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Recursive multi-step forecasting with exogenous variables

ForecasterAutoreg and ForecasterAutoregCustom allow to include exogenous variables as predictors as long as their future values are known, since they must be included during the predict process.

When using exogenous variables in recursive multi-step forecasting, their values should be aligned so that y[i] is regressed on exog[i].

Libraries

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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from skforecast.ForecasterAutoreg import ForecasterAutoreg
from sklearn.ensemble import RandomForestRegressor
from sklearn.metrics import mean_squared_error

Data

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# Download data
# ==============================================================================
url = ('https://raw.githubusercontent.com/JoaquinAmatRodrigo/skforecast/master/data/h2o_exog.csv')
data = pd.read_csv(url, sep=',', header=0, names=['datetime', 'y', 'exog_1', 'exog_2'])

# Data preprocessing
# ==============================================================================
data['datetime'] = pd.to_datetime(data['datetime'], format='%Y/%m/%d')
data = data.set_index('datetime')
data = data.asfreq('MS')
data = data.sort_index()

# Plot
# ==============================================================================
fig, ax=plt.subplots(figsize=(9, 4))
data.plot(ax=ax);


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# Split train-test
# ==============================================================================
steps = 36
data_train = data.iloc[:-steps, :]
data_test  = data.iloc[-steps:, :]

Create and train forecaster

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# Create and fit forecaster
# ==============================================================================
forecaster = ForecasterAutoreg(
                regressor = RandomForestRegressor(random_state=123),
                lags      = 15
             )

forecaster.fit(
    y    = data_train['y'],
    exog = data_train[['exog_1', 'exog_2']]
)

forecaster

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================= 
ForecasterAutoreg 
================= 
Regressor: RandomForestRegressor(random_state=123) 
Lags: [ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15] 
Window size: 15 
Included exogenous: True 
Type of exogenous variable: <class 'pandas.core.frame.DataFrame'> 
Exogenous variables names: ['exog_1', 'exog_2'] 
Training range: [Timestamp('1992-04-01 00:00:00'), Timestamp('2005-06-01 00:00:00')] 
Training index type: DatetimeIndex 
Training index frequency: MS 
Regressor parameters: {'bootstrap': True, 'ccp_alpha': 0.0, 'criterion': 'squared_error', 'max_depth': None, 'max_features': 'auto', 'max_leaf_nodes': None, 'max_samples': None, 'min_impurity_decrease': 0.0, 'min_samples_leaf': 1, 'min_samples_split': 2, 'min_weight_fraction_leaf': 0.0, 'n_estimators': 100, 'n_jobs': None, 'oob_score': False, 'random_state': 123, 'verbose': 0, 'warm_start': False} 
Creation date: 2022-01-02 16:24:18 
Last fit date: 2022-01-02 16:24:18 
Skforecast version: 0.4.2

Prediction

If the Forecaster has been trained with exogenous variables, they should be provided when predictions.

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# Predict
# ==============================================================================
steps = 36
predictions = forecaster.predict(
                steps = steps,
                exog = data_test[['exog_1', 'exog_2']]
               )
predictions.head(3)

datetime
2005-07-01    0.908832
2005-08-01    0.953925
2005-09-01    1.100887
Freq: MS, Name: pred, dtype: float64

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# Plot predictions
# ==============================================================================
fig, ax=plt.subplots(figsize=(9, 4))
data_train['y'].plot(ax=ax, label='train')
data_test['y'].plot(ax=ax, label='test')
predictions.plot(ax=ax, label='predictions')
ax.legend()


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# Prediction error
# ==============================================================================
error_mse = mean_squared_error(
                y_true = data_test['y'],
                y_pred = predictions
            )
print(f"Test error (mse): {error_mse}")

Test error (mse): 0.004022228812838391

Feature importance

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forecaster.get_feature_importance()
feature importance
lag_1 0.0133541
lag_2 0.0611202
lag_3 0.00908617
lag_4 0.00272094
lag_5 0.00247847
lag_6 0.00315493
lag_7 0.00217887
lag_8 0.00815443
lag_9 0.0103189
lag_10 0.0205869
lag_11 0.00703555
lag_12 0.773389
lag_13 0.00458297
lag_14 0.0181272
lag_15 0.00873237
exog_1 0.0103638
exog_2 0.0446156