Calendar features¶
Calendar features serve as key elements in time series forecasting. These features decompose date and time into basic units such as year, month, day, weekday, etc., allowing models to identify recurring patterns, understand seasonal variations, and identify trends. Calendar features can be used as exogenous variables because they are known for the period for which predictions are being made (the forecast horizon).
Dates and time in Pandas
Pandas provides a comprehensive set of capabilities tailored for handling time series data in various domains. Using the NumPy datetime64 and timedelta64 data types, Pandas combines a wide range of functionality from various Python libraries while introducing a wealth of novel tools to effectively manipulate time series data. This includes:
Easily parse date and time data from multiple sources and formats.
Generate sequences of fixed-frequency dates and time spans.
Streamline the manipulation and conversion of date-time information, including time zones.
Facilitate the resampling or conversion of time series data to specific frequencies.
For an in-depth exploration of Pandas' comprehensive time series and date capabilities, please refer to this resource.
Libraries and data¶
# Libraries
# ==============================================================================
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from skforecast.datasets import fetch_dataset
# Downloading data
# ==============================================================================
data = fetch_dataset(name="bike_sharing", raw=True)
data = data[['date_time', 'users']]
data.head()
bike_sharing ------------ 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. Fanaee-T,Hadi. (2013). Bike Sharing Dataset. UCI Machine Learning Repository. https://doi.org/10.24432/C5W894. Shape of the dataset: (17544, 12)
| date_time | users | |
|---|---|---|
| 0 | 2011-01-01 00:00:00 | 16.0 |
| 1 | 2011-01-01 01:00:00 | 40.0 |
| 2 | 2011-01-01 02:00:00 | 32.0 |
| 3 | 2011-01-01 03:00:00 | 13.0 |
| 4 | 2011-01-01 04:00:00 | 1.0 |
Extract calendar features¶
To take advantage of the date-time functionality offered by Pandas, the column of interest must be stored as datetime. Although not required, it is recommended to set it as an index for further integration with skforecast.
# Preprocess data
# ==============================================================================
data['date_time'] = pd.to_datetime(data['date_time'], format='%Y-%m-%d %H:%M:%S')
data = data.set_index('date_time')
data = data.asfreq('H')
data = data.sort_index()
data.head()
C:\Users\jaesc2\AppData\Local\Temp\ipykernel_33436\2221474675.py:5: FutureWarning: 'H' is deprecated and will be removed in a future version, please use 'h' instead.
data = data.asfreq('H')
| users | |
|---|---|
| date_time | |
| 2011-01-01 00:00:00 | 16.0 |
| 2011-01-01 01:00:00 | 40.0 |
| 2011-01-01 02:00:00 | 32.0 |
| 2011-01-01 03:00:00 | 13.0 |
| 2011-01-01 04:00:00 | 1.0 |
Next, several features are created from the date and time information: year, month, day of the week, and hour.
# Create calendar features
# ==============================================================================
data['year'] = data.index.year
data['month'] = data.index.month
data['day_of_week'] = data.index.dayofweek
data['hour'] = data.index.hour
data.head()
| users | year | month | day_of_week | hour | |
|---|---|---|---|---|---|
| date_time | |||||
| 2011-01-01 00:00:00 | 16.0 | 2011 | 1 | 5 | 0 |
| 2011-01-01 01:00:00 | 40.0 | 2011 | 1 | 5 | 1 |
| 2011-01-01 02:00:00 | 32.0 | 2011 | 1 | 5 | 2 |
| 2011-01-01 03:00:00 | 13.0 | 2011 | 1 | 5 | 3 |
| 2011-01-01 04:00:00 | 1.0 | 2011 | 1 | 5 | 4 |
Tip
Numerous calendar-related features can be generated, including day of the year, week of the year, hour of the day, and others. An easy approach to automate their extraction is to use the DatetimeFeatures transformer within the Feature-engine Python library. This class integrates seamlessly into the scikit-learn pipeline, making it compatible with skforecast as well. For a deeper understanding and detailed information, please refer to DatetimeFeatures.
# Create calendar features with Feature-engine
# ==============================================================================
from feature_engine.datetime import DatetimeFeatures
transformer = DatetimeFeatures(
variables = "index",
features_to_extract = "all" # It is also possible to select specific features
)
calendar_features = transformer.fit_transform(data)
calendar_features.head()
| users | year | month | day_of_week | hour | quarter | semester | week | day_of_month | day_of_year | ... | month_start | month_end | quarter_start | quarter_end | year_start | year_end | leap_year | days_in_month | minute | second | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| date_time | |||||||||||||||||||||
| 2011-01-01 00:00:00 | 16.0 | 2011 | 1 | 5 | 0 | 1 | 1 | 52 | 1 | 1 | ... | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 31 | 0 | 0 |
| 2011-01-01 01:00:00 | 40.0 | 2011 | 1 | 5 | 1 | 1 | 1 | 52 | 1 | 1 | ... | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 31 | 0 | 0 |
| 2011-01-01 02:00:00 | 32.0 | 2011 | 1 | 5 | 2 | 1 | 1 | 52 | 1 | 1 | ... | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 31 | 0 | 0 |
| 2011-01-01 03:00:00 | 13.0 | 2011 | 1 | 5 | 3 | 1 | 1 | 52 | 1 | 1 | ... | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 31 | 0 | 0 |
| 2011-01-01 04:00:00 | 1.0 | 2011 | 1 | 5 | 4 | 1 | 1 | 52 | 1 | 1 | ... | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 31 | 0 | 0 |
5 rows × 21 columns
Sunlight-Related Features¶
Sunlight often plays a key role in time series patterns. For example, a household's hourly electricity consumption may correlate significantly with whether it's nighttime, as more electricity is typically used for lighting during those hours. Understanding and incorporating sunlight-related characteristics into analyses can provide valuable insights into consumption patterns and behavioral trends. In addition, factors such as sunrise/sunset times, seasonal changes affecting daylight, and their influence on different data sets can provide deeper context and help predict consumption fluctuations. There are several Python libraries available for extracting sunrise and sunset times. Two of the most commonly used are ephem and astral.
