Global Forecasting Models: Time series with different lengths and different exogenous variables¶

When faced with a multi-series forecasting problem, it is common for the series to have varying lengths due to differences in the starting times of data recording. To address this scenario, the class ForecasterRecursiveMultiSeries allows the simultaneous modeling of time series of different lengths and using different exogenous variables.

• When the modeled series have different lengths, they must be stored in a Python dictionary. The keys of the dictionary are the names of the series and the values are the series themselves. All series must be of type pandas.Series, have a pandas.DatetimeIndex with the same frequency.

Series values	Allowed
[NaN, NaN, NaN, NaN, 4, 5, 6, 7, 8, 9]	✔️
[0, 1, 2, 3, 4, 5, 6, 7, 8, NaN]	✔️
[0, 1, 2, 3, 4, NaN, 6, 7, 8, 9]	✔️
[NaN, NaN, 2, 3, 4, NaN, 6, 7, 8, 9]	✔️

• When different exogenous variables are used for each series, or if the exogenous variables are the same but have different values for each series, they must be stored in a dictionary. The keys of the dictionary are the names of the series and the values are the exogenous variables themselves. All exogenous variables must be of type pandas.DataFrame or pandas.Series and have a pandas.DatetimeIndex with the same frequency.

💡 Tip

API Reference ForecasterRecursiveMultiSeries.

Libraries and data¶

In [1]:

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

from skforecast.plot import set_dark_theme
from skforecast.preprocessing import series_long_to_dict
from skforecast.preprocessing import exog_long_to_dict
from skforecast.preprocessing import RollingFeatures
from skforecast.recursive import ForecasterRecursiveMultiSeries
from skforecast.model_selection import TimeSeriesFold
from skforecast.model_selection import backtesting_forecaster_multiseries
from skforecast.model_selection import bayesian_search_forecaster_multiseries

# Libraries # ============================================================================== import numpy as np import pandas as pd import matplotlib.pyplot as plt from lightgbm import LGBMRegressor from skforecast.plot import set_dark_theme from skforecast.preprocessing import series_long_to_dict from skforecast.preprocessing import exog_long_to_dict from skforecast.preprocessing import RollingFeatures from skforecast.recursive import ForecasterRecursiveMultiSeries from skforecast.model_selection import TimeSeriesFold from skforecast.model_selection import backtesting_forecaster_multiseries from skforecast.model_selection import bayesian_search_forecaster_multiseries

The data for this example is stored in "long format" in a single DataFrame. The series_id column identifies the series to which each observation belongs. The timestamp column contains the date of the observation, and the value column contains the value of the series at that date. Each time series is of a different length.

The exogenous variables are stored in a separate DataFrame, also in "long format". The column series_id identifies the series to which each observation belongs. The column timestamp contains the date of the observation, and the remaining columns contain the values of the exogenous variables at that date.

In [2]:

# Load time series of multiple lengths and exogenous variables
# ==============================================================================
series = pd.read_csv(
    'https://raw.githubusercontent.com/skforecast/skforecast-datasets/main/data/demo_multi_series.csv'
)
exog = pd.read_csv(
    'https://raw.githubusercontent.com/skforecast/skforecast-datasets/main/data/demo_multi_series_exog.csv'
)

series['timestamp'] = pd.to_datetime(series['timestamp'])
exog['timestamp'] = pd.to_datetime(exog['timestamp'])

display(series.head())
print("")
display(exog.head())

# Load time series of multiple lengths and exogenous variables # ============================================================================== series = pd.read_csv( 'https://raw.githubusercontent.com/skforecast/skforecast-datasets/main/data/demo_multi_series.csv' ) exog = pd.read_csv( 'https://raw.githubusercontent.com/skforecast/skforecast-datasets/main/data/demo_multi_series_exog.csv' ) series['timestamp'] = pd.to_datetime(series['timestamp']) exog['timestamp'] = pd.to_datetime(exog['timestamp']) display(series.head()) print("") display(exog.head())

	series_id	timestamp	value
0	id_1000	2016-01-01	1012.500694
1	id_1000	2016-01-02	1158.500099
2	id_1000	2016-01-03	983.000099
3	id_1000	2016-01-04	1675.750496
4	id_1000	2016-01-05	1586.250694

	series_id	timestamp	sin_day_of_week	cos_day_of_week	air_temperature	wind_speed
0	id_1000	2016-01-01	-0.433884	-0.900969	6.416639	4.040115
1	id_1000	2016-01-02	-0.974928	-0.222521	6.366474	4.530395
2	id_1000	2016-01-03	-0.781831	0.623490	6.555272	3.273064
3	id_1000	2016-01-04	0.000000	1.000000	6.704778	4.865404
4	id_1000	2016-01-05	0.781831	0.623490	2.392998	5.228913

When series have different lengths, the data must be transformed into a dictionary. The keys of the dictionary are the names of the series and the values are the series themselves. To do this, the series_long_to_dict function is used, which takes the DataFrame in "long format" and returns a dict of pandas Series.

