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Forecasting time series with XGBoost
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Introduction¶
Gradient boosting models have gained popularity in the machine learning community due to their ability to achieve excellent results in a wide range of use cases, including both regression and classification. Although these models have traditionally been less common in forecasting, they can be highly effective in this domain. Some of the key benefits of using gradient boosting models for forecasting include:
The ease with which exogenous variables can be included in the model, in addition to autoregressive variables.
The ability to capture non-linear relationships between variables.
High scalability, allowing models to handle large volumes of data.
Some implementations allow the inclusion of categorical variables without the need for additional encoding, such as one-hot encoding.
Despite these benefits, the use of machine learning models for forecasting can present several challenges that can make analysts reluctant to use them, the main ones being:
Transforming the data so that it can be used as a regression problem.
Depending on how many future predictions are needed (prediction horizon), an iterative process may be required where each new prediction is based on previous ones.
Model validation requires specific strategies such as backtesting, walk-forward validation or time series cross-validation. Traditional cross-validation cannot be used.
The skforecast library provides automated solutions to these challenges, making it easier to apply and validate machine learning models to forecasting problems. The library supports several advanced gradient boosting models, including XGBoost.
✎ Note
This document is a summary of a more comprehensive guide to using gradient boosting models for time series forecasting. The complete guide is available at Forecasting time series with gradient boosting: Skforecast, XGBoost, LightGBM, Scikit-learn and CatBoost.Libraries¶
Libraries used in this document.
# Data processing
# ==============================================================================
import numpy as np
import pandas as pd
from skforecast.datasets import fetch_dataset
# Plots
# ==============================================================================
import matplotlib.pyplot as plt
from statsmodels.graphics.tsaplots import plot_acf
from statsmodels.graphics.tsaplots import plot_pacf
import plotly.graph_objects as go
import plotly.io as pio
import plotly.offline as poff
pio.templates.default = "seaborn"
poff.init_notebook_mode(connected=True)
plt.style.use('seaborn-v0_8-darkgrid')
# Modelling and Forecasting
# ==============================================================================
import xgboost
import skforecast
import sklearn
from xgboost import XGBRegressor
from sklearn.feature_selection import RFECV
from skforecast.ForecasterAutoreg import ForecasterAutoreg
from skforecast.model_selection import bayesian_search_forecaster
from skforecast.model_selection import backtesting_forecaster
from skforecast.model_selection import select_features
import shap
# Warnings 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 xgboost: {xgboost.__version__}")
print(f"{color}Version pandas: {pd.__version__}")
print(f"{color}Version numpy: {np.__version__}")
Data¶
The data in this document represent the hourly usage of the bike share system in the city of Washington, D.C. during the years 2011 and 2012. In addition to the number of users per hour, information about weather conditions and holidays is available. The original data was obtained from the UCI Machine Learning Repository.
# Downloading data
# ==============================================================================
data = fetch_dataset('bike_sharing_extended_features')
data.head(4)
To facilitate the training of the models, the search for optimal hyperparameters and the evaluation of their predictive accuracy, the data are divided into three separate sets: training, validation and test.
# Split train-validation-test
# ==============================================================================
end_train = '2012-03-31 23:59:00'
end_validation = '2012-08-31 23:59:00'
data_train = data.loc[: end_train, :]
data_val = data.loc[end_train:end_validation, :]
data_test = data.loc[end_validation:, :]
print(f"Dates train : {data_train.index.min()} --- {data_train.index.max()} (n={len(data_train)})")
print(f"Dates validacion : {data_val.index.min()} --- {data_val.index.max()} (n={len(data_val)})")
print(f"Dates test : {data_test.index.min()} --- {data_test.index.max()} (n={len(data_test)})")
Data exploration¶
Graphical exploration of time series can be an effective way of identifying trends, patterns, and seasonal variations. This, in turn, helps to guide the selection of the most appropriate forecasting model.
