Forecaster with Deep Learning¶
Recurrent Neural Networks (RNN) and Long Short-Term Memory (LSTM)¶
Recurrent Neural Networks (RNN) are a type of neural networks designed to process data that follows a sequential order. In conventional neural networks, such as feedforward networks, information flows in one direction, from input to output through hidden layers, without considering the sequential structure of the data. In contrast, RNNs maintain internal states or memories, which allow them to remember past information and use it to predict future data in the sequence.
The basic unit of an RNN is the recurrent cell. This cell takes two inputs: the current input and the previous hidden state. The hidden state can be understood as a "memory" that retains information from previous iterations. The current input and the previous hidden state are combined to calculate the current output and the new hidden state. This output is used as input for the next iteration, along with the next input in the data sequence.
Despite the advances that have been achieved with RNN architectures, they have limitations to capture long-term patterns. This is why variants such as Long Short-Term Memory (LSTM) and Gated Recurrent Units (GRU) have been developed, which address these problems and allow long-term information to be retained more effectively.
Long Short-Term Memory (LSTM) neural networks are a specialized type of RNNs designed to overcome the limitations associated with capturing long-term temporal dependencies. Unlike traditional RNNs, LSTMs incorporate a more complex architecture, introducing memory units and gate mechanisms to improve information management over time.
Structure of LSTMs
LSTMs have a modular structure consisting of three fundamental gates: the forget gate, the input gate, and the output gate. These gates work together to regulate the flow of information through the memory unit, allowing for more precise control over what information to retain and what to forget.
Forget Gate: Regulates how much information should be forgotten and how much should be retained, combining the current input and the previous output through a sigmoid function.
Input Gate: Decides how much new information should be added to long-term memory.
Output Gate: Determines how much information from the current memory will be used for the final output, combining the current input and memory information through a sigmoid function.
💡 Tip
To learn more about forecasting with deep learning models visit our examples:
Libraries¶
💡 Tip: Configuring your backend
As of Skforecast version 0.13.0, PyTorch backend support is available. You can configure the backend by exporting the KERAS_BACKEND environment variable or by editing your local configuration file at ~/.keras/keras.json. The available backend options are: "tensorflow" and "torch". Example:
import os
os.environ["KERAS_BACKEND"] = "torch"
import keras
⚠ Warning
Note: The backend must be configured before importing Keras, and the backend cannot be changed after the package has been imported.
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# Libraries
# ==============================================================================
import os
os.environ["KERAS_BACKEND"] = "torch" # 'tensorflow', 'jax´ or 'torch'
import keras
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.preprocessing import MinMaxScaler
import skforecast
from skforecast.datasets import fetch_dataset
from skforecast.plot import set_dark_theme
from skforecast.ForecasterRnn import ForecasterRnn
from skforecast.ForecasterRnn.utils import create_and_compile_model
from skforecast.model_selection_multiseries import backtesting_forecaster_multiseries
from keras.optimizers import Adam
from keras.losses import MeanSquaredError
from keras.callbacks import EarlyStopping
import warnings
warnings.filterwarnings('once')
print(f"skforecast version: {skforecast.__version__}")
print(f"keras version: {keras.__version__}")
if keras.__version__ > "3.0":
print(f"Using backend: {keras.backend.backend()}")
if keras.backend.backend() == "tensorflow":
import tensorflow
print(f"tensorflow version: {tensorflow.__version__}")
elif keras.backend.backend() == "torch":
import torch
print(f"torch version: {torch.__version__}")
else:
print("Backend not recognized. Please use 'tensorflow' or 'torch'.")
# Libraries
# ==============================================================================
import os
os.environ["KERAS_BACKEND"] = "torch" # 'tensorflow', 'jax´ or 'torch'
import keras
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.preprocessing import MinMaxScaler
import skforecast
from skforecast.datasets import fetch_dataset
from skforecast.plot import set_dark_theme
from skforecast.ForecasterRnn import ForecasterRnn
from skforecast.ForecasterRnn.utils import create_and_compile_model
from skforecast.model_selection_multiseries import backtesting_forecaster_multiseries
from keras.optimizers import Adam
from keras.losses import MeanSquaredError
from keras.callbacks import EarlyStopping
import warnings
warnings.filterwarnings('once')
print(f"skforecast version: {skforecast.__version__}")
print(f"keras version: {keras.__version__}")
if keras.__version__ > "3.0":
print(f"Using backend: {keras.backend.backend()}")
if keras.backend.backend() == "tensorflow":
import tensorflow
print(f"tensorflow version: {tensorflow.__version__}")
elif keras.backend.backend() == "torch":
import torch
print(f"torch version: {torch.__version__}")
else:
print("Backend not recognized. Please use 'tensorflow' or 'torch'.")
skforecast version: 0.13.0 keras version: 3.4.1 Using backend: torch torch version: 2.2.2+cpu
Data¶
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# Data download
# ==============================================================================
air_quality = fetch_dataset(name="air_quality_valencia")
# Data preparation
# ==============================================================================
air_quality = air_quality.interpolate(method="linear")
air_quality = air_quality.sort_index()
air_quality.head()
# Data download
# ==============================================================================
air_quality = fetch_dataset(name="air_quality_valencia")
# Data preparation
# ==============================================================================
air_quality = air_quality.interpolate(method="linear")
air_quality = air_quality.sort_index()
air_quality.head()
air_quality_valencia -------------------- Hourly measures of several air chemical pollutant (pm2.5, co, no, no2, pm10, nox, o3, so2) at Valencia city. Red de Vigilancia y Control de la Contaminación Atmosférica, 46250054-València - Centre, https://mediambient.gva.es/es/web/calidad-ambiental/datos-historicos. Shape of the dataset: (26304, 10)
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| pm2.5 | co | no | no2 | pm10 | nox | o3 | veloc. | direc. | so2 | |
|---|---|---|---|---|---|---|---|---|---|---|
| datetime | ||||||||||
| 2019-01-01 00:00:00 | 19.0 | 0.2 | 3.0 | 36.0 | 22.0 | 40.0 | 16.0 | 0.5 | 262.0 | 8.0 |
| 2019-01-01 01:00:00 | 26.0 | 0.1 | 2.0 | 40.0 | 32.0 | 44.0 | 6.0 | 0.6 | 248.0 | 8.0 |
| 2019-01-01 02:00:00 | 31.0 | 0.1 | 11.0 | 42.0 | 36.0 | 58.0 | 3.0 | 0.3 | 224.0 | 8.0 |
| 2019-01-01 03:00:00 | 30.0 | 0.1 | 15.0 | 41.0 | 35.0 | 63.0 | 3.0 | 0.2 | 220.0 | 10.0 |
| 2019-01-01 04:00:00 | 30.0 | 0.1 | 16.0 | 39.0 | 36.0 | 63.0 | 3.0 | 0.4 | 221.0 | 11.0 |
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# Checking the frequency of the time series
# ==============================================================================
print(f"Index: {air_quality.index.dtype}")
print(f"Frequency: {air_quality.index.freq}")
# Checking the frequency of the time series
# ==============================================================================
print(f"Index: {air_quality.index.dtype}")
print(f"Frequency: {air_quality.index.freq}")
Index: datetime64[ns] Frequency: <Hour>
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# Split train-validation-test
# ==============================================================================
end_train = "2021-03-31 23:59:00"
end_validation = "2021-09-30 23:59:00"
air_quality_train = air_quality.loc[:end_train, :].copy()
air_quality_val = air_quality.loc[end_train:end_validation, :].copy()
air_quality_test = air_quality.loc[end_validation:, :].copy()
print(
f"Dates train : {air_quality_train.index.min()} --- "
f"{air_quality_train.index.max()} (n={len(air_quality_train)})"
)
print(
f"Dates validation : {air_quality_val.index.min()} --- "
f"{air_quality_val.index.max()} (n={len(air_quality_val)})"
)
print(
f"Dates test : {air_quality_test.index.min()} --- "
f"{air_quality_test.index.max()} (n={len(air_quality_test)})"
)
# Split train-validation-test
# ==============================================================================
end_train = "2021-03-31 23:59:00"
end_validation = "2021-09-30 23:59:00"
air_quality_train = air_quality.loc[:end_train, :].copy()
air_quality_val = air_quality.loc[end_train:end_validation, :].copy()
air_quality_test = air_quality.loc[end_validation:, :].copy()
print(
f"Dates train : {air_quality_train.index.min()} --- "
f"{air_quality_train.index.max()} (n={len(air_quality_train)})"
)
print(
f"Dates validation : {air_quality_val.index.min()} --- "
f"{air_quality_val.index.max()} (n={len(air_quality_val)})"
)
print(
f"Dates test : {air_quality_test.index.min()} --- "
f"{air_quality_test.index.max()} (n={len(air_quality_test)})"
)
Dates train : 2019-01-01 00:00:00 --- 2021-03-31 23:00:00 (n=19704) Dates validation : 2021-04-01 00:00:00 --- 2021-09-30 23:00:00 (n=4392) Dates test : 2021-10-01 00:00:00 --- 2021-12-31 23:00:00 (n=2208)
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# Plotting one feature
# ==============================================================================
set_dark_theme()
fig, ax = plt.subplots(figsize=(8, 3))
air_quality_train["pm2.5"].rolling(100).mean().plot(ax=ax, label="train")
air_quality_val["pm2.5"].rolling(100).mean().plot(ax=ax, label="validation")
air_quality_test["pm2.5"].rolling(100).mean().plot(ax=ax, label="test")
ax.set_title("pm2.5")
ax.legend();
# Plotting one feature
# ==============================================================================
set_dark_theme()
fig, ax = plt.subplots(figsize=(8, 3))
air_quality_train["pm2.5"].rolling(100).mean().plot(ax=ax, label="train")
air_quality_val["pm2.5"].rolling(100).mean().plot(ax=ax, label="validation")
air_quality_test["pm2.5"].rolling(100).mean().plot(ax=ax, label="test")
ax.set_title("pm2.5")
ax.legend();
Types of problems in time series modeling¶
1:1 Single-Step Forecasting - Predict one step ahead of a single series using the same series as predictor.¶
This type of problem involves modeling a time series using only its own past. It is a typical autoregressive problem.