Similarly, when the exogenous variables are different (values or variables) for each series, the data must be transformed into a dictionary. The keys of the dictionary are the names of the series and the values are the exogenous variables themselves. The exog_long_to_dict function is used, which takes the DataFrame in "long format" and returns a dict of exogenous variables (pandas Series or pandas DataFrame).

In [3]:

# Transform series and exog to dictionaries
# ==============================================================================
series_dict = series_long_to_dict(
    data      = series,
    series_id = 'series_id',
    index     = 'timestamp',
    values    = 'value',
    freq      = 'D'
)

exog_dict = exog_long_to_dict(
    data      = exog,
    series_id = 'series_id',
    index     = 'timestamp',
    freq      = 'D'
)

# Transform series and exog to dictionaries # ============================================================================== series_dict = series_long_to_dict( data = series, series_id = 'series_id', index = 'timestamp', values = 'value', freq = 'D' ) exog_dict = exog_long_to_dict( data = exog, series_id = 'series_id', index = 'timestamp', freq = 'D' )

c:\Users\jaesc2\Miniconda3\envs\skforecast_py11_2\Lib\site-packages\skforecast\preprocessing\preprocessing.py:424: MissingValuesWarning: Series 'id_1003' is incomplete. NaNs have been introduced after setting the frequency. 
 You can suppress this warning using: warnings.simplefilter('ignore', category=MissingValuesWarning)
  warnings.warn(

Some exogenous variables are omitted for series 1 and 3 to illustrate that different exogenous variables can be used for each series.

In [4]:

# Drop some exogenous variables for series 'id_1000' and 'id_1003'
# ==============================================================================
exog_dict['id_1000'] = exog_dict['id_1000'].drop(columns=['air_temperature', 'wind_speed'])
exog_dict['id_1003'] = exog_dict['id_1003'].drop(columns=['cos_day_of_week'])

# Drop some exogenous variables for series 'id_1000' and 'id_1003' # ============================================================================== exog_dict['id_1000'] = exog_dict['id_1000'].drop(columns=['air_temperature', 'wind_speed']) exog_dict['id_1003'] = exog_dict['id_1003'].drop(columns=['cos_day_of_week'])

In [5]:

# Partition data in train and test
# ==============================================================================
end_train = '2016-07-31 23:59:00'

series_dict_train = {k: v.loc[: end_train,] for k, v in series_dict.items()}
exog_dict_train   = {k: v.loc[: end_train,] for k, v in exog_dict.items()}
series_dict_test  = {k: v.loc[end_train:,] for k, v in series_dict.items()}
exog_dict_test    = {k: v.loc[end_train:,] for k, v in exog_dict.items()}

# Partition data in train and test # ============================================================================== end_train = '2016-07-31 23:59:00' series_dict_train = {k: v.loc[: end_train,] for k, v in series_dict.items()} exog_dict_train = {k: v.loc[: end_train,] for k, v in exog_dict.items()} series_dict_test = {k: v.loc[end_train:,] for k, v in series_dict.items()} exog_dict_test = {k: v.loc[end_train:,] for k, v in exog_dict.items()}

In [6]:

# Plot series
# ==============================================================================
set_dark_theme()
colors = plt.rcParams['axes.prop_cycle'].by_key()['color']
fig, axs = plt.subplots(5, 1, figsize=(8, 4), sharex=True)

for i, s in enumerate(series_dict.values()):
    axs[i].plot(s, label=s.name, color=colors[i])
    axs[i].legend(loc='upper right', fontsize=8)
    axs[i].tick_params(axis='both', labelsize=8)
    axs[i].axvline(pd.to_datetime(end_train), color='white', linestyle='--', linewidth=1)  # End train

fig.suptitle('Series in `series_dict`', fontsize=15)
plt.tight_layout()

# Plot series # ============================================================================== set_dark_theme() colors = plt.rcParams['axes.prop_cycle'].by_key()['color'] fig, axs = plt.subplots(5, 1, figsize=(8, 4), sharex=True) for i, s in enumerate(series_dict.values()): axs[i].plot(s, label=s.name, color=colors[i]) axs[i].legend(loc='upper right', fontsize=8) axs[i].tick_params(axis='both', labelsize=8) axs[i].axvline(pd.to_datetime(end_train), color='white', linestyle='--', linewidth=1) # End train fig.suptitle('Series in `series_dict`', fontsize=15) plt.tight_layout()