Plot time series¶
Full time series
# Interactive plot of time series
# ==============================================================================
fig = go.Figure()
fig.add_trace(go.Scatter(x=data_train.index, y=data_train['users'], mode='lines', name='Train'))
fig.add_trace(go.Scatter(x=data_val.index, y=data_val['users'], mode='lines', name='Validation'))
fig.add_trace(go.Scatter(x=data_test.index, y=data_test['users'], mode='lines', name='Test'))
fig.update_layout(
title = 'Number of users',
xaxis_title="Time",
yaxis_title="Users",
legend_title="Partition:",
width=800,
height=350,
margin=dict(l=20, r=20, t=35, b=20),
legend=dict(
orientation="h",
yanchor="top",
y=1,
xanchor="left",
x=0.001
)
)
#fig.update_xaxes(rangeslider_visible=True)
fig.show()
Seasonality plots¶
Seasonal plots are a useful tool for identifying seasonal patterns and trends in a time series. They are created by averaging the values of each season over time and then plotting them against time.
# Annual, weekly and daily seasonality
# ==============================================================================
fig, axs = plt.subplots(2, 2, figsize=(8.5, 5.5), sharex=False, sharey=True)
axs = axs.ravel()
# Users distribution by month
data['month'] = data.index.month
data.boxplot(column='users', by='month', ax=axs[0])
data.groupby('month')['users'].median().plot(style='o-', linewidth=0.8, ax=axs[0])
axs[0].set_ylabel('Users')
axs[0].set_title('Users distribution by month', fontsize=10)
# Users distribution by week day
data['week_day'] = data.index.day_of_week + 1
data.boxplot(column='users', by='week_day', ax=axs[1])
data.groupby('week_day')['users'].median().plot(style='o-', linewidth=0.8, ax=axs[1])
axs[1].set_ylabel('Users')
axs[1].set_title('Users distribution by week day', fontsize=10)
# Users distribution by the hour of the day
data['hour_day'] = data.index.hour + 1
data.boxplot(column='users', by='hour_day', ax=axs[2])
data.groupby('hour_day')['users'].median().plot(style='o-', linewidth=0.8, ax=axs[2])
axs[2].set_ylabel('Users')
axs[2].set_title('Users distribution by the hour of the day', fontsize=10)
# Users distribution by week day and hour of the day
mean_day_hour = data.groupby(["week_day", "hour_day"])["users"].mean()
mean_day_hour.plot(ax=axs[3])
axs[3].set(
title = "Mean users during week",
xticks = [i * 24 for i in range(7)],
xticklabels = ["Mon", "Tue", "Wed", "Thu", "Fri", "Sat", "Sun"],
xlabel = "Day and hour",
ylabel = "Number of users"
)
axs[3].title.set_size(10)
fig.suptitle("Seasonality plots", fontsize=14)
fig.tight_layout()
There is a clear difference between weekdays and weekends. There is also a clear intra-day pattern, with a different influx of users depending on the time of day.
Autocorrelation plots¶
Auto-correlation plots are a useful tool for identifying the order of an autoregressive model. The autocorrelation function (ACF) is a measure of the correlation between the time series and a lagged version of itself. The partial autocorrelation function (PACF) is a measure of the correlation between the time series and a lagged version of itself, controlling for the values of the time series at all shorter lags. These plots are useful for identifying the lags to be included in the autoregressive model.
# Autocorrelation plot
# ==============================================================================
fig, ax = plt.subplots(figsize=(5, 2))
plot_acf(data['users'], ax=ax, lags=72)
plt.show()
# Partial autocorrelation plot
# ==============================================================================
fig, ax = plt.subplots(figsize=(5, 2))
plot_pacf(data['users'], ax=ax, lags=72, method='ywm')
plt.show()
The results of the autocorrelation study show that there is a significant correlation between the number of users in previous hours, as well as the days before, and the number of users in the future. This means that knowing the number of users during certain periods in the past could be valuable in predicting the number of users in the future.