# Features based on the sunligth
# ==============================================================================
from astral.sun import sun
from astral import LocationInfo
location = LocationInfo("Washington, D.C.", "USA")
sunrise_hour = [sun(location.observer, date=date)['sunrise'].hour for date in data.index]
sunset_hour = [sun(location.observer, date=date)['sunset'].hour for date in data.index]
sun_light_features = pd.DataFrame({
'sunrise_hour': sunrise_hour,
'sunset_hour': sunset_hour},
index = data.index
)
sun_light_features['daylight_hours'] = sun_light_features['sunset_hour'] - sun_light_features['sunrise_hour']
sun_light_features.head()
| sunrise_hour | sunset_hour | daylight_hours | |
|---|---|---|---|
| date_time | |||
| 2011-01-01 00:00:00 | 8 | 16 | 8 |
| 2011-01-01 01:00:00 | 8 | 16 | 8 |
| 2011-01-01 02:00:00 | 8 | 16 | 8 |
| 2011-01-01 03:00:00 | 8 | 16 | 8 |
| 2011-01-01 04:00:00 | 8 | 16 | 8 |
Cliclical encoding¶
Certain aspects of the calendar, such as hours of the day or days of the week, behave in cycles. For example, the hours of a day range from 0 to 23. If interpreted as a continuous variable, the hour of 23:00 would be 23 units away from the hour of 00:00. However, this is not true because 23:00 is only one hour away from 00:00. The same is true for the months of the year, since December is only one month away from January. Using techniques such as trigonometric functions - sine and cosine transformations - makes it possible to represent cyclic patterns and avoid inconsistencies in data representation. This technique is called cyclic coding and can significantly improve the predictive power of models.
# Ciclical encoding
# ==============================================================================
def cyclical_encoding(data: pd.Series, cycle_length: int) -> pd.DataFrame:
"""
Encode a cyclical feature with two new features sine and cosine.
The minimum value of the feature is assumed to be 0. The maximum value
of the feature is passed as an argument.
Parameters
----------
data : pd.Series
Series with the feature to encode.
cycle_length : int
The length of the cycle. For example, 12 for months, 24 for hours, etc.
This value is used to calculate the angle of the sin and cos.
Returns
-------
result : pd.DataFrame
Dataframe with the two new features sin and cos.
"""
sin = np.sin(2 * np.pi * data/cycle_length)
cos = np.cos(2 * np.pi * data/cycle_length)
result = pd.DataFrame({
f"{data.name}_sin": sin,
f"{data.name}_cos": cos
})
return result
# Ciclical encoding of month, day of week and hour
# ==============================================================================
month_encoded = cyclical_encoding(calendar_features['month'], cycle_length=12)
day_of_week_encoded = cyclical_encoding(calendar_features['day_of_week'], cycle_length=7)
hour_encoded = cyclical_encoding(calendar_features['hour'], cycle_length=24)
cyclical_features = pd.concat([month_encoded, day_of_week_encoded, hour_encoded], axis=1)
cyclical_features.head()
| month_sin | month_cos | day_of_week_sin | day_of_week_cos | hour_sin | hour_cos | |
|---|---|---|---|---|---|---|
| date_time | ||||||
| 2011-01-01 00:00:00 | 0.5 | 0.866025 | -0.974928 | -0.222521 | 0.000000 | 1.000000 |
| 2011-01-01 01:00:00 | 0.5 | 0.866025 | -0.974928 | -0.222521 | 0.258819 | 0.965926 |
| 2011-01-01 02:00:00 | 0.5 | 0.866025 | -0.974928 | -0.222521 | 0.500000 | 0.866025 |
| 2011-01-01 03:00:00 | 0.5 | 0.866025 | -0.974928 | -0.222521 | 0.707107 | 0.707107 |
| 2011-01-01 04:00:00 | 0.5 | 0.866025 | -0.974928 | -0.222521 | 0.866025 | 0.500000 |
# Plot value of sin and cos for each hour
# ==============================================================================
fig, ax = plt.subplots(figsize=(3.5, 3))
sp = ax.scatter(
hour_encoded["hour_sin"],
hour_encoded["hour_cos"],
c = calendar_features['hour'],
cmap = 'viridis'
)
ax.set(
xlabel="sin(hour)",
ylabel="cos(hour)",
)
_ = fig.colorbar(sp)
plt.show();
✎ Note
See Cyclical features in time series forecasting for a more detailed description of strategies for encoding cyclic features.