Although tensorflow-keras facilitates the process of creating deep learning architectures, it is not always trivial to determine the Xtrain and Ytrain dimensions requiered to run an LSTM model. The dimensions depend on how many time series are being modeled, how many of them are are used as predictors, and the length of the prediction horizon.
✎ Note
The create_and_compile_model function is designed to facilitate the creation of the Tensorflow model. Advanced users can create their own architectures and pass them to the skforecast RNN Forecaster. Input and output dimensions must match the use case to which the model will be applied. the Annex at the end of the document for more details.
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# Create model
# ==============================================================================
series = ["o3"] # Series used as predictors
levels = ["o3"] # Target serie to predict
lags = 32 # Past time steps to be used to predict the target
steps = 1 # Future time steps to be predicted
data = air_quality[series].copy()
data_train = air_quality_train[series].copy()
data_val = air_quality_val[series].copy()
data_test = air_quality_test[series].copy()
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=4,
dense_units=16,
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
model.summary()
# Create model
# ==============================================================================
series = ["o3"] # Series used as predictors
levels = ["o3"] # Target serie to predict
lags = 32 # Past time steps to be used to predict the target
steps = 1 # Future time steps to be predicted
data = air_quality[series].copy()
data_train = air_quality_train[series].copy()
data_val = air_quality_val[series].copy()
data_test = air_quality_test[series].copy()
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=4,
dense_units=16,
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
model.summary()
keras version: 3.4.1 Using backend: torch torch version: 2.2.2+cpu
Model: "functional"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ input_layer (InputLayer) │ (None, 32, 1) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ lstm (LSTM) │ (None, 4) │ 96 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense (Dense) │ (None, 16) │ 80 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_1 (Dense) │ (None, 1) │ 17 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ reshape (Reshape) │ (None, 1, 1) │ 0 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 193 (772.00 B)
Trainable params: 193 (772.00 B)
Non-trainable params: 0 (0.00 B)
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# Forecaster Definition
# ==============================================================================
forecaster = ForecasterRnn(
regressor=model,
levels=levels,
transformer_series=MinMaxScaler(),
fit_kwargs={
"epochs": 3, # Number of epochs to train the model.
"batch_size": 32, # Batch size to train the model.
"callbacks": [
EarlyStopping(monitor="val_loss", patience=5)
], # Callback to stop training when it is no longer learning.
"series_val": data_val, # Validation data for model training.
},
)
forecaster
# Forecaster Definition
# ==============================================================================
forecaster = ForecasterRnn(
regressor=model,
levels=levels,
transformer_series=MinMaxScaler(),
fit_kwargs={
"epochs": 3, # Number of epochs to train the model.
"batch_size": 32, # Batch size to train the model.
"callbacks": [
EarlyStopping(monitor="val_loss", patience=5)
], # Callback to stop training when it is no longer learning.
"series_val": data_val, # Validation data for model training.
},
)
forecaster
c:\Users\jaesc2\Miniconda3\envs\skforecast_py11\Lib\site-packages\skforecast\ForecasterRnn\ForecasterRnn.py:228: UserWarning: Setting `lags` = 'auto'. `lags` are inferred from the regressor architecture. Avoid the warning with lags=lags. warnings.warn( c:\Users\jaesc2\Miniconda3\envs\skforecast_py11\Lib\site-packages\skforecast\ForecasterRnn\ForecasterRnn.py:264: UserWarning: `steps` default value = 'auto'. `steps` inferred from regressor architecture. Avoid the warning with steps=steps. warnings.warn(
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=============
ForecasterRnn
=============
Regressor: <Functional name=functional, built=True>
Lags: [ 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 26 27 28 29 30 31 32]
Transformer for series: MinMaxScaler()
Window size: 32
Target series, levels: ['o3']
Multivariate series (names): None
Maximum steps predicted: [1]
Training range: None
Training index type: None
Training index frequency: None
Model parameters: {'name': 'functional', 'trainable': True, 'layers': [{'module': 'keras.layers', 'class_name': 'InputLayer', 'config': {'batch_shape': (None, 32, 1), 'dtype': 'float32', 'sparse': False, 'name': 'input_layer'}, 'registered_name': None, 'name': 'input_layer', 'inbound_nodes': []}, {'module': 'keras.layers', 'class_name': 'LSTM', 'config': {'name': 'lstm', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'return_sequences': False, 'return_state': False, 'go_backwards': False, 'stateful': False, 'unroll': False, 'zero_output_for_mask': False, 'units': 4, 'activation': 'relu', 'recurrent_activation': 'sigmoid', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'recurrent_initializer': {'module': 'keras.initializers', 'class_name': 'OrthogonalInitializer', 'config': {'gain': 1.0, 'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'unit_forget_bias': True, 'kernel_regularizer': None, 'recurrent_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'recurrent_constraint': None, 'bias_constraint': None, 'dropout': 0.0, 'recurrent_dropout': 0.0, 'seed': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 32, 1)}, 'name': 'lstm', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 32, 1), 'dtype': 'float32', 'keras_history': ['input_layer', 0, 0]}},), 'kwargs': {'training': False, 'mask': None}}]}, {'module': 'keras.layers', 'class_name': 'Dense', 'config': {'name': 'dense', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'units': 16, 'activation': 'relu', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'kernel_regularizer': None, 'bias_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 4)}, 'name': 'dense', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 4), 'dtype': 'float32', 'keras_history': ['lstm', 0, 0]}},), 'kwargs': {}}]}, {'module': 'keras.layers', 'class_name': 'Dense', 'config': {'name': 'dense_1', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'units': 1, 'activation': 'linear', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'kernel_regularizer': None, 'bias_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 16)}, 'name': 'dense_1', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 16), 'dtype': 'float32', 'keras_history': ['dense', 0, 0]}},), 'kwargs': {}}]}, {'module': 'keras.layers', 'class_name': 'Reshape', 'config': {'name': 'reshape', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'target_shape': (1, 1)}, 'registered_name': None, 'build_config': {'input_shape': (None, 1)}, 'name': 'reshape', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 1), 'dtype': 'float32', 'keras_history': ['dense_1', 0, 0]}},), 'kwargs': {}}]}], 'input_layers': [['input_layer', 0, 0]], 'output_layers': [['reshape', 0, 0]]}
Compile parameters: {'optimizer': {'module': 'keras.src.backend.torch.optimizers.torch_adam', 'class_name': 'Adam', 'config': {'name': 'adam', 'learning_rate': 0.009999999776482582, 'weight_decay': None, 'clipnorm': None, 'global_clipnorm': None, 'clipvalue': None, 'use_ema': False, 'ema_momentum': 0.99, 'ema_overwrite_frequency': None, 'loss_scale_factor': None, 'gradient_accumulation_steps': None, 'beta_1': 0.9, 'beta_2': 0.999, 'epsilon': 1e-07, 'amsgrad': False}, 'registered_name': 'Adam'}, 'loss': {'module': 'keras.losses', 'class_name': 'MeanSquaredError', 'config': {'name': 'mean_squared_error', 'reduction': 'sum_over_batch_size'}, 'registered_name': None}, 'loss_weights': None, 'metrics': None, 'weighted_metrics': None, 'run_eagerly': False, 'steps_per_execution': 1, 'jit_compile': False}
fit_kwargs: {'epochs': 3, 'batch_size': 32, 'callbacks': [<keras.src.callbacks.early_stopping.EarlyStopping object at 0x000002B51782FA50>]}
Creation date: 2024-07-30 13:05:10
Last fit date: None
Skforecast version: 0.13.0
Python version: 3.11.5
Forecaster id: None
⚠ Warning
The output warning indicates that the number of lags has been inferred from the model architecture. In this case, the model has an LSTM layer with 32 neurons, so the number of lags is 32. If a different number of lags is desired, the lags argument can be specified in the create_and_compile_model function.