Recursive multi-step forecasting with XGBoost¶
First, an ForecasterAutoreg model is trained using past values (lags) of the response variable as predictors. Later, exogenous variables are added to the model and the improvement in its performance is assessed. Since Gradient Boosting models have a large number of hyperparameters, a Bayesian Search is performed using the bayesian_search_forecaster() function to find the best combination of hyperparameters and lags. Finally, the predictive ability of the model is evaluated using a backtesting process.
Forecaster¶
# Create forecaster
# ==============================================================================
forecaster = ForecasterAutoreg(
regressor = XGBRegressor(random_state=15926, enable_categorical=True),
lags = 24
)
# Train forecaster
# ==============================================================================
forecaster.fit(y=data.loc[:end_validation, 'users'])
forecaster
# Predict
# ==============================================================================
forecaster.predict(steps=10)
Backtesting¶
In order to have a robust estimate of the predictive ability of the model, a backtesting process is carried out. The backtesting process consists of generating a forecast for each observation in the test set, following the same procedure as it would be done in production, and then comparing the predicted value with the actual value.
# Backtest model on test data
# ==============================================================================
metric, predictions = backtesting_forecaster(
forecaster = forecaster,
y = data['users'],
steps = 36,
metric = 'mean_absolute_error',
initial_train_size = len(data[:end_validation]),
refit = False,
n_jobs = 'auto',
verbose = False, # Change to False to see less information
show_progress = True
)
predictions.head()
# Backtesting error
# ==============================================================================
metric
Exogenous Variables¶
So far, only lagged values of the time series have been used as predictors. However, it is possible to include other variables as predictors. These variables are known as exogenous variables (features) and their use can improve the predictive capacity of the model. A very important point to keep in mind is that the values of the exogenous variables must be known at the time of prediction.
Common examples of exogenous variables are those derived from the calendar, such as the day of the week, month, year, or holidays. Weather variables such as temperature, humidity, and wind also fall into this category, as do economic variables such as inflation and interest rates.
⚠ Warning
Exogenous variables must be known at the time of the forecast. For example, if temperature is used as an exogenous variable, the temperature value for the next hour must be known at the time of the forecast. If the temperature value is not known, the forecast will not be possible.Weather variables should be used with caution. When the model is deployed into production, future weather conditions are not known, but are predictions made by meteorological services. Because they are predictions, they introduce errors into the forecasting model. As a result, the model's predictions are likely to get worse. One way to anticipate this problem, and to know (not avoid) the expected performance of the model, is to use the weather forecasts available at the time the model is trained, rather than the recorded conditions.
✎ Note
For a more detailed explanation of how to use exogenous variables, such as categorical features, visit:# Variables included as exogenous features
# ==============================================================================
exog_features = [
'month_sin',
'month_cos',
'week_of_year_sin',
'week_of_year_cos',
'week_day_sin',
'week_day_cos',
'hour_day_sin',
'hour_day_cos',
'sunrise_hour_sin',
'sunrise_hour_cos',
'sunset_hour_sin',
'sunset_hour_cos',
'holiday_previous_day',
'holiday_next_day',
'temp_roll_mean_1_day',
'temp_roll_mean_7_day',
'temp_roll_max_1_day',
'temp_roll_min_1_day',
'temp_roll_max_7_day',
'temp_roll_min_7_day',
'temp',
'holiday'
]
# Backtesting model with exogenous variables on test data
# ==============================================================================
metric, predictions = backtesting_forecaster(
forecaster = forecaster,
y = data['users'],
exog = data[exog_features],
steps = 36,
metric = 'mean_absolute_error',
initial_train_size = len(data[:end_validation]),
refit = False,
n_jobs = 'auto',
verbose = False,
show_progress = True
)
metric
Adding exogenous variables to the model improves its predictive capacity.
Hyperparameter tuning¶
Hyperparameter tuning is a critical step in developing effective machine learning models. The ForecasterAutoreg used in the previous sections included a XGBoost model with the default hyperparameters. However, there is no reason why these values are the most appropriate. To find the best hyperparameters, a Bayesian Search is performed using the bayesian_search_forecaster() function. The search is carried out using the same backtesting process as before, but each time, the model is trained with different combinations of hyperparameters and lags. It is important to note that the hyperparameter search must be done using the validation set, so the test data is never used.
