Recursive multi-step forecasting with exogenous variables¶

All forecasters allow to include exogenous variables as predictors as long as their future values are known. These variables must be included during the prediction process.

  Note

When using exogenous variables, their values should be aligned so that y[i] is regressed on exog[i].

  Warning

When including exogenous variables in a forecasting model, it is being assumed that all exogenous inputs are known into the future. Do not include exogenous variables as predictors if their future value will not be known when doing predictions.

Libraries¶

In [1]:

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

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¶

In [2]:

# 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);

# 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);

In [3]:

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

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

Train forecaster¶

In [4]:

# 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

# 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

Out[4]:

================= 
ForecasterAutoreg 
================= 
Regressor: RandomForestRegressor(random_state=123) 
Lags: [ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15] 
Transformer for y: None 
Transformer for exog: None 
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': 1.0, '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: 2022-09-24 08:19:51 
Last fit date: 2022-09-24 08:19:52 
Skforecast version: 0.5.0 
Python version: 3.9.13 

Prediction¶

If the Forecaster has been trained with exogenous variables, they shlud be provided when predictiong.

In [5]:

# Predict
# ==============================================================================
steps = 36
predictions = forecaster.predict(
                steps = steps,
                exog = data_test[['exog_1', 'exog_2']]
              )
# Add datetime index to predictions
predictions = pd.Series(data=predictions, index=data_test.index)
predictions.head(3)

# Predict # ============================================================================== steps = 36 predictions = forecaster.predict( steps = steps, exog = data_test[['exog_1', 'exog_2']] ) # Add datetime index to predictions predictions = pd.Series(data=predictions, index=data_test.index) predictions.head(3)

Out[5]:

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

In [6]:

# 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();

# 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();

In [7]:

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

# 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¶

In [8]:

forecaster.get_feature_importance()

forecaster.get_feature_importance()

Out[8]:

	feature	importance
0	lag_1	0.013354
1	lag_2	0.061120
2	lag_3	0.009086
3	lag_4	0.002721
4	lag_5	0.002478
5	lag_6	0.003155
6	lag_7	0.002179
7	lag_8	0.008154
8	lag_9	0.010319
9	lag_10	0.020587
10	lag_11	0.007036
11	lag_12	0.773389
12	lag_13	0.004583
13	lag_14	0.018127
14	lag_15	0.008732
15	exog_1	0.010364
16	exog_2	0.044616

In [9]:

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