Custom predictors for recursive multi-step forecasting¶

In forecasting time series data, it can be useful to consider additional characteristics beyond just the lagged values. For instance, the moving average of the previous n values can help capture the trend in the series.

The ForecasterAutoregCustom and ForecasterAutoregMultiSeriesCustom classes are similar to ForecasterAutoreg and ForecasterAutoregMultiSeries, respectively, but they allow the user to define their own function for generating predictors.

To create a custom predictor function, the user needs to write a function that takes a time series as input (a NumPy ndarray) and outputs another NumPy ndarray containing the predictors. The Forecaster parameters used to specify this function are fun_predictors and window_size.

  Warning

The window_size parameter specifies the size of the data window that fun_predictors uses to generate each row of predictors. Choosing the appropriate value for this parameter is crucial to avoid losing data when constructing the training matrices. Be sure to provide the correct value for window_size when using fun_predictors.

Libraries¶

In [1]:

# Libraries
# ==============================================================================
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from skforecast.ForecasterAutoregCustom import ForecasterAutoregCustom
from skforecast.ForecasterAutoregMultiSeriesCustom import ForecasterAutoregMultiSeriesCustom
from sklearn.ensemble import RandomForestRegressor
from sklearn.metrics import mean_squared_error

# Libraries # ============================================================================== import numpy as np import pandas as pd import matplotlib.pyplot as plt from skforecast.ForecasterAutoregCustom import ForecasterAutoregCustom from skforecast.ForecasterAutoregMultiSeriesCustom import ForecasterAutoregMultiSeriesCustom from sklearn.ensemble import RandomForestRegressor from sklearn.metrics import mean_squared_error

ForecasterAutoregCustom¶

In [2]:

# 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=(6, 3))
data_train.plot(ax=ax, label='train')
data_test.plot(ax=ax, label='test')
ax.legend();

# 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=(6, 3)) data_train.plot(ax=ax, label='train') data_test.plot(ax=ax, label='test') ax.legend();

Custom predictors¶

In [3]:

# Custom function to create predictors
# ==============================================================================
def create_predictors(y):
    """
    Create first 10 lags of a time series.
    Calculate moving average with window 20.
    """

    lags = y[-1:-11:-1]     # window_size = 10
    mean = np.mean(y[-20:]) # window_size = 20
    predictors = np.hstack([lags, mean])

    return predictors

# Custom function to create predictors # ============================================================================== def create_predictors(y): """ Create first 10 lags of a time series. Calculate moving average with window 20. """ lags = y[-1:-11:-1] # window_size = 10 mean = np.mean(y[-20:]) # window_size = 20 predictors = np.hstack([lags, mean]) return predictors

Train forecaster¶

In [4]:

# Create and fit forecaster
# ==============================================================================
forecaster = ForecasterAutoregCustom(
                 regressor      = RandomForestRegressor(random_state=123),
                 fun_predictors = create_predictors,
                 name_predictors = [f'lag {i}' for i in range(1, 11)] + ['moving_avg_20'],
                 window_size    = 20 # window_size needed by the mean is the most restrictive one
             )

forecaster.fit(y=data_train)
forecaster

# Create and fit forecaster # ============================================================================== forecaster = ForecasterAutoregCustom( regressor = RandomForestRegressor(random_state=123), fun_predictors = create_predictors, name_predictors = [f'lag {i}' for i in range(1, 11)] + ['moving_avg_20'], window_size = 20 # window_size needed by the mean is the most restrictive one ) forecaster.fit(y=data_train) forecaster

Out[4]:

======================= 
ForecasterAutoregCustom 
======================= 
Regressor: RandomForestRegressor(random_state=123) 
Predictors created with function: create_predictors 
Transformer for y: None 
Transformer for exog: None 
Window size: 20 
Weight function included: False 
Exogenous included: 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': 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} 
fit_kwargs: {} 
Creation date: 2023-05-19 20:55:27 
Last fit date: 2023-05-19 20:55:27 
Skforecast version: 0.8.0 
Python version: 3.9.13 
Forecaster id: None 