The search is performed by testing each combination of hyperparameters and lags as follows:
Train the model using only the training set.
The model is evaluated using the validation set via backtesting.
Select the combination of hyperparameters and lags that gives the lowest error.
Train the model again using the best combination found, this time using both the training and validation data.
By following these steps, one can obtain a model with optimized hyperparameters and avoid overfitting.
✎ Note
Starting at version0.12.0, lags are included in the search space (search_space).
# Hyperparameters search
# ==============================================================================
# Create forecaster
forecaster = ForecasterAutoreg(
regressor = XGBRegressor(random_state=15926, enable_categorical=True),
lags = 72
)
# Lags grid
lags_grid = [48, 72, [1, 2, 3, 23, 24, 25, 167, 168, 169]]
# Regressor hyperparameters search space
def search_space(trial):
search_space = {
'n_estimators' : trial.suggest_int('n_estimators', 400, 1200, step=100),
'max_depth' : trial.suggest_int('max_depth', 3, 10, step=1),
'learning_rate' : trial.suggest_float('learning_rate', 0.01, 1),
'subsample' : trial.suggest_float('subsample', 0.1, 1),
'colsample_bytree': trial.suggest_float('colsample_bytree', 0.1, 1),
'gamma' : trial.suggest_float('gamma', 0, 1),
'reg_alpha' : trial.suggest_float('reg_alpha', 0, 1),
'reg_lambda' : trial.suggest_float('reg_lambda', 0, 1),
'lags' : trial.suggest_categorical('lags', lags_grid)
}
return search_space
results_search, frozen_trial = bayesian_search_forecaster(
forecaster = forecaster,
y = data.loc[:end_validation, 'users'],
exog = data.loc[:end_validation, exog_features],
search_space = search_space,
steps = 36,
refit = False,
metric = 'mean_absolute_error',
initial_train_size = len(data_train),
fixed_train_size = False,
n_trials = 20,
random_state = 123,
return_best = True,
n_jobs = 'auto',
verbose = False,
show_progress = True
)
best_params = results_search['params'].iat[0]
best_lags = results_search['lags'].iat[0]
# Search results
# ==============================================================================
results_search.head(5)
Since return_best has been set to True, the forecaster object is automatically updated with the best configuration found and trained on the entire dataset. This final model can then be used for future predictions on new data.
# Best model
# ==============================================================================
forecaster
Once the best combination of hyperparameters has been identified using the validation data, the predictive capacity of the model is evaluated when applied to the test set. It is highly recommended to review the documentation for the backtesting_forecaster() function to gain a better understanding of its capabilities. This will help to utilize its full potential to analyze the predictive ability of the model.
# Backtesting model with exogenous variables on test data
# ==============================================================================
metric, predictions = backtesting_forecaster(
forecaster = forecaster,
y = data['users'],
exog = data[exog_features],
steps = 36,
metric = 'mean_absolute_error',
initial_train_size = len(data[:end_validation]),
refit = False,
n_jobs = 'auto',
verbose = False,
show_progress = True
)
metric
# Plot predictions vs real value
# ======================================================================================
fig = go.Figure()
trace1 = go.Scatter(x=data_test.index, y=data_test['users'], name="test", mode="lines")
trace2 = go.Scatter(x=predictions.index, y=predictions['pred'], name="prediction", mode="lines")
fig.add_trace(trace1)
fig.add_trace(trace2)
fig.update_layout(
title="Real value vs predicted in test data",
xaxis_title="Date time",
yaxis_title="Users",
width=800,
height=350,
margin=dict(l=20, r=20, t=35, b=20),
legend=dict(
orientation="h",
yanchor="top",
y=1.1,
xanchor="left",
x=0.001
)
)
fig.show()
After optimizing lags and hyperparameters, the prediction error of the autoregressive model is reduced.
