Skip to content

Direct multi-step forecaster

ForecasterAutoreg and ForecasterAutoregCustom models follow a recursive prediction strategy in which, each new prediction, builds on the previous prediction. An alternative is to train a model for each step that has to be predicted. This strategy, commonly known as direct multistep forecasting, is computationally more expensive than the recursive since it requires training several models. However, in some scenarios, it achieves better results. This type of model can be obtained with the ForecasterAutoregMultiOutput class and can also include one or multiple exogenous variables.

In order to train a ForecasterAutoregMultiOutput a different training matrix is created for each model.

Libraries

1
2
3
4
5
6
7
8
# Libraries
# ==============================================================================
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from skforecast.ForecasterAutoregMultiOutput import ForecasterAutoregMultiOutput
from sklearn.linear_model import Ridge
from sklearn.metrics import mean_squared_error

Data

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
# 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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
# Create and fit forecaster
# ==============================================================================
forecaster = ForecasterAutoregMultiOutput(
                    regressor = Ridge(),
                    steps     = 36,
                    lags      = 15
                )

forecaster.fit(y=data_train)
forecaster

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
============================ 
ForecasterAutoregMultiOutput 
============================ 
Regressor: Ridge() 
Lags: [ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15] 
Window size: 15 
Maximum steps predicted: 36 
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: {'alpha': 1.0, 'copy_X': True, 'fit_intercept': True, 'max_iter': None, 'normalize': 'deprecated', 'positive': False, 'random_state': None, 'solver': 'auto', 'tol': 0.001} 
Creation date: 2022-01-02 16:26:58 
Last fit date: 2022-01-02 16:26:58 
Skforecast version: 0.4.2

Prediction

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

1
2
3
4
# Predict
# ==============================================================================
predictions = forecaster.predict(steps=36)
predictions.head(3)

2005-07-01    0.952051
2005-08-01    1.004145
2005-09-01    1.114590
Freq: MS, Name: pred, dtype: float64

1
2
3
4
5
6
7
# 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();


1
2
3
4
5
6
7
# Prediction error
# ==============================================================================
error_mse = mean_squared_error(
                y_true = data_test,
                y_pred = predictions
            )
print(f"Test error (mse): {error_mse}")

Test error (mse): 0.008419597278831953

Feature importance

Since ForecasterAutoregMultiOutput fits one model per step,it is necessary to specify from which model retrieve its feature importance.

1
forecaster.get_coef(step=1)
feature coef
lag_1 0.139299
lag_2 0.0510889
lag_3 0.0441923
lag_4 -0.0198684
lag_5 -0.0179349
lag_6 -0.0132333
lag_7 -0.0210635
lag_8 -0.0125908
lag_9 0.0119178
lag_10 0.0205112
lag_11 0.15403
lag_12 0.551652
lag_13 0.0575131
lag_14 -0.0710707
lag_15 -0.0352375

Extract training matrix

Two steps are needed. One to create the whole training matrix and a second one to subset the data needed for each model (step).

1
2
3
4
5
6
7
8
9
X, y = forecaster.create_train_X_y(data_train)
# X and y to train model for step 1
X_1, y_1 = forecaster.filter_train_X_y_for_step(
                step    = 1,
                X_train = X,
                y_train = y,
            )
print(X_1.head(4))
print(y_1.head(4))
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
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
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
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
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
y_step_1
0.595223
0.771258
0.751503
0.387554