In [7]:

# Description of each partition
# ==============================================================================
for k in series_dict.keys():
    print(f"{k}:")
    try:
        print(
            f"\tTrain: len={len(series_dict_train[k])}, {series_dict_train[k].index[0]}"
            f" --- {series_dict_train[k].index[-1]}"
        )
    except:
        print("\tTrain: len=0")
    try:
        print(
            f"\tTest : len={len(series_dict_test[k])}, {series_dict_test[k].index[0]}"
            f" --- {series_dict_test[k].index[-1]}"
        )
    except:
        print("\tTest : len=0")

# Description of each partition # ============================================================================== for k in series_dict.keys(): print(f"{k}:") try: print( f"\tTrain: len={len(series_dict_train[k])}, {series_dict_train[k].index[0]}" f" --- {series_dict_train[k].index[-1]}" ) except: print("\tTrain: len=0") try: print( f"\tTest : len={len(series_dict_test[k])}, {series_dict_test[k].index[0]}" f" --- {series_dict_test[k].index[-1]}" ) except: print("\tTest : len=0")

id_1000:
	Train: len=213, 2016-01-01 00:00:00 --- 2016-07-31 00:00:00
	Test : len=153, 2016-08-01 00:00:00 --- 2016-12-31 00:00:00
id_1001:
	Train: len=30, 2016-07-02 00:00:00 --- 2016-07-31 00:00:00
	Test : len=153, 2016-08-01 00:00:00 --- 2016-12-31 00:00:00
id_1002:
	Train: len=183, 2016-01-01 00:00:00 --- 2016-07-01 00:00:00
	Test : len=0
id_1003:
	Train: len=213, 2016-01-01 00:00:00 --- 2016-07-31 00:00:00
	Test : len=153, 2016-08-01 00:00:00 --- 2016-12-31 00:00:00
id_1004:
	Train: len=91, 2016-05-02 00:00:00 --- 2016-07-31 00:00:00
	Test : len=31, 2016-08-01 00:00:00 --- 2016-08-31 00:00:00

In [8]:

# Exogenous variables for each series
# ==============================================================================
for k in series_dict.keys():
    print(f"{k}:")
    try:
        print(f"\t{exog_dict[k].columns.to_list()}")
    except:
        print("\tNo exogenous variables")

# Exogenous variables for each series # ============================================================================== for k in series_dict.keys(): print(f"{k}:") try: print(f"\t{exog_dict[k].columns.to_list()}") except: print("\tNo exogenous variables")

id_1000:
	['sin_day_of_week', 'cos_day_of_week']
id_1001:
	['sin_day_of_week', 'cos_day_of_week', 'air_temperature', 'wind_speed']
id_1002:
	['sin_day_of_week', 'cos_day_of_week', 'air_temperature', 'wind_speed']
id_1003:
	['sin_day_of_week', 'air_temperature', 'wind_speed']
id_1004:
	['sin_day_of_week', 'cos_day_of_week', 'air_temperature', 'wind_speed']

Train and predict¶

The fit method is used to train the model, it is passed the dictionary of series and the dictionary of exogenous variables where the keys of each dictionary are the names of the series.

In [9]:

# Fit forecaster
# ==============================================================================
regressor = LGBMRegressor(random_state=123, verbose=-1, max_depth=5)
forecaster = ForecasterRecursiveMultiSeries(
                 regressor          = regressor, 
                 lags               = 14, 
                 window_features    = RollingFeatures(stats=['mean', 'mean'], window_sizes=[7, 14]),
                 encoding           = "ordinal", 
                 dropna_from_series = False
             )

forecaster.fit(series=series_dict_train, exog=exog_dict_train, suppress_warnings=True)
forecaster

# Fit forecaster # ============================================================================== regressor = LGBMRegressor(random_state=123, verbose=-1, max_depth=5) forecaster = ForecasterRecursiveMultiSeries( regressor = regressor, lags = 14, window_features = RollingFeatures(stats=['mean', 'mean'], window_sizes=[7, 14]), encoding = "ordinal", dropna_from_series = False ) forecaster.fit(series=series_dict_train, exog=exog_dict_train, suppress_warnings=True) forecaster

Out[9]:

ForecasterRecursiveMultiSeries

General Information

• Regressor: LGBMRegressor
• Lags: [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14]
• Window features: ['roll_mean_7', 'roll_mean_14']
• Window size: 14
• Series encoding: ordinal
• Exogenous included: True
• Weight function included: False
• Series weights: None
• Differentiation order: None
• Creation date: 2024-11-10 17:23:28
• Last fit date: 2024-11-10 17:23:28
• Skforecast version: 0.14.0
• Python version: 3.11.10
• Forecaster id: None