Feature selection¶
Feature selection is the process of selecting a subset of relevant features for use in model construction. It is an important step in the machine learning process, as it can help to reduce overfitting, improve model accuracy, and reduce training time. Since the underlying regressors of skforecast follow the scikit-learn API, it is possible to apply the feature selection methods available in scikit-learn with the function select_features(). Two of the most popular methods are Recursive Feature Elimination and Sequential Feature Selection.
💡 Tip
Feature selection is a powerful tool for improving the performance of machine learning models. However, it is computationally expensive and can be time-consuming. Since the goal is to find the best subset of features, not the best model, it is not necessary to use the entire data set or a highly complex model. Instead, it is recommended to use a small subset of the data and a simple model. Once the best subset of features has been identified, the model can then be trained using the entire dataset and a more complex configuration.# Create forecaster
# ==============================================================================
regressor = XGBRegressor(
n_estimators = 100,
max_depth = 5,
random_state = 15926,
enable_categorical = True
)
forecaster = ForecasterAutoreg(
regressor = regressor,
lags = [1, 2, 3, 23, 24, 25, 167, 168, 169],
)
# Recursive feature elimination with cross-validation
# ==============================================================================
selector = RFECV(
estimator = regressor,
step = 1,
cv = 3,
min_features_to_select = 10,
n_jobs = -1
)
selected_lags, selected_exog = select_features(
forecaster = forecaster,
selector = selector,
y = data_train['users'],
exog = data_train[exog_features],
select_only = None,
force_inclusion = None,
subsample = 0.5,
random_state = 123,
verbose = True,
)
Scikit-learn's RFECV starts by training a model on the initial set of features, and obtaining the importance of each feature (through attributes such as coef_ or feature_importances_). Then, in each round, the least important features are iteratively removed, followed by cross-validation to calculate the performance of the model with the remaining features. This process continues until further feature removal doesn't improve or starts to degrade the performance of the model (based on a chosen metric), or the min_features_to_select is reached.
The final result is an optimal subset of features that ideally balances model simplicity and predictive power, as determined by the cross-validation process.
The forecaster is trained and re-evaluated using the best subset of features.
# Create a forecaster with the selected features
# ==============================================================================
forecaster = ForecasterAutoreg(
regressor = XGBRegressor(**best_params, random_state=15926, enable_categorical=True),
lags = selected_lags
)
# Backtesting model with exogenous variables on test data
# ==============================================================================
metric, predictions = backtesting_forecaster(
forecaster = forecaster,
y = data['users'],
exog = data[selected_exog],
steps = 36,
metric = 'mean_absolute_error',
initial_train_size = len(data[:end_validation]),
refit = False,
n_jobs = 'auto',
verbose = False,
show_progress = True
)
metric
The performance of the model remains similar to that of the model trained with all the features. However, the model is now simpler, which will make it faster to train and less prone to overfitting.
# Actualizar las variables exógenas utilizadas
# ==============================================================================
exog_features = selected_exog
Model explanaibility¶
Due to the complex nature of many modern machine learning models, such as ensemble methods, they often function as black boxes, making it difficult to understand why a particular prediction was made. Explanability techniques aim to demystify these models, providing insight into their inner workings and helping to build trust, improve transparency, and meet regulatory requirements in various domains. Enhancing model explainability not only helps to understand model behavior, but also helps to identify biases, improve model performance, and enable stakeholders to make more informed decisions based on machine learning insights.
Skforecast is compatible with some of the most popular model explainability methods: model-specific feature importances, SHAP values, and partial dependence plots.
# Create and train forecaster
# ==============================================================================
forecaster = ForecasterAutoreg(
regressor = XGBRegressor(**best_params, random_state=15926, enable_categorical=True),
lags = best_lags
)
forecaster.fit(
y = data.loc[:end_validation, 'users'],
exog = data.loc[:end_validation, exog_features]
)
Model-specific feature importance¶
# Extract feature importance
# ==============================================================================
importance = forecaster.get_feature_importances()
importance.head(10)
⚠ Warning
Theget_feature_importances() method will only return values if the forecaster's regressor has either the coef_ or feature_importances_ attribute, which is the default in scikit-learn.
