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Introduction¶

Although historical data is available in many real use cases of forecasting, not all of it is reliable. Some examples of these scenarios are:

• IoT sensors: within the Internet of Things, sensors capture the raw data from the physical world. Often the sensors are deployed or installed in harsh environments. This inevitably means that the sensors are prone to failure, malfunction, and rapid attrition, causing the sensor to produce unusual and erroneous readings.

• Factory shutdown: every certain period of operation, factories need to be shut down for repair, overhaul, or maintenance activities. These events cause production to stop, generating a gap in the data.

• Pandemic (COVID-19): the COVID-19 pandemic changed population behavior significantly, directly impacting many time series such as production, sales, and transportation.

The presence of unreliable or unrepresentative values in the data history is a major problem, as it hinders model learning. For most forecasting algorithms, removing that part of the data is not an option because they require the time series to be complete. An alternative solution is to reduce the weight of the affected observations during model training. This document shows two examples of how skforecast makes it easy to apply this strategy.

Libraries¶

# Data processing
# ==============================================================================
import pandas as pd
import numpy as np
from skforecast.datasets import fetch_dataset

# Plots
# ==============================================================================
import matplotlib.pyplot as plt
from skforecast.plot import set_dark_theme

# Modelling and Forecasting
# ==============================================================================
import skforecast
import sklearn
from sklearn.linear_model import Ridge
from skforecast.recursive import ForecasterRecursive
from skforecast.model_selection import TimeSeriesFold
from skforecast.model_selection import backtesting_forecaster

# Configuration
# ==============================================================================
import warnings
warnings.filterwarnings('once')

color = '\033[1m\033[38;5;208m'
print(f"{color}Version skforecast: {skforecast.__version__}")
print(f"{color}Version scikit-learn: {sklearn.__version__}")
print(f"{color}Version pandas: {pd.__version__}")
print(f"{color}Version numpy: {np.__version__}")

Version skforecast: 0.25.0
Version scikit-learn: 1.7.2
Version pandas: 2.3.3
Version numpy: 2.4.6

COVID-19 lockdown¶

During the lockdown period imposed as a consequence of the COVID-19 pandemic, the behavior of the population was altered. An example of this can be seen in the use of the bicycle rental service in the city of Madrid (Spain).

Data¶

# Data download
# ==============================================================================
data = fetch_dataset('bicimad')
data.head()

╭──────────────────────────────────── bicimad ─────────────────────────────────────╮
│ Description:                                                                     │
│ This dataset contains the daily users of the bicycle rental service (BiciMad) in │
│ the city of Madrid (Spain) from 2014-06-23 to 2022-09-30.                        │
│                                                                                  │
│ Source:                                                                          │
│ The original data was obtained from: Portal de datos abiertos del Ayuntamiento   │
│ de Madrid https://datos.madrid.es/portal/site/egob                               │
│                                                                                  │
│ URL:                                                                             │
│ https://raw.githubusercontent.com/skforecast/skforecast-                         │
│ datasets/main/data/bicimad_users.csv                                             │
│                                                                                  │
│ Shape: 3022 rows x 1 columns                                                     │
╰──────────────────────────────────────────────────────────────────────────────────╯

# Split data into train-test
# ==============================================================================
data = data.loc['2020-01-01': '2021-12-31']
end_train = '2021-06-01 23:59:00'
data_train = data.loc[: end_train, :]
data_test  = data.loc[end_train:, :]

print(
    f'Dates train : {data_train.index.min()} --- {data_train.index.max()}  '
    f'(n={len(data_train)})'
)
print(
    f'Dates test  : {data_test.index.min()} --- {data_test.index.max()}  '
    f'(n={len(data_test)})'
)

Dates train : 2020-01-01 00:00:00 --- 2021-06-01 00:00:00  (n=518)
Dates test  : 2021-06-02 00:00:00 --- 2021-12-31 00:00:00  (n=213)

# Time series plot
# ==============================================================================
set_dark_theme()
fig, ax = plt.subplots(figsize=(8, 3))
data_train.users.plot(ax=ax, label='train', linewidth=1)
data_test.users.plot(ax=ax, label='test', linewidth=1)
ax.axvspan(
    pd.to_datetime('2020-03-16'),
    pd.to_datetime('2020-04-21'), 
    label="Covid-19 confinement",
    color="red",
    alpha=0.3
)

ax.axvspan(
    pd.to_datetime('2020-04-21'),
    pd.to_datetime('2020-05-31'), 
    label="Recovery time",
    color="white",
    alpha=0.3
)

ax.set_title('Number of users BiciMAD')
ax.legend();

Include the whole time series¶

A forecaster is initialized without taking into consideration the lockdown period.

