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Recursive multi-step forecasting

Since the value of t(n) is required to predict the point t(n-1), and t(n-1) is unknown, it is necessary to make recursive predictions in which, each new prediction, is based on the previous one. This process is known as recursive forecasting or recursive multi-step forecasting.

The main challenge when using machine learning models for recursive multi-step forecasting is transforming the time series in an matrix where, each value of the series, is related to the time window (lags) that precedes it. This forecasting strategy can be easily generated with the classes ForecasterAutoreg and ForecasterAutoregCustom.

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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url = ('https://raw.githubusercontent.com/JoaquinAmatRodrigo/skforecast/master/data/h2o.csv')
data = pd.read_csv(url, sep=',', header=0, names=['y', 'datetime'])

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

steps = 36
data_train = data[:-steps]
data_test  = data[-steps:]

fig, ax=plt.subplots(figsize=(9, 4))
data_train.plot(ax=ax, label='train')
data_test.plot(ax=ax, label='test')
ax.legend()

Create and train forecaster

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forecaster = ForecasterAutoreg(
                regressor = RandomForestRegressor(random_state=123),
                lags      = 15
             )

forecaster.fit(y=data_train)
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: False 
Type of exogenous variable: None 
Exogenous variables names: None 
Training range: [Timestamp('1991-07-01 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': None, 'verbose': 0, 'warm_start': False} 
Creation date: 2021-12-06 23:22:17 
Last fit date: 2021-12-06 23:22:17 
Skforecast version: 0.4.1

Prediction

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predictions = forecaster.predict(steps=36)
predictions.head(3)

2005-07-01    0.921840
2005-08-01    0.954921
2005-09-01    1.101716
Freq: MS, Name: pred, dtype: float64

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


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error_mse = mean_squared_error(
                y_true = data_test,
                y_pred = predictions
            )
print(f"Test error (mse): {error_mse}")

Test error (mse): 0.00429855684785846

Feature importance

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forecaster.get_feature_importance()
feature importance
lag_1 0.0123397
lag_2 0.0851603
lag_3 0.0134071
lag_4 0.00437446
lag_5 0.00318805
lag_6 0.00343593
lag_7 0.00313612
lag_8 0.00714094
lag_9 0.00783053
lag_10 0.0127507
lag_11 0.00901919
lag_12 0.807098
lag_13 0.00481128
lag_14 0.0163282
lag_15 0.0099792

Extract training matrix

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X, y = forecaster.create_train_X_y(data_train)
print(X)
print(y)
datetime lag_1 lag_2 lag_3 lag_4 lag_5 lag_6 lag_7 lag_8 lag_9 lag_10 lag_11 lag_12 lag_13 lag_14 lag_15
1992-10-01 00:00:00 0.534761 0.475463 0.483389 0.410534 0.361801 0.379808 0.351348 0.33622 0.660119 0.602652 0.502369 0.492543 0.432159 0.400906 0.429795
1992-11-01 00:00:00 0.568606 0.534761 0.475463 0.483389 0.410534 0.361801 0.379808 0.351348 0.33622 0.660119 0.602652 0.502369 0.492543 0.432159 0.400906
1992-12-01 00:00:00 0.595223 0.568606 0.534761 0.475463 0.483389 0.410534 0.361801 0.379808 0.351348 0.33622 0.660119 0.602652 0.502369 0.492543 0.432159
1993-01-01 00:00:00 0.771258 0.595223 0.568606 0.534761 0.475463 0.483389 0.410534 0.361801 0.379808 0.351348 0.33622 0.660119 0.602652 0.502369 0.492543
1993-02-01 00:00:00 0.751503 0.771258 0.595223 0.568606 0.534761 0.475463 0.483389 0.410534 0.361801 0.379808 0.351348 0.33622 0.660119 0.602652 0.502369
datetime y
1992-10-01 00:00:00 0.568606
1992-11-01 00:00:00 0.595223
1992-12-01 00:00:00 0.771258
1993-01-01 00:00:00 0.751503
1993-02-01 00:00:00 0.387554