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Custom predictors for recursive multi-step forecasting

It may be interesting to include additional characteristics of the time series in addition to the lags, for example, the moving average of the n last values ​​can be used to capture the trend of the series.

The ForecasterAutoregCustom class is very similar to the ForecasterAutoreg class described in the previous section, but it is the user who defines the function used to create the predictors.

Libraries

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# Libraries
# ==============================================================================
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

from skforecast.ForecasterAutoregCustom import ForecasterAutoregCustom
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=',')

# Data preprocessing
# ==============================================================================
data['fecha'] = pd.to_datetime(data['fecha'], format='%Y/%m/%d')
data = data.set_index('fecha')
data = data.rename(columns={'x': 'y'})
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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# Custom function to create poredictors
# ==============================================================================
def create_predictors(y):
    '''
    Create first 10 lags of a time series.
    Calculate moving average with window 20.
    '''

    X_train = pd.DataFrame({'y':y.copy()})
    for i in range(0, 10):
        X_train[f'lag_{i+1}'] = X_train['y'].shift(i)

    X_train['moving_avg'] = X_train['y'].rolling(20).mean()

    X_train = X_train.drop(columns='y').tail(1).to_numpy()  

    return X_train 

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# Create and fit forecaster
# ==============================================================================
forecaster = ForecasterAutoregCustom(
                    regressor      = RandomForestRegressor(random_state=123),
                    fun_predictors = create_predictors,
                    window_size    = 20
                )

forecaster.fit(y=data_train)
forecaster

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=======================ForecasterAutoregCustom=======================
Regressor: RandomForestRegressor(random_state=123)
Predictors created with: create_predictors
Window size: 20
Exogenous variable: False
Parameters: {'bootstrap': True, 'ccp_alpha': 0.0, 'criterion': 'mse', 'max_depth': None, 'max_features': 'auto', 'max_leaf_nodes': None, 'max_samples': None, 'min_impurity_decrease': 0.0, 'min_impurity_split': None, '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}

Prediction

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# Predict
# ==============================================================================
steps = 36
predictions = forecaster.predict(steps=steps)
# Add datetime index to predictions
predictions = pd.Series(data=predictions, index=data_test.index)
predictions.head(3)

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fecha
2005-07-01    0.926598
2005-08-01    0.948202
2005-09-01    1.020947
Freq: MS, 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): 0.04487765885818191

Feature importance

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# When using as regressor LinearRegression, Ridge or Lasso
# forecaster.get_coef()

# When using as regressor RandomForestRegressor or GradientBoostingRegressor
forecaster.get_feature_importances()

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array([0.53971953, 0.11909726, 0.04640365, 0.0241653 , 0.03056669,
       0.01513909, 0.04288317, 0.012742  , 0.01893797, 0.10863873,
       0.04170661])

Extract training matrix

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X, y = forecaster.create_train_X_y(data_train)