Exogenous Variables

sin_day_of_week, cos_day_of_week, air_temperature, wind_speed

Data Transformations

• Transformer for series: None
• Transformer for exog: None

Training Information

• Series names (levels): id_1000, id_1001, id_1002, id_1003, id_1004
• Training range: 'id_1000': ['2016-01-01', '2016-07-31'], 'id_1001': ['2016-07-02', '2016-07-31'], 'id_1002': ['2016-01-01', '2016-07-01'], 'id_1003': ['2016-01-01', '2016-07-31'], 'id_1004': ['2016-05-02', '2016-07-31']
• Training index type: DatetimeIndex
• Training index frequency: D

Regressor Parameters

{'boosting_type': 'gbdt', 'class_weight': None, 'colsample_bytree': 1.0, 'importance_type': 'split', 'learning_rate': 0.1, 'max_depth': 5, 'min_child_samples': 20, 'min_child_weight': 0.001, 'min_split_gain': 0.0, 'n_estimators': 100, 'n_jobs': None, 'num_leaves': 31, 'objective': None, 'random_state': 123, 'reg_alpha': 0.0, 'reg_lambda': 0.0, 'subsample': 1.0, 'subsample_for_bin': 200000, 'subsample_freq': 0, 'verbose': -1}

Fit Kwargs

{}

🛈 API Reference    🗎 User Guide

Only series whose last window of data ends at the same datetime index can be predicted together. If levels = None, series that do not reach the maximum index are excluded from prediction. In this example, series 'id_1002' is excluded because it does not reach the maximum index.

In [10]:

# Predict
# ==============================================================================
predictions = forecaster.predict(steps=5, exog=exog_dict_test, suppress_warnings=True)
predictions

# Predict # ============================================================================== predictions = forecaster.predict(steps=5, exog=exog_dict_test, suppress_warnings=True) predictions

Out[10]:

	id_1000	id_1001	id_1003	id_1004
2016-08-01	1453.312971	2849.347882	2706.851726	7496.555367
2016-08-02	1440.763196	2947.579536	2310.075968	8685.425990
2016-08-03	1410.151437	2875.847691	1997.329410	8961.631705
2016-08-04	1348.787299	3160.533645	1923.897012	8764.338331
2016-08-05	1301.504387	2920.424937	1940.149954	8694.134833

Missing values in the series¶

When working with time series of different lengths, it is common for some series to have missing values. As not all the regressors allow missing values, the argument dropna_from_series can be used to remove the missing values from the training matrices.

• If False, leave NaNs in X_train and warn the user. (default)

• If True, drop NaNs in X_train and same rows in y_train and warn the user.

y_train NaNs (and same rows from X_train) are always dropped because the target variable cannot have NaN values.

In [11]:

# Sample data with interspersed NaNs
# ==============================================================================
series_dict_nan = {
    'id_1000': series_dict['id_1000'].copy(),
    'id_1003': series_dict['id_1003'].copy()
}

# Create NaNs
series_dict_nan['id_1000'].loc['2016-03-01':'2016-04-01',] = np.nan
series_dict_nan['id_1000'].loc['2016-05-01':'2016-05-07',] = np.nan
series_dict_nan['id_1003'].loc['2016-07-01',] = np.nan

# Plot series
# ==============================================================================
fig, axs = plt.subplots(2, 1, figsize=(8, 2.5), sharex=True)

for i, s in enumerate(series_dict_nan.values()):
    axs[i].plot(s, label=s.name, color=colors[i])
    axs[i].legend(loc='upper right', fontsize=8)
    axs[i].tick_params(axis='both', labelsize=8)
    axs[i].axvline(pd.to_datetime(end_train), color='white', linestyle='--', linewidth=1)  # End train

fig.suptitle('Series in `series_dict_nan`', fontsize=15)
plt.tight_layout()

# Sample data with interspersed NaNs # ============================================================================== series_dict_nan = { 'id_1000': series_dict['id_1000'].copy(), 'id_1003': series_dict['id_1003'].copy() } # Create NaNs series_dict_nan['id_1000'].loc['2016-03-01':'2016-04-01',] = np.nan series_dict_nan['id_1000'].loc['2016-05-01':'2016-05-07',] = np.nan series_dict_nan['id_1003'].loc['2016-07-01',] = np.nan # Plot series # ============================================================================== fig, axs = plt.subplots(2, 1, figsize=(8, 2.5), sharex=True) for i, s in enumerate(series_dict_nan.values()): axs[i].plot(s, label=s.name, color=colors[i]) axs[i].legend(loc='upper right', fontsize=8) axs[i].tick_params(axis='both', labelsize=8) axs[i].axvline(pd.to_datetime(end_train), color='white', linestyle='--', linewidth=1) # End train fig.suptitle('Series in `series_dict_nan`', fontsize=15) plt.tight_layout()

When dropna_from_series = False, the NaNs in X_train are kept and the user is warned. This is useful if the user wants to keep the NaNs in the series and use a regressor that can handle them.