To omit the warning, set lags=lags and steps=steps arguments can be specified in the initialization of the ForecasterRnn.
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# Fit forecaster
# ==============================================================================
forecaster.fit(data_train)
# Fit forecaster
# ==============================================================================
forecaster.fit(data_train)
Epoch 1/3 615/615 ━━━━━━━━━━━━━━━━━━━━ 18s 30ms/step - loss: 0.0551 - val_loss: 0.0382 Epoch 2/3 615/615 ━━━━━━━━━━━━━━━━━━━━ 19s 31ms/step - loss: 0.0412 - val_loss: 0.0364 Epoch 3/3 615/615 ━━━━━━━━━━━━━━━━━━━━ 26s 42ms/step - loss: 0.0408 - val_loss: 0.0388
Overfitting can be tracked by moniting the loss function on the validation set. Metrics are automatically stored in the history attribute of the ForecasterRnn object. The method plot_history can be used to visualize the training and validation loss.
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# Track training and overfitting
# ==============================================================================
fig, ax = plt.subplots(figsize=(6, 2.5))
forecaster.plot_history(ax=ax)
# Track training and overfitting
# ==============================================================================
fig, ax = plt.subplots(figsize=(6, 2.5))
forecaster.plot_history(ax=ax)
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# Predictions
# ==============================================================================
predictions = forecaster.predict()
predictions
# Predictions
# ==============================================================================
predictions = forecaster.predict()
predictions
Out[10]:
| o3 | |
|---|---|
| 2021-04-01 | 52.653137 |
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# Backtesting with test data
# ==============================================================================
metrics, predictions = backtesting_forecaster_multiseries(
forecaster=forecaster,
steps=forecaster.max_step,
series=data,
levels=forecaster.levels,
initial_train_size=len(data.loc[:end_validation, :]), # Training + Validation Data
metric="mean_absolute_error",
verbose=False, # Set to True to print detailed information
refit=False,
)
# Backtesting with test data
# ==============================================================================
metrics, predictions = backtesting_forecaster_multiseries(
forecaster=forecaster,
steps=forecaster.max_step,
series=data,
levels=forecaster.levels,
initial_train_size=len(data.loc[:end_validation, :]), # Training + Validation Data
metric="mean_absolute_error",
verbose=False, # Set to True to print detailed information
refit=False,
)
Epoch 1/3 752/752 ━━━━━━━━━━━━━━━━━━━━ 30s 40ms/step - loss: 0.0398 - val_loss: 0.0390 Epoch 2/3 752/752 ━━━━━━━━━━━━━━━━━━━━ 25s 33ms/step - loss: 0.0402 - val_loss: 0.0341 Epoch 3/3 752/752 ━━━━━━━━━━━━━━━━━━━━ 21s 27ms/step - loss: 0.0399 - val_loss: 0.0359
0%| | 0/2208 [00:00<?, ?it/s]
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# Backtesting predictions
# ==============================================================================
predictions
# Backtesting predictions
# ==============================================================================
predictions
Out[12]:
| o3 | |
|---|---|
| 2021-10-01 00:00:00 | 54.899395 |
| 2021-10-01 01:00:00 | 54.899395 |
| 2021-10-01 02:00:00 | 54.899395 |
| 2021-10-01 03:00:00 | 54.899395 |
| 2021-10-01 04:00:00 | 54.899395 |
| ... | ... |
| 2021-12-31 19:00:00 | 54.899395 |
| 2021-12-31 20:00:00 | 54.899395 |
| 2021-12-31 21:00:00 | 54.899395 |
| 2021-12-31 22:00:00 | 54.899395 |
| 2021-12-31 23:00:00 | 54.899395 |
2208 rows × 1 columns
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# % Error vs series mean
# ==============================================================================
rel_mse = 100 * metrics.loc[0, 'mean_absolute_error'] / np.mean(data["o3"])
print(f"Serie mean: {np.mean(data['o3']):0.2f}")
print(f"Relative error (mae): {rel_mse:0.2f} %")
# % Error vs series mean
# ==============================================================================
rel_mse = 100 * metrics.loc[0, 'mean_absolute_error'] / np.mean(data["o3"])
print(f"Serie mean: {np.mean(data['o3']):0.2f}")
print(f"Relative error (mae): {rel_mse:0.2f} %")
Serie mean: 54.52 Relative error (mae): 33.31 %
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# Plotting predictions vs real values in the test set
# ==============================================================================
fig, ax = plt.subplots(figsize=(8, 3))
data_test["o3"].plot(ax=ax, label="test")
predictions["o3"].plot(ax=ax, label="predictions")
ax.set_title("O3")
ax.legend();
# Plotting predictions vs real values in the test set
# ==============================================================================
fig, ax = plt.subplots(figsize=(8, 3))
data_test["o3"].plot(ax=ax, label="test")
predictions["o3"].plot(ax=ax, label="predictions")
ax.set_title("O3")
ax.legend();
1:1 Multiple-Step Forecasting - Predict a single series using the same series as predictor. Multiple steps ahead.¶
The next case is similar to the previous one, but now the goal is to predict multiple future values. In this scenario multiple future steps of a single time series are modeled using only its past values.
A similar architecture to the previous one will be used, but with a greater number of neurons in the LSTM layer and in the first dense layer. This will allow the model to have greater flexibility to predict the time series.
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# Model creation
# ==============================================================================
series = ["o3"] # Series used as predictors
levels = ["o3"] # Target serie to predict
lags = 32 # Past time steps to be used to predict the target
steps = 5 # Future time steps to be predicted
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=50,
dense_units=32,
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
model.summary()
# Model creation
# ==============================================================================
series = ["o3"] # Series used as predictors
levels = ["o3"] # Target serie to predict
lags = 32 # Past time steps to be used to predict the target
steps = 5 # Future time steps to be predicted
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=50,
dense_units=32,
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
model.summary()
keras version: 3.4.1 Using backend: torch torch version: 2.2.2+cpu
Model: "functional_1"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ input_layer_1 (InputLayer) │ (None, 32, 1) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ lstm_1 (LSTM) │ (None, 50) │ 10,400 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_2 (Dense) │ (None, 32) │ 1,632 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_3 (Dense) │ (None, 5) │ 165 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ reshape_1 (Reshape) │ (None, 5, 1) │ 0 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 12,197 (47.64 KB)
Trainable params: 12,197 (47.64 KB)
Non-trainable params: 0 (0.00 B)
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# Forecaster Creation
# ==============================================================================
forecaster = ForecasterRnn(
regressor=model,
levels=levels,
transformer_series=MinMaxScaler(),
fit_kwargs={
"epochs": 3, # Number of epochs to train the model.
"batch_size": 32, # Batch size to train the model.
"callbacks": [
EarlyStopping(monitor="val_loss", patience=5)
], # Callback to stop training when it is no longer learning.
"series_val": data_val, # Validation data for model training.
},
)
forecaster
# Forecaster Creation
# ==============================================================================
forecaster = ForecasterRnn(
regressor=model,
levels=levels,
transformer_series=MinMaxScaler(),
fit_kwargs={
"epochs": 3, # Number of epochs to train the model.
"batch_size": 32, # Batch size to train the model.
