Automatic Encoding for Categorical Variables

To encode calendar features as categorical variables, we can use any suitable encoding method from the sklearn.preprocessing module, such as OneHotEncoder, TargetEncoder, or OrdinalEncoder.

In three examples, we will use OneHotEncoder to encode the categorical variables in our dataset. This method creates new binary columns for each category in the original variable.

from sklearn.preprocessing import OneHotEncoder
import numpy as np
import pandas as pd
from peshbeen.models import ml_forecaster
from lightgbm import LGBMRegressor
from xgboost import XGBRegressor

date_range = pd.date_range(start='2020-01-01', periods=720, freq='D')
# create a non-stationary arbitrary flower sales data with an upward trend, weekly seasonality, and yearly seasonality
np.random.seed(42)
data = 30 + 0.07 * np.arange(720) + 10 * np.sin(2 * np.pi * date_range.dayofyear / 7) + 10 * np.sin(2 * np.pi * date_range.dayofyear / 365) + np.random.normal(0, 5, 720)

sales_data = pd.DataFrame(data, index=date_range, columns=['sales'])
sales_data["week_day"] = sales_data.index.dayofweek
sales_data["month"] = sales_data.index.month
cat_vars = ["week_day", "month"]
train = sales_data.iloc[:-30]
test = sales_data.iloc[-30:]

# Example of using OneHotEncoder for XGBoost
ohe = OneHotEncoder(sparse_output=False, handle_unknown="ignore", drop="first")

xgb = ml_forecaster(target_col="sales", model=XGBRegressor(n_estimators=100, random_state=42),
                    lags = 6,
                    cat_variables=cat_vars, categorical_encoder=ohe)
xgb.fit(train)
xgb_forecasts = xgb.forecast(30, exog=test[cat_vars])
# How the transformed features look like for XGBoost
xgb.X.head()
week_day_1 week_day_2 week_day_3 week_day_4 week_day_5 week_day_6 month_2 month_3 month_4 month_5 ... month_9 month_10 month_11 month_12 sales_lag_1 sales_lag_2 sales_lag_3 sales_lag_4 sales_lag_5 sales_lag_6
2020-01-07 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 22.392017 20.219602 34.174336 38.233477 39.472174 40.474019
2020-01-08 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 39.518145 22.392017 20.219602 34.174336 38.233477 39.472174
2020-01-09 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 43.518276 39.518145 22.392017 20.219602 34.174336 38.233477
2020-01-10 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 39.504995 43.518276 39.518145 22.392017 20.219602 34.174336
2020-01-11 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 39.394569 39.504995 43.518276 39.518145 22.392017 20.219602

5 rows × 23 columns

## Example of using TargetEncoder for LightGBM
from sklearn.preprocessing import TargetEncoder
te = TargetEncoder(cv=5)
lgb = ml_forecaster(target_col="sales", model=LGBMRegressor(n_estimators=100, random_state=42, verbose=-1),
                    lags = 6,
                    cat_variables=cat_vars, categorical_encoder=te)
lgb.fit(train)
lgb_forecasts = lgb.forecast(30, exog=test[cat_vars])
# How the transformed features look like for LightGBM
lgb.X.head()
week_day month sales_lag_1 sales_lag_2 sales_lag_3 sales_lag_4 sales_lag_5 sales_lag_6
2020-01-07 50.118039 46.945004 22.392017 20.219602 34.174336 38.233477 39.472174 40.474019
2020-01-08 55.195593 47.235865 39.518145 22.392017 20.219602 34.174336 38.233477 39.472174
2020-01-09 59.591927 46.210753 43.518276 39.518145 22.392017 20.219602 34.174336 38.233477
2020-01-10 59.436795 46.478067 39.504995 43.518276 39.518145 22.392017 20.219602 34.174336
2020-01-11 57.761881 49.035528 39.394569 39.504995 43.518276 39.518145 22.392017 20.219602

Automatic Transformations for Rolling Window Features

peshbeen supports user-specified rolling window features — such as rolling means and standard deviations — which can be particularly useful for ML regressors as they capture recent dynamics in the series. Beyond feature engineering, peshbeen can automatically apply a Box-Cox transformation to the target variable when the data exhibits heteroscedasticity, stabilising variance before model fitting and improving forecast reliability.

import matplotlib.pyplot as plt
from peshbeen.transformations import rolling_mean, rolling_quantile, rolling_std, expanding_mean
from peshbeen.models import ml_forecaster
from sklearn.linear_model import LinearRegression

transformations = [rolling_std(window_size=30, shift=1), rolling_mean(window_size=30, shift=7),
                   rolling_quantile(window_size=30, shift=1, quantile=0.25),
                   rolling_quantile(window_size=30, shift=1, quantile=0.75), expanding_mean(shift=1)]
linear_model = ml_forecaster(model=LinearRegression(),
              target_col='sales', lags = 7, box_cox=0.5,
              lag_transform=transformations, cat_variables=cat_vars, categorical_encoder=ohe)
linear_model.fit(train)
# linear_model.data_prep(train)
forecasts = linear_model.forecast(H=30, exog=test[cat_vars])