In [12]:

# Create Matrices, dropna_from_series = False
# ==============================================================================
regressor = LGBMRegressor(random_state=123, verbose=-1, max_depth=5)
forecaster = ForecasterRecursiveMultiSeries(
                 regressor          = regressor, 
                 lags               = 3, 
                 encoding           = "ordinal", 
                 dropna_from_series = False
             )

X, y = forecaster.create_train_X_y(series=series_dict_nan)

display(X.head(3))
print("Observations per series:")
print(X['_level_skforecast'].value_counts())
print("")
print("NaNs per series:")
print(X.isnull().sum())

# Create Matrices, dropna_from_series = False # ============================================================================== regressor = LGBMRegressor(random_state=123, verbose=-1, max_depth=5) forecaster = ForecasterRecursiveMultiSeries( regressor = regressor, lags = 3, encoding = "ordinal", dropna_from_series = False ) X, y = forecaster.create_train_X_y(series=series_dict_nan) display(X.head(3)) print("Observations per series:") print(X['_level_skforecast'].value_counts()) print("") print("NaNs per series:") print(X.isnull().sum())

c:\Users\jaesc2\Miniconda3\envs\skforecast_py11_2\Lib\site-packages\skforecast\recursive\_forecaster_recursive_multiseries.py:1057: MissingValuesWarning: NaNs detected in `y_train`. They have been dropped because the target variable cannot have NaN values. Same rows have been dropped from `X_train` to maintain alignment. This is caused by series with interspersed NaNs. 
 You can suppress this warning using: warnings.simplefilter('ignore', category=MissingValuesWarning)
  warnings.warn(
c:\Users\jaesc2\Miniconda3\envs\skforecast_py11_2\Lib\site-packages\skforecast\recursive\_forecaster_recursive_multiseries.py:1079: MissingValuesWarning: NaNs detected in `X_train`. Some regressors do not allow NaN values during training. If you want to drop them, set `forecaster.dropna_from_series = True`. 
 You can suppress this warning using: warnings.simplefilter('ignore', category=MissingValuesWarning)
  warnings.warn(

	lag_1	lag_2	lag_3	_level_skforecast
2016-01-04	983.000099	1158.500099	1012.500694	0
2016-01-05	1675.750496	983.000099	1158.500099	0
2016-01-06	1586.250694	1675.750496	983.000099	0

Observations per series:
_level_skforecast
0    324
1    216
Name: count, dtype: int64

NaNs per series:
lag_1                 5
lag_2                 9
lag_3                13
_level_skforecast     0
dtype: int64

When dropna_from_series = True, the NaNs in X_train are removed and the user is warned. This is useful if the user chooses a regressor that cannot handle missing values.

In [13]:

# Create Matrices, dropna_from_series = False
# ==============================================================================
regressor = LGBMRegressor(random_state=123, verbose=-1, max_depth=5)
forecaster = ForecasterRecursiveMultiSeries(
                 regressor          = regressor, 
                 lags               = 3, 
                 encoding           = "ordinal", 
                 dropna_from_series = True
             )

X, y = forecaster.create_train_X_y(series=series_dict_nan)

display(X.head(3))
print("Observations per series:")
print(X['_level_skforecast'].value_counts())
print("")
print("NaNs per series:")
print(X.isnull().sum())

# Create Matrices, dropna_from_series = False # ============================================================================== regressor = LGBMRegressor(random_state=123, verbose=-1, max_depth=5) forecaster = ForecasterRecursiveMultiSeries( regressor = regressor, lags = 3, encoding = "ordinal", dropna_from_series = True ) X, y = forecaster.create_train_X_y(series=series_dict_nan) display(X.head(3)) print("Observations per series:") print(X['_level_skforecast'].value_counts()) print("") print("NaNs per series:") print(X.isnull().sum())