"callbacks": [
EarlyStopping(monitor="val_loss", patience=5)
], # Callback to stop training when it is no longer learning.
"series_val": data_val, # Validation data for model training.
},
)
forecaster
c:\Users\jaesc2\Miniconda3\envs\skforecast_py11\Lib\site-packages\skforecast\ForecasterRnn\ForecasterRnn.py:228: UserWarning: Setting `lags` = 'auto'. `lags` are inferred from the regressor architecture. Avoid the warning with lags=lags. warnings.warn( c:\Users\jaesc2\Miniconda3\envs\skforecast_py11\Lib\site-packages\skforecast\ForecasterRnn\ForecasterRnn.py:264: UserWarning: `steps` default value = 'auto'. `steps` inferred from regressor architecture. Avoid the warning with steps=steps. warnings.warn(
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=============
ForecasterRnn
=============
Regressor: <Functional name=functional_1, built=True>
Lags: [ 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 26 27 28 29 30 31 32]
Transformer for series: MinMaxScaler()
Window size: 32
Target series, levels: ['o3']
Multivariate series (names): None
Maximum steps predicted: [1 2 3 4 5]
Training range: None
Training index type: None
Training index frequency: None
Model parameters: {'name': 'functional_1', 'trainable': True, 'layers': [{'module': 'keras.layers', 'class_name': 'InputLayer', 'config': {'batch_shape': (None, 32, 1), 'dtype': 'float32', 'sparse': False, 'name': 'input_layer_1'}, 'registered_name': None, 'name': 'input_layer_1', 'inbound_nodes': []}, {'module': 'keras.layers', 'class_name': 'LSTM', 'config': {'name': 'lstm_1', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'return_sequences': False, 'return_state': False, 'go_backwards': False, 'stateful': False, 'unroll': False, 'zero_output_for_mask': False, 'units': 50, 'activation': 'relu', 'recurrent_activation': 'sigmoid', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'recurrent_initializer': {'module': 'keras.initializers', 'class_name': 'OrthogonalInitializer', 'config': {'gain': 1.0, 'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'unit_forget_bias': True, 'kernel_regularizer': None, 'recurrent_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'recurrent_constraint': None, 'bias_constraint': None, 'dropout': 0.0, 'recurrent_dropout': 0.0, 'seed': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 32, 1)}, 'name': 'lstm_1', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 32, 1), 'dtype': 'float32', 'keras_history': ['input_layer_1', 0, 0]}},), 'kwargs': {'training': False, 'mask': None}}]}, {'module': 'keras.layers', 'class_name': 'Dense', 'config': {'name': 'dense_2', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'units': 32, 'activation': 'relu', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'kernel_regularizer': None, 'bias_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 50)}, 'name': 'dense_2', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 50), 'dtype': 'float32', 'keras_history': ['lstm_1', 0, 0]}},), 'kwargs': {}}]}, {'module': 'keras.layers', 'class_name': 'Dense', 'config': {'name': 'dense_3', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'units': 5, 'activation': 'linear', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'kernel_regularizer': None, 'bias_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 32)}, 'name': 'dense_3', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 32), 'dtype': 'float32', 'keras_history': ['dense_2', 0, 0]}},), 'kwargs': {}}]}, {'module': 'keras.layers', 'class_name': 'Reshape', 'config': {'name': 'reshape_1', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'target_shape': (5, 1)}, 'registered_name': None, 'build_config': {'input_shape': (None, 5)}, 'name': 'reshape_1', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 5), 'dtype': 'float32', 'keras_history': ['dense_3', 0, 0]}},), 'kwargs': {}}]}], 'input_layers': [['input_layer_1', 0, 0]], 'output_layers': [['reshape_1', 0, 0]]}
Compile parameters: {'optimizer': {'module': 'keras.src.backend.torch.optimizers.torch_adam', 'class_name': 'Adam', 'config': {'name': 'adam', 'learning_rate': 0.009999999776482582, 'weight_decay': None, 'clipnorm': None, 'global_clipnorm': None, 'clipvalue': None, 'use_ema': False, 'ema_momentum': 0.99, 'ema_overwrite_frequency': None, 'loss_scale_factor': None, 'gradient_accumulation_steps': None, 'beta_1': 0.9, 'beta_2': 0.999, 'epsilon': 1e-07, 'amsgrad': False}, 'registered_name': 'Adam'}, 'loss': {'module': 'keras.losses', 'class_name': 'MeanSquaredError', 'config': {'name': 'mean_squared_error', 'reduction': 'sum_over_batch_size'}, 'registered_name': None}, 'loss_weights': None, 'metrics': None, 'weighted_metrics': None, 'run_eagerly': False, 'steps_per_execution': 1, 'jit_compile': False}
fit_kwargs: {'epochs': 3, 'batch_size': 32, 'callbacks': [<keras.src.callbacks.early_stopping.EarlyStopping object at 0x000002B51E58C990>]}
Creation date: 2024-07-30 13:08:24
Last fit date: None
Skforecast version: 0.13.0
Python version: 3.11.5
Forecaster id: None
✎ Note
The fit_kwargs parameter allows the user to set any Tensorflow-based configuration in the model. In the example, 10 training epochs are defined with a batch size of 32. An EarlyStopping callback is configured to stop training when the validation loss stops decreasing for 5 epochs (patience=5). Other callbacks can also be configured, such as ModelCheckpoint to save the model at each epoch, or even Tensorboard to visualize the training and validation loss in real time.
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# Fit forecaster
# ==============================================================================
forecaster.fit(data_train)
# Fit forecaster
# ==============================================================================
forecaster.fit(data_train)
Epoch 1/3 615/615 ━━━━━━━━━━━━━━━━━━━━ 32s 52ms/step - loss: 0.0292 - val_loss: 0.0176 Epoch 2/3 615/615 ━━━━━━━━━━━━━━━━━━━━ 36s 59ms/step - loss: 0.0140 - val_loss: 0.0122 Epoch 3/3 615/615 ━━━━━━━━━━━━━━━━━━━━ 37s 60ms/step - loss: 0.0123 - val_loss: 0.0128
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# Train and overfitting tracking
# ==============================================================================
fig, ax = plt.subplots(figsize=(6, 2.5))
forecaster.plot_history(ax=ax)
# Train and overfitting tracking
# ==============================================================================
fig, ax = plt.subplots(figsize=(6, 2.5))
forecaster.plot_history(ax=ax)
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# Prediction
# ==============================================================================
predictions = forecaster.predict()
predictions
# Prediction
# ==============================================================================
predictions = forecaster.predict()
predictions
Out[19]:
| o3 | |
|---|---|
| 2021-04-01 00:00:00 | 43.579914 |
| 2021-04-01 01:00:00 | 43.036030 |
| 2021-04-01 02:00:00 | 38.125568 |
| 2021-04-01 03:00:00 | 35.505390 |
| 2021-04-01 04:00:00 | 37.147205 |
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# Specific step predictions
# ==============================================================================
predictions = forecaster.predict(steps=[1, 3])
predictions
# Specific step predictions
# ==============================================================================
predictions = forecaster.predict(steps=[1, 3])
predictions
Out[20]:
| o3 | |
|---|---|
| 2021-04-01 00:00:00 | 43.579914 |
| 2021-04-01 02:00:00 | 38.125568 |
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# Backtesting
# ==============================================================================
metrics, predictions = backtesting_forecaster_multiseries(
forecaster=forecaster,
steps=forecaster.max_step,
series=data,
levels=forecaster.levels,
initial_train_size=len(data.loc[:end_validation, :]),
metric="mean_absolute_error",
verbose=False,
refit=False,
)
# Backtesting
# ==============================================================================
metrics, predictions = backtesting_forecaster_multiseries(
forecaster=forecaster,
steps=forecaster.max_step,
series=data,
levels=forecaster.levels,
initial_train_size=len(data.loc[:end_validation, :]),
metric="mean_absolute_error",
verbose=False,
refit=False,
)
Epoch 1/3 752/752 ━━━━━━━━━━━━━━━━━━━━ 41s 54ms/step - loss: 0.0121 - val_loss: 0.0115 Epoch 2/3 752/752 ━━━━━━━━━━━━━━━━━━━━ 41s 55ms/step - loss: 0.0119 - val_loss: 0.0120 Epoch 3/3 752/752 ━━━━━━━━━━━━━━━━━━━━ 46s 61ms/step - loss: 0.0116 - val_loss: 0.0114
0%| | 0/442 [00:00<?, ?it/s]
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# Backtesting predictions
# ==============================================================================
predictions
# Backtesting predictions
# ==============================================================================
predictions
Out[22]:
| o3 | |
|---|---|
| 2021-10-01 00:00:00 | 57.922863 |
| 2021-10-01 01:00:00 | 55.142830 |
| 2021-10-01 02:00:00 | 53.163837 |
| 2021-10-01 03:00:00 | 50.351650 |
| 2021-10-01 04:00:00 | 48.197075 |
| ... | ... |
| 2021-12-31 19:00:00 | 21.249779 |
| 2021-12-31 20:00:00 | 23.083706 |
| 2021-12-31 21:00:00 | 18.573345 |
| 2021-12-31 22:00:00 | 16.224133 |
| 2021-12-31 23:00:00 | 16.216816 |
2208 rows × 1 columns
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# Plotting predictions vs real values in the test set
# ==============================================================================
fig, ax = plt.subplots(figsize=(8, 3))
data_test["o3"].plot(ax=ax, label="test")
predictions["o3"].plot(ax=ax, label="predictions")
ax.set_title("O3")
ax.legend();
# Plotting predictions vs real values in the test set
# ==============================================================================
fig, ax = plt.subplots(figsize=(8, 3))
data_test["o3"].plot(ax=ax, label="test")
predictions["o3"].plot(ax=ax, label="predictions")
ax.set_title("O3")
ax.legend();
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# Backtesting metrics
# ==============================================================================
metrics
# Backtesting metrics
# ==============================================================================
metrics
Out[24]:
| levels | mean_absolute_error | |
|---|---|---|
| 0 | o3 | 9.561174 |
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# % Error vs series mean
# ==============================================================================
rel_mse = 100 * metrics.loc[0, 'mean_absolute_error'] / np.mean(data["o3"])
print(f"Serie mean: {np.mean(data['o3']):0.2f}")
print(f"Relative error (mae): {rel_mse:0.2f} %")
# % Error vs series mean
# ==============================================================================
rel_mse = 100 * metrics.loc[0, 'mean_absolute_error'] / np.mean(data["o3"])
print(f"Serie mean: {np.mean(data['o3']):0.2f}")
print(f"Relative error (mae): {rel_mse:0.2f} %")
Serie mean: 54.52 Relative error (mae): 17.54 %
N:1 Multiple-Step Forecasting - Predict one series using multiple series as predictors.¶
In this case, a single series will be predicted, but using multiple time series as predictors. Now, the past values of multiple time series will influence the prediction of a single time series.