# plot the forecast and the actual values
plt.figure(figsize=(12, 6))
plt.plot(train.index[-120:], train['sales'][-120:], label='Train')
plt.plot(test.index, test['sales'], label='Test')
plt.plot(test.index, forecasts, label='Linear Regression Forecast')
plt.title('Linear Regression Forecast')
plt.xlabel('Date')
plt.ylabel('Sales')
plt.legend()
plt.show()

# How the transformed features look like for Linear Regression
linear_model.X.head()
week_day_1 week_day_2 week_day_3 week_day_4 week_day_5 week_day_6 month_2 month_3 month_4 month_5 ... sales_lag_3 sales_lag_4 sales_lag_5 sales_lag_6 sales_lag_7 rolling_std_30_shift_1 rolling_mean_30_shift_7 rolling_quantile_30_shift_1_q0.25 rolling_quantile_30_shift_1_q0.75 expanding_mean_shift_1
2020-01-08 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ... 6.993242 9.691764 10.366645 10.565377 10.723839 1.581041 10.723839 8.577902 10.569034 9.482514
2020-01-09 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ... 7.464041 6.993242 9.691764 10.366645 10.565377 1.583857 10.644608 9.134833 10.610479 9.696410
2020-01-10 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 ... 10.572692 7.464041 6.993242 9.691764 10.366645 1.509947 10.551954 9.691764 10.572692 9.793542
2020-01-11 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 ... 11.193677 10.572692 7.464041 6.993242 9.691764 1.443708 10.336906 9.860484 10.572169 9.869489
2020-01-12 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 ... 10.570600 11.193677 10.572692 7.464041 6.993242 1.460908 9.668173 8.937674 10.571646 9.716225

5 rows × 29 columns

Fourier Terms for Seasonal Patterns

For series with strong seasonal patterns, peshbeen can automatically generate Fourier terms as a DataFrame indexed to match the original series — making them ready to merge as exogenous variables in a single line. Calendar features such as month or day of week can be added directly to the same DataFrame, and peshbeen will automatically encode them as categorical variables. This covers a wide range of calendar effects, from weekend sales spikes to holiday demand shifts.

from peshbeen.transformations import fourier_terms
# create fourier terms for yearly seasonality with period 365 and number of terms 2 to be used as exogenous variables in the model
sales_exog = sales_data.copy() # create a copy of the original data to store the fourier terms

sales_exog.drop(columns=["month"], inplace=True) # drop month column because we will use fourier terms to capture the yearly seasonality instead of using month as a categorical variable
fourier_trms = fourier_terms(index=sales_exog.index, period=365, num_terms=2)
sales_exog = sales_exog.merge(fourier_trms, left_index=True, right_index=True) # merge the fourier terms with the original data to be used as exogenous variables in the model
sales_exog.head()
sales week_day sin_1_365 sin_2_365 cos_1_365 cos_2_365
2020-01-01 40.474019 2 0.000000 0.000000 1.000000 1.000000
2020-01-02 39.472174 3 0.017213 0.034422 0.999852 0.999407
2020-01-03 38.233477 4 0.034422 0.068802 0.999407 0.997630
2020-01-04 34.174336 5 0.051620 0.103102 0.998667 0.994671
2020-01-05 20.219602 6 0.068802 0.137279 0.997630 0.990532 
# split the data into train and test
from sklearn.linear_model import Lasso
train_exog = sales_exog.iloc[:-30]
test_exog = sales_exog.iloc[-30:].drop(columns=['sales']) # drop the target column from the exogenous variables for the test set
# ml forecast using Linear Regression with fourier terms as exogenous variables
lr_model = ml_forecaster(model=Lasso(alpha=0.1),
              target_col='sales', lags = 7, lag_transform=transformations,
              cat_variables=["week_day"], categorical_encoder=ohe)
lr_model.fit(train_exog)
lr_forecast = lr_model.forecast(H=30, exog=test_exog)
# plot the forecast and the actual values
plt.figure(figsize=(12, 6))
plt.plot(train.index[-120:], train['sales'][-120:], label='Train')
plt.plot(test.index, test['sales'], label='Test')
plt.plot(test.index, lr_forecast, label='Linear Regression Forecast with Fourier Terms')
plt.title('Linear Regression Forecast with Fourier Terms')
plt.xlabel('Date')
plt.ylabel('Sales')
plt.legend()
plt.show()