# Create recursive multi-step forecaster (ForecasterRecursive)
# ==============================================================================
forecaster = ForecasterRecursive(
                 estimator = Ridge(random_state=123),
                 lags      = 21,
             )
forecaster

Once the model is created, a backtesting process is run with backtesting_forecaster and TimeSeriesFold to simulate the behavior of the forecaster if it had predicted the test set in 7-day batches.

# Backtesting: predict next 7 days at a time.
# ==============================================================================
cv = TimeSeriesFold(
        steps              = 7,
        initial_train_size = len(data_train),
        fixed_train_size   = False,
        refit              = False,
)
metric, predictions_backtest = backtesting_forecaster(
                                   forecaster = forecaster,
                                   y          = data.users,
                                   cv         = cv,
                                   metric     = 'mean_absolute_error',
                                   verbose    = False
                               )
metric

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Exclude part of the time series¶

To minimize the influence of these dates on the model, a custom function is created and passed to the forecaster through the weight_func argument. Each time the forecaster is fitted, this function receives the index of the training matrix (the date of the target value of each row) and must return one weight per row. The function follows these rules:

• Weight of 0 if the index date is:

  • Within the lockdown period (2020-03-16 to 2020-04-21).

  • Within the recovery period (2020-04-21 to 2020-05-31).

  • Within the 21 days after the recovery period (2020-06-01 to 2020-06-21). The forecaster uses lags = 21, so the rows of the training matrix whose target falls in these dates still use impacted values as predictors.

• Weight of 1 otherwise.

If an observation has a weight of 0, it has no influence during model training.

# Custom function to create weights
# ==============================================================================
def custom_weights(index):
    """
    Return a weight of 0 for dates between 2020-03-16 and 2020-06-21 (lockdown,
    recovery and the 21 days affected through the lags) and 1 otherwise.
    """
    weights = np.where((index >= '2020-03-16') & (index <= '2020-06-21'), 0, 1)

    return weights

Again, a ForecasterRecursive is created, this time passing custom_weights to the weight_func argument. The function is called automatically every time the forecaster is fitted: only once in this backtesting, since refit=False, and on every refit if refit=True.

# Create recursive multi-step forecaster (ForecasterRecursive)
# ==============================================================================
forecaster = ForecasterRecursive(
                 estimator   = Ridge(random_state=123),
                 lags        = 21,
                 weight_func = custom_weights
             )

# Backtesting: predict next 7 days at a time.
# ==============================================================================
metric, predictions_backtest = backtesting_forecaster(
                                   forecaster = forecaster,
                                   y          = data.users,
                                   cv         = cv,
                                   metric     = 'mean_absolute_error',
                                   verbose    = False
                               )

metric

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Giving a weight of 0 to the lockdown period (excluding it from the model training) reduces the mean absolute error from 1469 to 1405 users (about 4%).

Power plant shutdown¶

Power plants used to generate energy are very complex installations that require a high level of maintenance. It is common that, every certain period of operation, the plant has to be shut down for repair, overhaul, or maintenance activities.

Data¶

# Data download
# ==============================================================================
url = ('https://raw.githubusercontent.com/skforecast/skforecast-datasets/refs/'
       'heads/main/data/energy_production_shutdown.csv')
data = pd.read_csv(url, sep=',')

# Data preprocessing
# ==============================================================================
data['date'] = pd.to_datetime(data['date'], format='%Y-%m-%d')
data = data.set_index('date')
data = data.sort_index()
data = data.asfreq('D')
data.head()

# Split data into train-test
# ==============================================================================
data = data.loc['2012-01-01 00:00:00': '2014-12-30 23:00:00']
end_train = '2013-12-31 23:59:00'
data_train = data.loc[: end_train, :]
data_test  = data.loc[end_train:, :]

print(
    f'Dates train : {data_train.index.min()} --- {data_train.index.max()}  '
    f'(n={len(data_train)})'
)
print(
    f'Dates test  : {data_test.index.min()} --- {data_test.index.max()}  '
    f'(n={len(data_test)})'
)

Dates train : 2012-01-01 00:00:00 --- 2013-12-31 00:00:00  (n=731)
Dates test  : 2014-01-01 00:00:00 --- 2014-12-30 00:00:00  (n=364)

# Time series plot
# ==============================================================================
fig, ax = plt.subplots(figsize=(8, 3))
data_train.production.plot(ax=ax, label='train', linewidth=1)
data_test.production.plot(ax=ax, label='test', linewidth=1)
ax.axvspan(
    pd.to_datetime('2012-06-01'),
    pd.to_datetime('2012-09-30'), 
    label="Shutdown",
    color="white",
    alpha=0.2
)
ax.set_title('Energy production')
ax.legend();

Include the whole time series¶

A forecaster is initialized without taking into consideration the shutdown period.