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# Model creation
# ==============================================================================
# Time series used in the training. Now, it is multiseries
series = ['pm2.5', 'co', 'no', 'no2', 'pm10', 'nox', 'o3', 'veloc.', 'direc.','so2']
levels = ["o3"]
lags = 32
steps = 5
data = air_quality[series].copy()
data_train = air_quality_train[series].copy()
data_val = air_quality_val[series].copy()
data_test = air_quality_test[series].copy()
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=[100, 50],
dense_units=[64, 32],
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
model.summary()
# Model creation
# ==============================================================================
# Time series used in the training. Now, it is multiseries
series = ['pm2.5', 'co', 'no', 'no2', 'pm10', 'nox', 'o3', 'veloc.', 'direc.','so2']
levels = ["o3"]
lags = 32
steps = 5
data = air_quality[series].copy()
data_train = air_quality_train[series].copy()
data_val = air_quality_val[series].copy()
data_test = air_quality_test[series].copy()
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=[100, 50],
dense_units=[64, 32],
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
model.summary()
keras version: 3.4.1 Using backend: torch torch version: 2.2.2+cpu
Model: "functional_2"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ input_layer_2 (InputLayer) │ (None, 32, 10) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ lstm_2 (LSTM) │ (None, 32, 100) │ 44,400 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ lstm_3 (LSTM) │ (None, 50) │ 30,200 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_4 (Dense) │ (None, 64) │ 3,264 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_5 (Dense) │ (None, 32) │ 2,080 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_6 (Dense) │ (None, 5) │ 165 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ reshape_2 (Reshape) │ (None, 5, 1) │ 0 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 80,109 (312.93 KB)
Trainable params: 80,109 (312.93 KB)
Non-trainable params: 0 (0.00 B)
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# Forecaster creation
# ==============================================================================
forecaster = ForecasterRnn(
regressor=model,
levels=levels,
steps=steps,
lags=lags,
transformer_series=MinMaxScaler(),
fit_kwargs={
"epochs": 4,
"batch_size": 128,
"series_val": data_val,
},
)
forecaster
# Forecaster creation
# ==============================================================================
forecaster = ForecasterRnn(
regressor=model,
levels=levels,
steps=steps,
lags=lags,
transformer_series=MinMaxScaler(),
fit_kwargs={
"epochs": 4,
"batch_size": 128,
"series_val": data_val,
},
)
forecaster
Out[27]:
=============
ForecasterRnn
=============
Regressor: <Functional name=functional_2, built=True>
Lags: [ 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 26 27 28 29 30 31 32]
Transformer for series: MinMaxScaler()
Window size: 32
Target series, levels: ['o3']
Multivariate series (names): None
Maximum steps predicted: [1 2 3 4 5]
Training range: None
Training index type: None
Training index frequency: None
Model parameters: {'name': 'functional_2', 'trainable': True, 'layers': [{'module': 'keras.layers', 'class_name': 'InputLayer', 'config': {'batch_shape': (None, 32, 10), 'dtype': 'float32', 'sparse': False, 'name': 'input_layer_2'}, 'registered_name': None, 'name': 'input_layer_2', 'inbound_nodes': []}, {'module': 'keras.layers', 'class_name': 'LSTM', 'config': {'name': 'lstm_2', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'return_sequences': True, 'return_state': False, 'go_backwards': False, 'stateful': False, 'unroll': False, 'zero_output_for_mask': False, 'units': 100, 'activation': 'relu', 'recurrent_activation': 'sigmoid', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'recurrent_initializer': {'module': 'keras.initializers', 'class_name': 'OrthogonalInitializer', 'config': {'gain': 1.0, 'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'unit_forget_bias': True, 'kernel_regularizer': None, 'recurrent_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'recurrent_constraint': None, 'bias_constraint': None, 'dropout': 0.0, 'recurrent_dropout': 0.0, 'seed': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 32, 10)}, 'name': 'lstm_2', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 32, 10), 'dtype': 'float32', 'keras_history': ['input_layer_2', 0, 0]}},), 'kwargs': {'training': False, 'mask': None}}]}, {'module': 'keras.layers', 'class_name': 'LSTM', 'config': {'name': 'lstm_3', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'return_sequences': False, 'return_state': False, 'go_backwards': False, 'stateful': False, 'unroll': False, 'zero_output_for_mask': False, 'units': 50, 'activation': 'relu', 'recurrent_activation': 'sigmoid', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'recurrent_initializer': {'module': 'keras.initializers', 'class_name': 'OrthogonalInitializer', 'config': {'gain': 1.0, 'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'unit_forget_bias': True, 'kernel_regularizer': None, 'recurrent_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'recurrent_constraint': None, 'bias_constraint': None, 'dropout': 0.0, 'recurrent_dropout': 0.0, 'seed': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 32, 100)}, 'name': 'lstm_3', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 32, 100), 'dtype': 'float32', 'keras_history': ['lstm_2', 0, 0]}},), 'kwargs': {'training': False, 'mask': None}}]}, {'module': 'keras.layers', 'class_name': 'Dense', 'config': {'name': 'dense_4', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'units': 64, 'activation': 'relu', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'kernel_regularizer': None, 'bias_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 50)}, 'name': 'dense_4', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 50), 'dtype': 'float32', 'keras_history': ['lstm_3', 0, 0]}},), 'kwargs': {}}]}, {'module': 'keras.layers', 'class_name': 'Dense', 'config': {'name': 'dense_5', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'units': 32, 'activation': 'relu', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'kernel_regularizer': None, 'bias_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 64)}, 'name': 'dense_5', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 64), 'dtype': 'float32', 'keras_history': ['dense_4', 0, 0]}},), 'kwargs': {}}]}, {'module': 'keras.layers', 'class_name': 'Dense', 'config': {'name': 'dense_6', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'units': 5, 'activation': 'linear', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'kernel_regularizer': None, 'bias_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 32)}, 'name': 'dense_6', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 32), 'dtype': 'float32', 'keras_history': ['dense_5', 0, 0]}},), 'kwargs': {}}]}, {'module': 'keras.layers', 'class_name': 'Reshape', 'config': {'name': 'reshape_2', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'target_shape': (5, 1)}, 'registered_name': None, 'build_config': {'input_shape': (None, 5)}, 'name': 'reshape_2', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 5), 'dtype': 'float32', 'keras_history': ['dense_6', 0, 0]}},), 'kwargs': {}}]}], 'input_layers': [['input_layer_2', 0, 0]], 'output_layers': [['reshape_2', 0, 0]]}