c:\Users\jaesc2\Miniconda3\envs\skforecast_py11_2\Lib\site-packages\skforecast\recursive\_forecaster_recursive_multiseries.py:1057: MissingValuesWarning: NaNs detected in `y_train`. They have been dropped because the target variable cannot have NaN values. Same rows have been dropped from `X_train` to maintain alignment. This is caused by series with interspersed NaNs. 
 You can suppress this warning using: warnings.simplefilter('ignore', category=MissingValuesWarning)
  warnings.warn(
c:\Users\jaesc2\Miniconda3\envs\skforecast_py11_2\Lib\site-packages\skforecast\recursive\_forecaster_recursive_multiseries.py:1070: MissingValuesWarning: NaNs detected in `X_train`. They have been dropped. If you want to keep them, set `forecaster.dropna_from_series = False`. Same rows have been removed from `y_train` to maintain alignment. This caused by series with interspersed NaNs. 
 You can suppress this warning using: warnings.simplefilter('ignore', category=MissingValuesWarning)
  warnings.warn(

	lag_1	lag_2	lag_3	_level_skforecast
2016-01-04	983.000099	1158.500099	1012.500694	0
2016-01-05	1675.750496	983.000099	1158.500099	0
2016-01-06	1586.250694	1675.750496	983.000099	0

Observations per series:
_level_skforecast
0    318
1    207
Name: count, dtype: int64

NaNs per series:
lag_1                0
lag_2                0
lag_3                0
_level_skforecast    0
dtype: int64

During the training process, the warnings can be suppressed by setting suppress_warnings = True.

In [14]:

# Suppress warnings during fit method
# ==============================================================================
forecaster.fit(series=series_dict_nan, suppress_warnings=True)
forecaster

# Suppress warnings during fit method # ============================================================================== forecaster.fit(series=series_dict_nan, suppress_warnings=True) forecaster

Out[14]:

ForecasterRecursiveMultiSeries

General Information

• Regressor: LGBMRegressor
• Lags: [1 2 3]
• Window features: None
• Window size: 3
• Series encoding: ordinal
• Exogenous included: False
• Weight function included: False
• Series weights: None
• Differentiation order: None
• Creation date: 2024-11-10 17:23:28
• Last fit date: 2024-11-10 17:23:28
• Skforecast version: 0.14.0
• Python version: 3.11.10
• Forecaster id: None

Exogenous Variables

None

Data Transformations

• Transformer for series: None
• Transformer for exog: None

Training Information

• Series names (levels): id_1000, id_1003
• Training range: 'id_1000': ['2016-01-01', '2016-12-31'], 'id_1003': ['2016-01-01', '2016-12-31']
• Training index type: DatetimeIndex
• Training index frequency: D

Regressor Parameters

{'boosting_type': 'gbdt', 'class_weight': None, 'colsample_bytree': 1.0, 'importance_type': 'split', 'learning_rate': 0.1, 'max_depth': 5, 'min_child_samples': 20, 'min_child_weight': 0.001, 'min_split_gain': 0.0, 'n_estimators': 100, 'n_jobs': None, 'num_leaves': 31, 'objective': None, 'random_state': 123, 'reg_alpha': 0.0, 'reg_lambda': 0.0, 'subsample': 1.0, 'subsample_for_bin': 200000, 'subsample_freq': 0, 'verbose': -1}

Fit Kwargs

{}

🛈 API Reference    🗎 User Guide

Backtesting¶

As in the predict method, the levels at which backtesting is performed must be indicated.

When series have different lengths, the backtesting process only returns predictions for the date-times that are present in the series.

In [15]:

# Backtesting
# ==============================================================================
forecaster = ForecasterRecursiveMultiSeries(
                 regressor          = regressor, 
                 lags               = 14, 
                 window_features    = RollingFeatures(stats=['mean', 'mean'], window_sizes=[7, 14]),
                 encoding           = "ordinal", 
                 dropna_from_series = False
             )

cv = TimeSeriesFold(
         steps                 = 24,
         initial_train_size    = len(series_dict_train["id_1000"]),
         refit                 = False,
         allow_incomplete_fold = True,
     )

metrics_levels, backtest_predictions = backtesting_forecaster_multiseries(
    forecaster            = forecaster,
    series                = series_dict,
    exog                  = exog_dict,
    cv                    = cv,
    levels                = None,
    metric                = "mean_absolute_error",
    add_aggregated_metric = True,
    n_jobs                ="auto",
    verbose               = True,
    show_progress         = True,
    suppress_warnings     = True
)

display(metrics_levels)
print("")
display(backtest_predictions)

# Backtesting # ============================================================================== forecaster = ForecasterRecursiveMultiSeries( regressor = regressor, lags = 14, window_features = RollingFeatures(stats=['mean', 'mean'], window_sizes=[7, 14]), encoding = "ordinal", dropna_from_series = False ) cv = TimeSeriesFold( steps = 24, initial_train_size = len(series_dict_train["id_1000"]), refit = False, allow_incomplete_fold = True, ) metrics_levels, backtest_predictions = backtesting_forecaster_multiseries( forecaster = forecaster, series = series_dict, exog = exog_dict, cv = cv, levels = None, metric = "mean_absolute_error", add_aggregated_metric = True, n_jobs ="auto", verbose = True, show_progress = True, suppress_warnings = True ) display(metrics_levels) print("") display(backtest_predictions)

Information of folds
--------------------
Number of observations used for initial training: 213
Number of observations used for backtesting: 153
    Number of folds: 7
    Number skipped folds: 0 
    Number of steps per fold: 24
    Number of steps to exclude between last observed data (last window) and predictions (gap): 0
    Last fold only includes 9 observations.