Shap values¶
SHAP (SHapley Additive exPlanations) values are a popular method for explaining machine learning models, as they help to understand how variables and values influence predictions visually and quantitatively.
It is possible to generate SHAP-values explanations from skforecast models with just two essential elements:
The internal regressor of the forecaster.
The training matrices created from the time series and used to fit the forecaster.
By leveraging these two components, users can create insightful and interpretable explanations for their skforecast models. These explanations can be used to verify the reliability of the model, identify the most significant factors that contribute to model predictions, and gain a deeper understanding of the underlying relationship between the input variables and the target variable.
# Training matrices used by the forecaster to fit the internal regressor
# ==============================================================================
X_train, y_train = forecaster.create_train_X_y(
y = data.loc[:end_validation, 'users'],
exog = data.loc[:end_validation, exog_features]
)
display(X_train.head(3))
display(y_train.head(3))
# Create SHAP explainer (for three base models)
# ==============================================================================
explainer = shap.TreeExplainer(forecaster.regressor)
# Sample 50% of the data to speed up the calculation
rng = np.random.default_rng(seed=785412)
sample = rng.choice(X_train.index, size=int(len(X_train)*0.5), replace=False)
X_train_sample = X_train.loc[sample, :]
shap_values = explainer.shap_values(X_train_sample)
✎ Note
Shap library has several explainers, each designed for a different type of model. Theshap.TreeExplainer explainer is used for tree-based models, such as the LGBMRegressor used in this example. For more information, see the SHAP documentation.
# Shap summary plot (top 10)
# ==============================================================================
shap.initjs()
shap.summary_plot(shap_values, X_train_sample, max_display=10, show=False)
fig, ax = plt.gcf(), plt.gca()
ax.set_title("SHAP Summary plot")
ax.tick_params(labelsize=8)
fig.set_size_inches(7, 3)
# Force plot for the first observation
# ==============================================================================
shap.force_plot(explainer.expected_value, shap_values[0,:], X_train_sample.iloc[0,:])
Session information¶
import session_info
session_info.show(html=False)
Bibliography¶
Hyndman, R.J., & Athanasopoulos, G. (2021) Forecasting: principles and practice, 3rd edition, OTexts: Melbourne, Australia.
Time Series Analysis and Forecasting with ADAM Ivan Svetunkov.
Joseph, M. (2022). Modern time series forecasting with Python: Explore industry-ready time series forecasting using modern machine learning and Deep Learning. Packt Publishing.
Citation¶
How to cite this document
If you use this document or any part of it, please acknowledge the source, thank you!
Forecasting time series with gradient XGBoost by Joaquín Amat Rodrigo and Javier Escobar Ortiz, available under a Attribution-NonCommercial-ShareAlike 4.0 International at https://www.cienciadedatos.net/documentos/py55-forecasting-time-series-with-xgboost.html
How to cite skforecast
If you use skforecast for a scientific publication, we would appreciate it if you cite the published software.
Zenodo:
Amat Rodrigo, Joaquin, & Escobar Ortiz, Javier. (2023). skforecast (v0.13.0). Zenodo. https://doi.org/10.5281/zenodo.8382788
APA:
Amat Rodrigo, J., & Escobar Ortiz, J. (2023). skforecast (Version 0.13.0) [Computer software]. https://doi.org/10.5281/zenodo.8382788
BibTeX:
@software{skforecast, author = {Amat Rodrigo, Joaquin and Escobar Ortiz, Javier}, title = {skforecast}, version = {0.13.0}, month = {8}, year = {2024}, license = {BSD-3-Clause}, url = {https://skforecast.org/}, doi = {10.5281/zenodo.8382788} }
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This work by Joaquín Amat Rodrigo and Javier Escobar Ortiz is licensed under a Attribution-NonCommercial-ShareAlike 4.0 International.