Prediction¶

In [5]:

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

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

Out[5]:

2005-07-01    0.926598
2005-08-01    0.948202
2005-09-01    1.020947
Freq: MS, Name: pred, dtype: float64

In [6]:

# Plot predictions
# ==============================================================================
fig, ax = plt.subplots(figsize=(6, 3))
data_train.plot(ax=ax, label='train')
data_test.plot(ax=ax, label='test')
predictions.plot(ax=ax, label='predictions')
ax.legend();

# Plot predictions # ============================================================================== fig, ax = plt.subplots(figsize=(6, 3)) data_train.plot(ax=ax, label='train') data_test.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_pred = predictions
            )

print(f"Test error (mse): {error_mse}")

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

Test error (mse): 0.04487765885818191

Feature importances¶

In [8]:

forecaster.get_feature_importances()

forecaster.get_feature_importances()

Out[8]:

	feature	importance
0	lag 1	0.539720
1	lag 2	0.119097
2	lag 3	0.046404
3	lag 4	0.024165
4	lag 5	0.030567
5	lag 6	0.015139
6	lag 7	0.042883
7	lag 8	0.012742
8	lag 9	0.018938
9	lag 10	0.108639
10	moving_avg_20	0.041707

Extract training matrices¶

In [9]:

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

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

Out[9]:

	lag 1	lag 2	lag 3	lag 4	lag 5	lag 6	lag 7	lag 8	lag 9	lag 10	moving_avg_20
datetime
1993-03-01	0.387554	0.751503	0.771258	0.595223	0.568606	0.534761	0.475463	0.483389	0.410534	0.361801	0.496401
1993-04-01	0.427283	0.387554	0.751503	0.771258	0.595223	0.568606	0.534761	0.475463	0.483389	0.410534	0.496275
1993-05-01	0.413890	0.427283	0.387554	0.751503	0.771258	0.595223	0.568606	0.534761	0.475463	0.483389	0.496924
1993-06-01	0.428859	0.413890	0.427283	0.387554	0.751503	0.771258	0.595223	0.568606	0.534761	0.475463	0.496759
1993-07-01	0.470126	0.428859	0.413890	0.427283	0.387554	0.751503	0.771258	0.595223	0.568606	0.534761	0.495638

In [10]:

y.head()

y.head()

Out[10]:

datetime
1993-03-01    0.427283
1993-04-01    0.413890
1993-05-01    0.428859
1993-06-01    0.470126
1993-07-01    0.509210
Freq: MS, Name: y, dtype: float64

ForecasterAutoregMultiSeriesCustom¶

All the methods available for ForecasterAutoregMultiSeries can also be applied to ForecasterAutoregMultiSeriesCustom. To learn more about these methods, please refer to the Multi-series forecasting page.

In [11]:

# Data download
# ==============================================================================
url = ('https://raw.githubusercontent.com/JoaquinAmatRodrigo/skforecast/master/'
       'data/simulated_items_sales.csv')
data = pd.read_csv(url, sep=',')

# Data preparation
# ==============================================================================
data['date'] = pd.to_datetime(data['date'], format='%Y-%m-%d')
data = data.set_index('date')
data = data.asfreq('D')
data = data.sort_index()
data.head()

# Data download # ============================================================================== url = ('https://raw.githubusercontent.com/JoaquinAmatRodrigo/skforecast/master/' 'data/simulated_items_sales.csv') data = pd.read_csv(url, sep=',') # Data preparation # ============================================================================== data['date'] = pd.to_datetime(data['date'], format='%Y-%m-%d') data = data.set_index('date') data = data.asfreq('D') data = data.sort_index() data.head()