Compile parameters: {'optimizer': {'module': 'keras.src.backend.torch.optimizers.torch_adam', 'class_name': 'Adam', 'config': {'name': 'adam', 'learning_rate': 0.009999999776482582, 'weight_decay': None, 'clipnorm': None, 'global_clipnorm': None, 'clipvalue': None, 'use_ema': False, 'ema_momentum': 0.99, 'ema_overwrite_frequency': None, 'loss_scale_factor': None, 'gradient_accumulation_steps': None, 'beta_1': 0.9, 'beta_2': 0.999, 'epsilon': 1e-07, 'amsgrad': False}, 'registered_name': 'Adam'}, 'loss': {'module': 'keras.losses', 'class_name': 'MeanSquaredError', 'config': {'name': 'mean_squared_error', 'reduction': 'sum_over_batch_size'}, 'registered_name': None}, 'loss_weights': None, 'metrics': None, 'weighted_metrics': None, 'run_eagerly': False, 'steps_per_execution': 1, 'jit_compile': False}
fit_kwargs: {'epochs': 4, 'batch_size': 128}
Creation date: 2024-07-30 13:12:37
Last fit date: None
Skforecast version: 0.13.0
Python version: 3.11.5
Forecaster id: None
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# Fit forecaster
# ==============================================================================
forecaster.fit(data_train)
# Fit forecaster
# ==============================================================================
forecaster.fit(data_train)
Epoch 1/4 154/154 ━━━━━━━━━━━━━━━━━━━━ 23s 152ms/step - loss: 0.0470 - val_loss: 0.0178 Epoch 2/4 154/154 ━━━━━━━━━━━━━━━━━━━━ 24s 153ms/step - loss: 0.0134 - val_loss: 0.0122 Epoch 3/4 154/154 ━━━━━━━━━━━━━━━━━━━━ 22s 145ms/step - loss: 0.0110 - val_loss: 0.0127 Epoch 4/4 154/154 ━━━━━━━━━━━━━━━━━━━━ 25s 162ms/step - loss: 0.0100 - val_loss: 0.0127
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# Trainig and overfitting tracking
# ==============================================================================
fig, ax = plt.subplots(figsize=(7, 3))
forecaster.plot_history(ax=ax)
# Trainig and overfitting tracking
# ==============================================================================
fig, ax = plt.subplots(figsize=(7, 3))
forecaster.plot_history(ax=ax)
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# Prediction
# ==============================================================================
predictions = forecaster.predict()
predictions
# Prediction
# ==============================================================================
predictions = forecaster.predict()
predictions
Out[30]:
| o3 | |
|---|---|
| 2021-04-01 00:00:00 | 43.277061 |
| 2021-04-01 01:00:00 | 40.084240 |
| 2021-04-01 02:00:00 | 37.378689 |
| 2021-04-01 03:00:00 | 34.141743 |
| 2021-04-01 04:00:00 | 30.391361 |
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# Backtesting with test data
# ==============================================================================
metrics, predictions = backtesting_forecaster_multiseries(
forecaster=forecaster,
steps=forecaster.max_step,
series=data,
levels=forecaster.levels,
initial_train_size=len(data.loc[:end_validation, :]), # Datos de entrenamiento + validación
metric="mean_absolute_error",
verbose=False,
refit=False,
)
# Backtesting with test data
# ==============================================================================
metrics, predictions = backtesting_forecaster_multiseries(
forecaster=forecaster,
steps=forecaster.max_step,
series=data,
levels=forecaster.levels,
initial_train_size=len(data.loc[:end_validation, :]), # Datos de entrenamiento + validación
metric="mean_absolute_error",
verbose=False,
refit=False,
)
Epoch 1/4 188/188 ━━━━━━━━━━━━━━━━━━━━ 30s 157ms/step - loss: 0.0098 - val_loss: 0.0113 Epoch 2/4 188/188 ━━━━━━━━━━━━━━━━━━━━ 28s 150ms/step - loss: 0.0095 - val_loss: 0.0111 Epoch 3/4 188/188 ━━━━━━━━━━━━━━━━━━━━ 30s 159ms/step - loss: 0.0093 - val_loss: 0.0121 Epoch 4/4 188/188 ━━━━━━━━━━━━━━━━━━━━ 34s 182ms/step - loss: 0.0093 - val_loss: 0.0113
0%| | 0/442 [00:00<?, ?it/s]
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# Backtesting metrics
# ==============================================================================
metrics
# Backtesting metrics
# ==============================================================================
metrics
Out[32]:
| levels | mean_absolute_error | |
|---|---|---|
| 0 | o3 | 10.363694 |
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# % Error vs series mean
# ==============================================================================
rel_mse = 100 * metrics.loc[0, 'mean_absolute_error'] / np.mean(data["o3"])
print(f"Serie mean: {np.mean(data['o3']):0.2f}")
print(f"Relative error (mae): {rel_mse:0.2f} %")
# % Error vs series mean
# ==============================================================================
rel_mse = 100 * metrics.loc[0, 'mean_absolute_error'] / np.mean(data["o3"])
print(f"Serie mean: {np.mean(data['o3']):0.2f}")
print(f"Relative error (mae): {rel_mse:0.2f} %")
Serie mean: 54.52 Relative error (mae): 19.01 %
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# Backtesting predictions
# ==============================================================================
predictions
# Backtesting predictions
# ==============================================================================
predictions
Out[34]:
| o3 | |
|---|---|
| 2021-10-01 00:00:00 | 49.819893 |
| 2021-10-01 01:00:00 | 46.665585 |
| 2021-10-01 02:00:00 | 42.649746 |
| 2021-10-01 03:00:00 | 37.113007 |
| 2021-10-01 04:00:00 | 32.271500 |
| ... | ... |
| 2021-12-31 19:00:00 | 17.417406 |
| 2021-12-31 20:00:00 | 11.689775 |
| 2021-12-31 21:00:00 | 3.200252 |
| 2021-12-31 22:00:00 | 4.635203 |
| 2021-12-31 23:00:00 | 6.826915 |
2208 rows × 1 columns
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# Plotting predictions vs real values in the test set
# ==============================================================================
fig, ax = plt.subplots(figsize=(8, 3))
data_test["o3"].plot(ax=ax, label="test")
predictions["o3"].plot(ax=ax, label="predictions")
ax.set_title("O3")
ax.legend();
# Plotting predictions vs real values in the test set
# ==============================================================================
fig, ax = plt.subplots(figsize=(8, 3))
data_test["o3"].plot(ax=ax, label="test")
predictions["o3"].plot(ax=ax, label="predictions")
ax.set_title("O3")
ax.legend();
N:M Multiple-Step Forecasting - Multiple time series with multiple outputs¶
This is a more complex scenario in which multiple time series are predicted using multiple time series as predictors. It is therefore a scenario in which multiple series are modeled simultaneously using a single model. This has special application in many real scenarios, such as the prediction of stock values for several companies based on the stock history, the price of energy and commodities. Or the case of forecasting multiple products in an online store, based on the sales of other products, the price of the products, etc.