Fold: 0
    Training:   2016-01-01 00:00:00 -- 2016-07-31 00:00:00  (n=213)
    Validation: 2016-08-01 00:00:00 -- 2016-08-24 00:00:00  (n=24)
Fold: 1
    Training:   No training in this fold
    Validation: 2016-08-25 00:00:00 -- 2016-09-17 00:00:00  (n=24)
Fold: 2
    Training:   No training in this fold
    Validation: 2016-09-18 00:00:00 -- 2016-10-11 00:00:00  (n=24)
Fold: 3
    Training:   No training in this fold
    Validation: 2016-10-12 00:00:00 -- 2016-11-04 00:00:00  (n=24)
Fold: 4
    Training:   No training in this fold
    Validation: 2016-11-05 00:00:00 -- 2016-11-28 00:00:00  (n=24)
Fold: 5
    Training:   No training in this fold
    Validation: 2016-11-29 00:00:00 -- 2016-12-22 00:00:00  (n=24)
Fold: 6
    Training:   No training in this fold
    Validation: 2016-12-23 00:00:00 -- 2016-12-31 00:00:00  (n=9)

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	levels	mean_absolute_error
0	id_1000	167.502214
1	id_1001	1103.313887
2	id_1002	NaN
3	id_1003	280.492603
4	id_1004	711.078359
5	average	565.596766
6	weighted_average	572.944127
7	pooling	572.944127

	id_1000	id_1001	id_1003	id_1004
2016-08-01	1453.312971	2849.347882	2706.851726	7496.555367
2016-08-02	1440.763196	2947.579536	2310.075968	8685.425990
2016-08-03	1410.151437	2875.847691	1997.329410	8961.631705
2016-08-04	1348.787299	3160.533645	1923.897012	8764.338331
2016-08-05	1301.504387	2920.424937	1940.149954	8694.134833
...	...	...	...	...
2016-12-27	1667.998267	1108.052845	2121.157763	NaN
2016-12-28	1579.306861	1111.236661	2050.252915	NaN
2016-12-29	1487.230722	1113.581933	2063.309008	NaN
2016-12-30	1481.331642	1132.535774	2089.261345	NaN
2016-12-31	1393.128313	1106.034061	2064.475030	NaN

153 rows × 4 columns

Note that if a series has no observations in the test set, the backtesting process will not return any predictions for that series and the metric will be NaN, as happened with series 'id_1002'.

In [16]:

# Plot backtesting predictions
# ==============================================================================
fig, axs = plt.subplots(5, 1, figsize=(8, 4), sharex=True)

for i, s in enumerate(series_dict.keys()):
    axs[i].plot(series_dict[s], label=series_dict[s].name, color=colors[i])
    axs[i].axvline(pd.to_datetime(end_train), color='white', linestyle='--', linewidth=1)  # End train
    try:
        axs[i].plot(backtest_predictions[s], label='prediction', color="white")
    except:
        pass
    axs[i].legend(loc='upper right', fontsize=8)
    axs[i].tick_params(axis='both', labelsize=8)

fig.suptitle('Backtest Predictions', fontsize=15)
plt.tight_layout()

# Plot backtesting predictions # ============================================================================== fig, axs = plt.subplots(5, 1, figsize=(8, 4), sharex=True) for i, s in enumerate(series_dict.keys()): axs[i].plot(series_dict[s], label=series_dict[s].name, color=colors[i]) axs[i].axvline(pd.to_datetime(end_train), color='white', linestyle='--', linewidth=1) # End train try: axs[i].plot(backtest_predictions[s], label='prediction', color="white") except: pass axs[i].legend(loc='upper right', fontsize=8) axs[i].tick_params(axis='both', labelsize=8) fig.suptitle('Backtest Predictions', fontsize=15) plt.tight_layout()

Hyperparameter tuning and lags selection¶

The grid_search_forecaster_multiseries, random_search_forecaster_multiseries and bayesian_search_forecaster_multiseries functions in the model_selection module allow for lags and hyperparameter optimization. It is performed using the backtesting strategy for validation as in other Forecasters.

