 Amazon.com, Inc. or its affiliates. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License").
# You may not use this file except in compliance with the License.
# A copy of the License is located at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# or in the "license" file accompanying this file. This file is distributed
# on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
# express or implied. See the License for the specific language governing
# permissions and limitations under the License.
from typing import Optional
import numpy as np
from gluonts.time_feature import get_seasonality
[docs]def calculate_seasonal_error(
past_data: np.ndarray,
freq: Optional[str] = None,
seasonality: Optional[int] = None,
):
r"""
.. math::
seasonal\_error = mean(|Y[t] - Y[t-m]|)
where m is the seasonal frequency. See [HA21]_ for more details.
"""
# Check if the length of the time series is larger than the seasonal
# frequency
if not seasonality:
assert freq is not None, "Either freq or seasonality must be provided"
seasonality = get_seasonality(freq)
if seasonality < len(past_data):
forecast_freq = seasonality
else:
# edge case: the seasonal freq is larger than the length of ts
# revert to freq=1
# logging.info('The seasonal frequency is larger than the length of the
# time series. Reverting to freq=1.')
forecast_freq = 1
y_t = past_data[:-forecast_freq]
y_tm = past_data[forecast_freq:]
return np.mean(abs(y_t - y_tm))
[docs]def mse(target: np.ndarray, forecast: np.ndarray) -> float:
r"""
.. math::
mse = mean((Y - \hat{Y})^2)
See [HA21]_ for more details.
"""
return np.mean(np.square(target - forecast))
[docs]def abs_error(target: np.ndarray, forecast: np.ndarray) -> float:
r"""
Absolute error.
.. math::
abs\_error = sum(|Y - \hat{Y}|)
"""
return np.sum(np.abs(target - forecast))
[docs]def quantile_loss(target: np.ndarray, forecast: np.ndarray, q: float) -> float:
r"""
Quantile loss.
.. math::
quantile\_loss = 2 * sum(|(Y - \hat{Y}) * (Y <= \hat{Y}) - q|)
"""
return 2 * np.sum(np.abs((forecast - target) * ((target <= forecast) - q)))
[docs]def coverage(target: np.ndarray, forecast: np.ndarray) -> float:
r"""
coverage.
.. math::
coverage = mean(Y <= \hat{Y})
"""
return float(np.mean(target <= forecast))
[docs]def mase(
target: np.ndarray,
forecast: np.ndarray,
seasonal_error: float,
) -> float:
r"""
.. math::
mase = mean(|Y - \hat{Y}|) / seasonal\_error
See [HA21]_ for more details.
"""
return np.mean(np.abs(target - forecast)) / seasonal_error
[docs]def mape(target: np.ndarray, forecast: np.ndarray) -> float:
r"""
.. math::
mape = mean(|Y - \hat{Y}| / |Y|))
See [HA21]_ for more details.
"""
return np.mean(np.abs(target - forecast) / np.abs(target))
[docs]def smape(target: np.ndarray, forecast: np.ndarray) -> float:
r"""
.. math::
smape = 2 * mean(|Y - \hat{Y}| / (|Y| + |\hat{Y}|))
See [HA21]_ for more details.
"""
return 2 * np.mean(
np.abs(target - forecast) / (np.abs(target) + np.abs(forecast))
)
[docs]def msis(
target: np.ndarray,
lower_quantile: np.ndarray,
upper_quantile: np.ndarray,
seasonal_error: float,
alpha: float,
) -> float:
r"""
.. math::
msis = mean(U - L + 2/alpha * (L-Y) * I[Y<L] + 2/alpha * (Y-U) * I[Y>U]) / seasonal\_error
See [SSA20]_ for more details.
""" # noqa: E501
numerator = np.mean(
upper_quantile
- lower_quantile
+ 2.0 / alpha * (lower_quantile - target) * (target < lower_quantile)
+ 2.0 / alpha * (target - upper_quantile) * (target > upper_quantile)
)
return numerator / seasonal_error
[docs]def abs_target_sum(target) -> float:
r"""
Absolute target sum.
.. math::
abs\_target\_sum = sum(|Y|)
"""
return np.sum(np.abs(target))
[docs]def abs_target_mean(target) -> float:
r"""
Absolute target mean.
.. math::
abs\_target\_mean = mean(|Y|)
"""
return np.mean(np.abs(target))
[docs]def num_masked_values(target) -> float:
"""
Count number of masked values in target.
"""
if np.ma.isMaskedArray(target):
return np.ma.count_masked(target)
else:
return 0