Out[11]:

	item_1	item_2	item_3
date
2012-01-01	8.253175	21.047727	19.429739
2012-01-02	22.777826	26.578125	28.009863
2012-01-03	27.549099	31.751042	32.078922
2012-01-04	25.895533	24.567708	27.252276
2012-01-05	21.379238	18.191667	20.357737

In [12]:

# Split data into train-val-test
# ==============================================================================
end_train = '2014-07-15 23:59:00'
data_train = data.loc[:end_train, :].copy()
data_test  = data.loc[end_train:, :].copy()

print(
    f"Train dates : {data_train.index.min()} --- {data_train.index.max()}  "
    f"(n={len(data_train)})"
)
print(
    f"Test dates  : {data_test.index.min()} --- {data_test.index.max()}  "
    f"(n={len(data_test)})"
)

# Split data into train-val-test # ============================================================================== end_train = '2014-07-15 23:59:00' data_train = data.loc[:end_train, :].copy() data_test = data.loc[end_train:, :].copy() print( f"Train dates : {data_train.index.min()} --- {data_train.index.max()} " f"(n={len(data_train)})" ) print( f"Test dates : {data_test.index.min()} --- {data_test.index.max()} " f"(n={len(data_test)})" )

Train dates : 2012-01-01 00:00:00 --- 2014-07-15 00:00:00  (n=927)
Test dates  : 2014-07-16 00:00:00 --- 2015-01-01 00:00:00  (n=170)

In [13]:

# Plot time series
# ==============================================================================
fig, axes = plt.subplots(nrows=3, ncols=1, figsize=(7.5, 4), sharex=True)

data_train['item_1'].plot(label='train', ax=axes[0])
data_test['item_1'].plot(label='test', ax=axes[0])
axes[0].set_xlabel('')
axes[0].set_ylabel('sales')
axes[0].set_title('Item 1')
axes[0].legend()

data_train['item_2'].plot(label='train', ax=axes[1])
data_test['item_2'].plot(label='test', ax=axes[1])
axes[1].set_xlabel('')
axes[1].set_ylabel('sales')
axes[1].set_title('Item 2')

data_train['item_3'].plot(label='train', ax=axes[2])
data_test['item_3'].plot(label='test', ax=axes[2])
axes[2].set_xlabel('')
axes[2].set_ylabel('sales')
axes[2].set_title('Item 3')

fig.tight_layout()
plt.show();

# Plot time series # ============================================================================== fig, axes = plt.subplots(nrows=3, ncols=1, figsize=(7.5, 4), sharex=True) data_train['item_1'].plot(label='train', ax=axes[0]) data_test['item_1'].plot(label='test', ax=axes[0]) axes[0].set_xlabel('') axes[0].set_ylabel('sales') axes[0].set_title('Item 1') axes[0].legend() data_train['item_2'].plot(label='train', ax=axes[1]) data_test['item_2'].plot(label='test', ax=axes[1]) axes[1].set_xlabel('') axes[1].set_ylabel('sales') axes[1].set_title('Item 2') data_train['item_3'].plot(label='train', ax=axes[2]) data_test['item_3'].plot(label='test', ax=axes[2]) axes[2].set_xlabel('') axes[2].set_ylabel('sales') axes[2].set_title('Item 3') fig.tight_layout() plt.show();

Train¶

In [14]:

# Custom function to create predictors
# ==============================================================================
def create_complex_predictors(y):
    """
    Create first 10 lags of a time series.
    Calculate moving average with window 20.
    """

    lags = y[-1:-11:-1]     # window_size = 10  
    mean = np.mean(y[-20:]) # window_size = 20
    predictors = np.hstack([lags, mean])

    return predictors

# Custom function to create predictors # ============================================================================== def create_complex_predictors(y): """ Create first 10 lags of a time series. Calculate moving average with window 20. """ lags = y[-1:-11:-1] # window_size = 10 mean = np.mean(y[-20:]) # window_size = 20 predictors = np.hstack([lags, mean]) return predictors