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# Model creation
# ==============================================================================
# Now, we have multiple series and multiple targets
series = ['pm2.5', 'co', 'no', 'no2', 'pm10', 'nox', 'o3', 'veloc.', 'direc.','so2']
levels = ['pm2.5', 'co', 'no', "o3"] # Features to predict. It can be all the series or less
lags = 32
steps = 5
data = air_quality[series].copy()
data_train = air_quality_train[series].copy()
data_val = air_quality_val[series].copy()
data_test = air_quality_test[series].copy()
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=[100, 50],
dense_units=[64, 32],
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
model.summary()
# Model creation
# ==============================================================================
# Now, we have multiple series and multiple targets
series = ['pm2.5', 'co', 'no', 'no2', 'pm10', 'nox', 'o3', 'veloc.', 'direc.','so2']
levels = ['pm2.5', 'co', 'no', "o3"] # Features to predict. It can be all the series or less
lags = 32
steps = 5
data = air_quality[series].copy()
data_train = air_quality_train[series].copy()
data_val = air_quality_val[series].copy()
data_test = air_quality_test[series].copy()
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=[100, 50],
dense_units=[64, 32],
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
model.summary()
keras version: 3.4.1 Using backend: torch torch version: 2.2.2+cpu
Model: "functional_3"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ input_layer_3 (InputLayer) │ (None, 32, 10) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ lstm_4 (LSTM) │ (None, 32, 100) │ 44,400 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ lstm_5 (LSTM) │ (None, 50) │ 30,200 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_7 (Dense) │ (None, 64) │ 3,264 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_8 (Dense) │ (None, 32) │ 2,080 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_9 (Dense) │ (None, 20) │ 660 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ reshape_3 (Reshape) │ (None, 5, 4) │ 0 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 80,604 (314.86 KB)
Trainable params: 80,604 (314.86 KB)
Non-trainable params: 0 (0.00 B)
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# Forecaster creation
# ==============================================================================
forecaster = ForecasterRnn(
regressor=model,
levels=levels,
steps=steps,
lags=lags,
transformer_series=MinMaxScaler(),
fit_kwargs={
"epochs": 10,
"batch_size": 128,
"callbacks": [
EarlyStopping(monitor="val_loss", patience=3)
],
"series_val": data_val,
},
)
forecaster
# Forecaster creation
# ==============================================================================
forecaster = ForecasterRnn(
regressor=model,
levels=levels,
steps=steps,
lags=lags,
transformer_series=MinMaxScaler(),
fit_kwargs={
"epochs": 10,
"batch_size": 128,
"callbacks": [
EarlyStopping(monitor="val_loss", patience=3)
],
"series_val": data_val,
},
)
forecaster
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=============
ForecasterRnn
=============
Regressor: <Functional name=functional_3, built=True>
Lags: [ 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 26 27 28 29 30 31 32]
Transformer for series: MinMaxScaler()
Window size: 32
Target series, levels: ['pm2.5', 'co', 'no', 'o3']
Multivariate series (names): None
Maximum steps predicted: [1 2 3 4 5]
Training range: None
Training index type: None
Training index frequency: None
Model parameters: {'name': 'functional_3', 'trainable': True, 'layers': [{'module': 'keras.layers', 'class_name': 'InputLayer', 'config': {'batch_shape': (None, 32, 10), 'dtype': 'float32', 'sparse': False, 'name': 'input_layer_3'}, 'registered_name': None, 'name': 'input_layer_3', 'inbound_nodes': []}, {'module': 'keras.layers', 'class_name': 'LSTM', 'config': {'name': 'lstm_4', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'return_sequences': True, 'return_state': False, 'go_backwards': False, 'stateful': False, 'unroll': False, 'zero_output_for_mask': False, 'units': 100, 'activation': 'relu', 'recurrent_activation': 'sigmoid', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'recurrent_initializer': {'module': 'keras.initializers', 'class_name': 'OrthogonalInitializer', 'config': {'gain': 1.0, 'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'unit_forget_bias': True, 'kernel_regularizer': None, 'recurrent_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'recurrent_constraint': None, 'bias_constraint': None, 'dropout': 0.0, 'recurrent_dropout': 0.0, 'seed': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 32, 10)}, 'name': 'lstm_4', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 32, 10), 'dtype': 'float32', 'keras_history': ['input_layer_3', 0, 0]}},), 'kwargs': {'training': False, 'mask': None}}]}, {'module': 'keras.layers', 'class_name': 'LSTM', 'config': {'name': 'lstm_5', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'return_sequences': False, 'return_state': False, 'go_backwards': False, 'stateful': False, 'unroll': False, 'zero_output_for_mask': False, 'units': 50, 'activation': 'relu', 'recurrent_activation': 'sigmoid', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'recurrent_initializer': {'module': 'keras.initializers', 'class_name': 'OrthogonalInitializer', 'config': {'gain': 1.0, 'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'unit_forget_bias': True, 'kernel_regularizer': None, 'recurrent_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'recurrent_constraint': None, 'bias_constraint': None, 'dropout': 0.0, 'recurrent_dropout': 0.0, 'seed': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 32, 100)}, 'name': 'lstm_5', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 32, 100), 'dtype': 'float32', 'keras_history': ['lstm_4', 0, 0]}},), 'kwargs': {'training': False, 'mask': None}}]}, {'module': 'keras.layers', 'class_name': 'Dense', 'config': {'name': 'dense_7', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'units': 64, 'activation': 'relu', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'kernel_regularizer': None, 'bias_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 50)}, 'name': 'dense_7', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 50), 'dtype': 'float32', 'keras_history': ['lstm_5', 0, 0]}},), 'kwargs': {}}]}, {'module': 'keras.layers', 'class_name': 'Dense', 'config': {'name': 'dense_8', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'units': 32, 'activation': 'relu', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'kernel_regularizer': None, 'bias_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 64)}, 'name': 'dense_8', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 64), 'dtype': 'float32', 'keras_history': ['dense_7', 0, 0]}},), 'kwargs': {}}]}, {'module': 'keras.layers', 'class_name': 'Dense', 'config': {'name': 'dense_9', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'units': 20, 'activation': 'linear', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'kernel_regularizer': None, 'bias_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 32)}, 'name': 'dense_9', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 32), 'dtype': 'float32', 'keras_history': ['dense_8', 0, 0]}},), 'kwargs': {}}]}, {'module': 'keras.layers', 'class_name': 'Reshape', 'config': {'name': 'reshape_3', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'target_shape': (5, 4)}, 'registered_name': None, 'build_config': {'input_shape': (None, 20)}, 'name': 'reshape_3', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 20), 'dtype': 'float32', 'keras_history': ['dense_9', 0, 0]}},), 'kwargs': {}}]}], 'input_layers': [['input_layer_3', 0, 0]], 'output_layers': [['reshape_3', 0, 0]]}
Compile parameters: {'optimizer': {'module': 'keras.src.backend.torch.optimizers.torch_adam', 'class_name': 'Adam', 'config': {'name': 'adam', 'learning_rate': 0.009999999776482582, 'weight_decay': None, 'clipnorm': None, 'global_clipnorm': None, 'clipvalue': None, 'use_ema': False, 'ema_momentum': 0.99, 'ema_overwrite_frequency': None, 'loss_scale_factor': None, 'gradient_accumulation_steps': None, 'beta_1': 0.9, 'beta_2': 0.999, 'epsilon': 1e-07, 'amsgrad': False}, 'registered_name': 'Adam'}, 'loss': {'module': 'keras.losses', 'class_name': 'MeanSquaredError', 'config': {'name': 'mean_squared_error', 'reduction': 'sum_over_batch_size'}, 'registered_name': None}, 'loss_weights': None, 'metrics': None, 'weighted_metrics': None, 'run_eagerly': False, 'steps_per_execution': 1, 'jit_compile': False}
fit_kwargs: {'epochs': 10, 'batch_size': 128, 'callbacks': [<keras.src.callbacks.early_stopping.EarlyStopping object at 0x000002B51CA05910>]}
Creation date: 2024-07-30 13:16:58
Last fit date: None
Skforecast version: 0.13.0
Python version: 3.11.5
Forecaster id: None
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# Fit forecaster
# ==============================================================================
forecaster.fit(data_train)
# Fit forecaster
# ==============================================================================
forecaster.fit(data_train)
Epoch 1/10 154/154 ━━━━━━━━━━━━━━━━━━━━ 25s 160ms/step - loss: 0.0138 - val_loss: 0.0100 Epoch 2/10 154/154 ━━━━━━━━━━━━━━━━━━━━ 25s 166ms/step - loss: 0.0050 - val_loss: 0.0094 Epoch 3/10 154/154 ━━━━━━━━━━━━━━━━━━━━ 27s 175ms/step - loss: 0.0043 - val_loss: 0.0084 Epoch 4/10 154/154 ━━━━━━━━━━━━━━━━━━━━ 26s 172ms/step - loss: 0.0038 - val_loss: 0.0076 Epoch 5/10 154/154 ━━━━━━━━━━━━━━━━━━━━ 27s 174ms/step - loss: 0.0036 - val_loss: 0.0073 Epoch 6/10 154/154 ━━━━━━━━━━━━━━━━━━━━ 23s 149ms/step - loss: 0.0035 - val_loss: 0.0072 Epoch 7/10 154/154 ━━━━━━━━━━━━━━━━━━━━ 25s 163ms/step - loss: 0.0034 - val_loss: 0.0076 Epoch 8/10 154/154 ━━━━━━━━━━━━━━━━━━━━ 25s 163ms/step - loss: 0.0034 - val_loss: 0.0069 Epoch 9/10 154/154 ━━━━━━━━━━━━━━━━━━━━ 24s 158ms/step - loss: 0.0033 - val_loss: 0.0069 Epoch 10/10 154/154 ━━━━━━━━━━━━━━━━━━━━ 27s 175ms/step - loss: 0.0032 - val_loss: 0.0073
The prediction can also be made for specific steps, as long as they are within the prediction horizon defined in the model.
