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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 scikit-learn 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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# Libraries
# ==============================================================================
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.csv')
data = pd.read_csv(url, sep=',', header=0, names=['y', 'datetime'])

# Data preprocessing
# ==============================================================================
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()

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

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

forecaster.fit(y=data_train)
forecaster

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================= 
ForecasterAutoreg 
================= 
Regressor: RandomForestRegressor() 
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: 0.4.0

Prediction

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

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2005-07-01    0.916878
2005-08-01    0.946228
2005-09-01    1.107921
Freq: MS, Name: pred, dtype: float64

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

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Test error (mse): 0.003811271443540486

Feature importance

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forecaster.get_feature_importance()

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| feature   |   importance |
|:----------|-------------:|
| lag_1     |   0.0121745  |
| lag_2     |   0.0857522  |
| lag_3     |   0.0166948  |
| lag_4     |   0.00287025 |
| lag_5     |   0.00346738 |
| lag_6     |   0.00333398 |
| lag_7     |   0.00331932 |
| lag_8     |   0.00757049 |
| lag_9     |   0.00997129 |
| lag_10    |   0.01222    |
| lag_11    |   0.0120539  |
| lag_12    |   0.794896   |
| lag_13    |   0.00438497 |
| lag_14    |   0.0161486  |
| lag_15    |   0.0151425  |

Extract training matrix

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X, y = forecaster.create_train_X_y(data_train)
print(X)
print(y)

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| 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 |