# Create recursive multi-step forecaster (ForecasterRecursive)
# ==============================================================================
forecaster = ForecasterRecursive(
                 estimator = Ridge(random_state=123),
                 lags      = 21,
             )

# Backtesting: predict next 10 days at a time.
# ==============================================================================
cv = TimeSeriesFold(
        steps              = 10,
        initial_train_size = len(data_train),
        refit              = False,
)
metric, predictions_backtest = backtesting_forecaster(
                                   forecaster = forecaster,
                                   y          = data.production,
                                   cv         = cv,
                                   metric     = 'mean_absolute_error',
                                   verbose    = False
                               )
metric

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Exclude part of the time series¶

The power plant shutdown took place from 2012-06-01 to 2012-09-30. As in the previous example, a custom function assigns a weight of 0 if the index date is within the shutdown period or up to 21 days later, and 1 otherwise. The extra 21 days are needed because the rows of the training matrix whose target is dated between 2012-10-01 and 2012-10-21 still use values from the shutdown as lags.

# Custom function to create weights
# ==============================================================================
def custom_weights(index):
    """
    Return a weight of 0 for dates between 2012-06-01 and 2012-10-21 (shutdown
    plus the 21 days affected through the lags) and 1 otherwise.
    """
    weights = np.where((index >= '2012-06-01') & (index <= '2012-10-21'), 0, 1)
    return weights

# Create recursive multi-step forecaster (ForecasterRecursive)
# ==============================================================================
forecaster = ForecasterRecursive(
                 estimator   = Ridge(random_state=123),
                 lags        = 21,
                 weight_func = custom_weights
             )

# Backtesting: predict next 10 days at a time.
# ==============================================================================
metric, predictions_backtest = backtesting_forecaster(
                                   forecaster = forecaster,
                                   y          = data.production,
                                   cv         = cv,
                                   metric     = 'mean_absolute_error',
                                   verbose    = False
                               )
metric

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As in the previous example, excluding the observations of the shutdown period slightly improves the forecasting performance: the mean absolute error goes from 28.4 to 27.8 (about 2%).

In both examples the weights were used only to include or exclude observations, but any non-negative value is allowed: a weight between 0 and 1 reduces the influence of a period without removing it completely, and a weight greater than 1 increases it.

Session information¶

import session_info
session_info.show(html=False)

-----
matplotlib          3.10.9
numpy               2.4.6
pandas              2.3.3
session_info        v1.0.1
skforecast          0.25.0
sklearn             1.7.2
-----
IPython             9.15.0
jupyter_client      8.9.1
jupyter_core        5.9.1
-----
Python 3.13.14 | packaged by conda-forge | (main, Jun 12 2026, 09:44:26) [MSC v.1944 64 bit (AMD64)]
Windows-11-10.0.26200-SP0
-----
Session information updated at 2026-09-18 16:24

Citation¶

How to cite this document

If you use this document or any part of it, please acknowledge the source, thank you!

Mitigating the Impact of Covid on Forecasting Models by Joaquín Amat Rodrigo and Javier Escobar Ortiz, available under Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0 DEED) at https://www.cienciadedatos.net/documentos/py45-weighted-time-series-forecasting.html

How to cite skforecast

If you use skforecast for a publication, we would appreciate it if you cite the published software.

Zenodo:

Amat Rodrigo, Joaquin, & Escobar Ortiz, Javier. (2026). skforecast (v0.25.0). Zenodo. https://doi.org/10.5281/zenodo.8382788

APA:

Amat Rodrigo, J., & Escobar Ortiz, J. (2026). skforecast (Version 0.25.0) [Computer software]. https://doi.org/10.5281/zenodo.8382788

BibTeX:

@software{skforecast, author = {Amat Rodrigo, Joaquin and Escobar Ortiz, Javier}, title = {skforecast}, version = {0.25.0}, month = {09}, year = {2026}, license = {BSD-3-Clause}, url = {https://skforecast.org/}, doi = {10.5281/zenodo.8382788} }

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