In [15]:

# Create and fit forecaster
# ==============================================================================
forecaster = ForecasterAutoregMultiSeriesCustom(
                 regressor       = RandomForestRegressor(random_state=123),
                 fun_predictors  = create_complex_predictors,
                 name_predictors = [f'lag {i}' for i in range(1, 11)] + ['moving_avg_20'],
                 window_size     = 20 # window_size needed by the mean is the most restrictive one
             )

forecaster.fit(series=data_train)
forecaster

# Create and fit forecaster # ============================================================================== forecaster = ForecasterAutoregMultiSeriesCustom( regressor = RandomForestRegressor(random_state=123), fun_predictors = create_complex_predictors, name_predictors = [f'lag {i}' for i in range(1, 11)] + ['moving_avg_20'], window_size = 20 # window_size needed by the mean is the most restrictive one ) forecaster.fit(series=data_train) forecaster

Out[15]:

================================== 
ForecasterAutoregMultiSeriesCustom 
================================== 
Regressor: RandomForestRegressor(random_state=123) 
Predictors created with function: create_complex_predictors 
Transformer for series: None 
Transformer for exog: None 
Window size: 20 
Series levels (names): ['item_1', 'item_2', 'item_3'] 
Series weights: None 
Weight function included: False 
Exogenous included: False 
Type of exogenous variable: None 
Exogenous variables names: None 
Training range: [Timestamp('2012-01-01 00:00:00'), Timestamp('2014-07-15 00:00:00')] 
Training index type: DatetimeIndex 
Training index frequency: D 
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} 
fit_kwargs: {} 
Creation date: 2023-05-19 20:55:29 
Last fit date: 2023-05-19 20:55:32 
Skforecast version: 0.8.0 
Python version: 3.9.13 
Forecaster id: None 

Predict¶

If no value is specified for the levels argument, predictions will be computed for all available levels.

In [16]:

# Predict
# ==============================================================================
steps = 36
predictions = forecaster.predict(steps=steps, levels=None)
predictions.head(3)

# Predict # ============================================================================== steps = 36 predictions = forecaster.predict(steps=steps, levels=None) predictions.head(3)

Out[16]:

	item_1	item_2	item_3
2014-07-16	25.737550	11.265323	11.328083
2014-07-17	25.649209	10.784593	12.283007
2014-07-18	25.602333	11.273438	12.722012

Training matrices¶

In [17]:

X_train, y_train, _, _ = forecaster.create_train_X_y(data_train)
X_train.head()

X_train, y_train, _, _ = forecaster.create_train_X_y(data_train) X_train.head()

Out[17]:

	lag 1	lag 2	lag 3	lag 4	lag 5	lag 6	lag 7	lag 8	lag 9	lag 10	moving_avg_20	item_1	item_2	item_3
0	24.018768	24.772249	29.245869	26.636444	20.228468	18.976196	20.784194	21.758617	21.751748	21.717691	21.954065	1.0	0.0	0.0
1	22.503533	24.018768	24.772249	29.245869	26.636444	20.228468	18.976196	20.784194	21.758617	21.751748	22.666583	1.0	0.0	0.0
2	20.794986	22.503533	24.018768	24.772249	29.245869	26.636444	20.228468	18.976196	20.784194	21.758617	22.567441	1.0	0.0	0.0
3	23.981037	20.794986	22.503533	24.018768	24.772249	29.245869	26.636444	20.228468	18.976196	20.784194	22.389038	1.0	0.0	0.0
4	28.018830	23.981037	20.794986	22.503533	24.018768	24.772249	29.245869	26.636444	20.228468	18.976196	22.495203	1.0	0.0	0.0

In [18]:

y_train.head()

y_train.head()

Out[18]:

0    22.503533
1    20.794986
2    23.981037
3    28.018830
4    28.747482
Name: y, dtype: float64

In [19]:

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