When using series of different lengths, the metric is calculated as a weighted average of the backtesting metrics of the selected series (levels) and their number of predictions.

More information about: Hyperparameter tuning and lags selection Multi-Series.

In [17]:

# Bayesian search hyperparameters and lags with Optuna
# ==============================================================================
forecaster = ForecasterRecursiveMultiSeries(
                 regressor          = LGBMRegressor(random_state=123, verbose=-1), 
                 lags               = 14, 
                 window_features    = RollingFeatures(stats=['mean', 'mean'], window_sizes=[7, 14]),
                 encoding           = "ordinal", 
                 dropna_from_series = False
             )

# Search space
def search_space(trial):
    search_space  = {
        'lags'            : trial.suggest_categorical('lags', [7, 14]),
        'min_samples_leaf': trial.suggest_int('min_samples_leaf', 10, 30),
        'max_depth'       : trial.suggest_int('max_depth', 3, 7)
    }

    return search_space

cv = TimeSeriesFold(
         steps              = 24,
         initial_train_size = len(series_dict_train["id_1000"]),
         refit              = False
     )

results, best_trial = bayesian_search_forecaster_multiseries(
    forecaster            = forecaster,
    series                = series_dict,
    exog                  = exog_dict,
    search_space          = search_space,
    cv                    = cv,
    levels                = None,
    metric                = 'mean_absolute_error',
    n_trials              = 10,
    random_state          = 123,
    return_best           = False,
    n_jobs                = 'auto',
    verbose               = False,
    show_progress         = True,
    suppress_warnings     = True
)

results.head(4)

# Bayesian search hyperparameters and lags with Optuna # ============================================================================== forecaster = ForecasterRecursiveMultiSeries( regressor = LGBMRegressor(random_state=123, verbose=-1), lags = 14, window_features = RollingFeatures(stats=['mean', 'mean'], window_sizes=[7, 14]), encoding = "ordinal", dropna_from_series = False ) # Search space def search_space(trial): search_space = { 'lags' : trial.suggest_categorical('lags', [7, 14]), 'min_samples_leaf': trial.suggest_int('min_samples_leaf', 10, 30), 'max_depth' : trial.suggest_int('max_depth', 3, 7) } return search_space cv = TimeSeriesFold( steps = 24, initial_train_size = len(series_dict_train["id_1000"]), refit = False ) results, best_trial = bayesian_search_forecaster_multiseries( forecaster = forecaster, series = series_dict, exog = exog_dict, search_space = search_space, cv = cv, levels = None, metric = 'mean_absolute_error', n_trials = 10, random_state = 123, return_best = False, n_jobs = 'auto', verbose = False, show_progress = True, suppress_warnings = True ) results.head(4)

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Out[17]:

	levels	lags	params	mean_absolute_error__weighted_average	mean_absolute_error__average	mean_absolute_error__pooling	min_samples_leaf	max_depth
0	[id_1000, id_1001, id_1002, id_1003, id_1004]	[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]	{'min_samples_leaf': 29, 'max_depth': 5}	531.573194	510.885119	510.885119	29	5
1	[id_1000, id_1001, id_1002, id_1003, id_1004]	[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]	{'min_samples_leaf': 11, 'max_depth': 5}	542.700963	557.169748	557.169748	11	5
2	[id_1000, id_1001, id_1002, id_1003, id_1004]	[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]	{'min_samples_leaf': 18, 'max_depth': 4}	572.011630	559.198862	559.198862	18	4
3	[id_1000, id_1001, id_1002, id_1003, id_1004]	[1, 2, 3, 4, 5, 6, 7]	{'min_samples_leaf': 30, 'max_depth': 6}	591.817179	595.234722	595.234722	30	6

Categorical variables¶

⚠ Warning

Starting with version 0.13.0, the ForecasterRecursiveMultiSeries class can use encoding='ordinal_category' for encoding time series identifiers. This approach creates a new column (_level_skforecast) of type pandas category. Consequently, the regressors must be able to handle categorical variables. If the regressors do not support categorical variables, the user should set the encoding to 'ordinal' or 'onehot' for compatibility.

Some examples of regressors that support categorical variables and how to enable them are:

HistGradientBoostingRegressor

HistGradientBoostingRegressor(categorical_features="from_dtype")

LightGBM

LGBMRegressor does not allow configuration of categorical features during initialization, but rather in its fit method. Therefore, use Forecaster' argument fit_kwargs = {'categorical_feature':'auto'}. This is the default behavior of LGBMRegressor if no indication is given.

XGBoost

XGBRegressor(enable_categorical=True)