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# Specific step predictions
# ==============================================================================
forecaster.predict(steps=[1, 5], levels="o3")
# Specific step predictions
# ==============================================================================
forecaster.predict(steps=[1, 5], levels="o3")
Out[39]:
| o3 | |
|---|---|
| 2021-04-01 00:00:00 | 36.963165 |
| 2021-04-01 04:00:00 | 24.514666 |
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# Prediction
# ==============================================================================
predictions = forecaster.predict()
predictions
# Prediction
# ==============================================================================
predictions = forecaster.predict()
predictions
Out[40]:
| pm2.5 | co | no | o3 | |
|---|---|---|---|---|
| 2021-04-01 00:00:00 | 14.250182 | 0.114879 | 1.290489 | 36.963165 |
| 2021-04-01 01:00:00 | 14.238721 | 0.102153 | 1.658386 | 34.069336 |
| 2021-04-01 02:00:00 | 14.098439 | 0.116550 | 0.644113 | 30.392138 |
| 2021-04-01 03:00:00 | 13.381383 | 0.113979 | 1.317875 | 25.742840 |
| 2021-04-01 04:00:00 | 13.152705 | 0.117441 | 1.632742 | 24.514666 |
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# Backtesting with test data
# ==============================================================================
metrics, predictions = backtesting_forecaster_multiseries(
forecaster=forecaster,
steps=forecaster.max_step,
series=data,
levels=forecaster.levels,
initial_train_size=len(data.loc[:end_validation, :]),
metric="mean_absolute_error",
verbose=False,
refit=False,
)
# Backtesting with test data
# ==============================================================================
metrics, predictions = backtesting_forecaster_multiseries(
forecaster=forecaster,
steps=forecaster.max_step,
series=data,
levels=forecaster.levels,
initial_train_size=len(data.loc[:end_validation, :]),
metric="mean_absolute_error",
verbose=False,
refit=False,
)
Epoch 1/10 188/188 ━━━━━━━━━━━━━━━━━━━━ 30s 161ms/step - loss: 0.0030 - val_loss: 0.0066 Epoch 2/10 188/188 ━━━━━━━━━━━━━━━━━━━━ 31s 167ms/step - loss: 0.0030 - val_loss: 0.0067 Epoch 3/10 188/188 ━━━━━━━━━━━━━━━━━━━━ 29s 153ms/step - loss: 0.0030 - val_loss: 0.0067 Epoch 4/10 188/188 ━━━━━━━━━━━━━━━━━━━━ 34s 181ms/step - loss: 0.0029 - val_loss: 0.0067
0%| | 0/442 [00:00<?, ?it/s]
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# Backtesting metrics
# ==============================================================================
metrics
# Backtesting metrics
# ==============================================================================
metrics
Out[42]:
| levels | mean_absolute_error | |
|---|---|---|
| 0 | pm2.5 | 3.521863 |
| 1 | co | 0.025072 |
| 2 | no | 2.873905 |
| 3 | o3 | 11.518277 |
| 4 | average | 4.484779 |
| 5 | weighted_average | 4.484779 |
| 6 | pooling | 4.484779 |
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# Plot all the predicted variables as rows in the plot
# ==============================================================================
fig, ax = plt.subplots(len(levels), 1, figsize=(8, 3*len(levels)), sharex=True)
for i, level in enumerate(levels):
data_test[level].plot(ax=ax[i], label="test")
predictions[level].plot(ax=ax[i], label="predictions")
ax[i].set_title(level)
ax[i].legend()
# Plot all the predicted variables as rows in the plot
# ==============================================================================
fig, ax = plt.subplots(len(levels), 1, figsize=(8, 3*len(levels)), sharex=True)
for i, level in enumerate(levels):
data_test[level].plot(ax=ax[i], label="test")
predictions[level].plot(ax=ax[i], label="predictions")
ax[i].set_title(level)
ax[i].legend()
Create and compile Tensorflow models¶
To improve the user experience and speed up the prototyping, development, and production process, skforecast has the create_and_compile_model function, with which, by indicating just a few arguments, the architecture is inferred and the model is created.
series: Time series to be used to train the modellevels: Time series to be predicted.lags: Number of time steps to be used to predict the next value.steps: Number of time steps to be predicted.recurrent_layer: Type of recurrent layer to use. By default, an LSTM layer is used.recurrent_units: Number of units in the recurrent layer. By default, 100 is used. If a list is passed, a recurrent layer will be created for each element in the list.dense_units: Number of units in the dense layer. By default, 64 is used. If a list is passed, a dense layer will be created for each element in the list.optimizer: Optimizer to use. By default, Adam with a learning rate of 0.01 is used.loss: Loss function to use. By default, Mean Squared Error is used.
✎ Note
The following examples use recurrent_layer="LSTM" but it is also possible to use "RNN" layers.
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# Create model
# ==============================================================================
series = ["o3"] # Series used as predictors
levels = ["o3"] # Target series to predict
lags = 32 # Past time steps to be used to predict the target
steps = 1 # Future time steps to be predicted
data = air_quality[series].copy()
data_train = air_quality_train[series].copy()
data_val = air_quality_val[series].copy()
data_test = air_quality_test[series].copy()
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=4,
dense_units=16,
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
model.summary()
# Create model
# ==============================================================================
series = ["o3"] # Series used as predictors
levels = ["o3"] # Target series to predict
lags = 32 # Past time steps to be used to predict the target
steps = 1 # Future time steps to be predicted
data = air_quality[series].copy()
data_train = air_quality_train[series].copy()
data_val = air_quality_val[series].copy()
data_test = air_quality_test[series].copy()
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=4,
dense_units=16,
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
model.summary()
keras version: 3.4.1 Using backend: torch torch version: 2.2.2+cpu
Model: "functional_4"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ input_layer_4 (InputLayer) │ (None, 32, 1) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ lstm_6 (LSTM) │ (None, 4) │ 96 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_10 (Dense) │ (None, 16) │ 80 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_11 (Dense) │ (None, 1) │ 17 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ reshape_4 (Reshape) │ (None, 1, 1) │ 0 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 193 (772.00 B)
Trainable params: 193 (772.00 B)
Non-trainable params: 0 (0.00 B)
In this case, a simple LSTM network is used, with a single recurrent layer with 4 neurons and a hidden dense layer with 16 neurons. The following table shows a detailed description of each layer:
| Layer | Type | Output Shape | Parameters | Description |
|---|---|---|---|---|
| Input Layer (InputLayer) | InputLayer |
(None, 32, 1) |
0 | This is the input layer of the model. It receives sequences of length 32, corresponding to the number of lags with a dimension at each time step. |
| LSTM Layer (Long Short-Term Memory) | LSTM |
(None, 4) |
96 | The LSTM layer is a long and short-term memory layer that processes the input sequence. It has 4 LSTM units and connects to the next layer. |
| First Dense Layer (Dense) | Dense |
(None, 16) |
80 | This is a fully connected layer with 16 units and uses a default activation function (relu) in the provided architecture. |
| Second Dense Layer (Dense) | Dense |
(None, 1) |
17 | Another fully connected dense layer, this time with a single output unit. It also uses a default activation function. |
| Reshape Layer (Reshape) | Reshape |
(None, 1, 1) |
0 | This layer reshapes the output of the previous dense layer to have a specific shape (None, 1, 1). This layer is not strictly necessary, but is included to make the module generalizable to other multi-output forecasting problems. The dimension of this output layer is (None, steps_to_predict_future, series_to_predict). In this case, steps=1 and levels="o3", so the dimension is (None, 1, 1) |
| Total Parameters and Trainable | - | - | 193 | Total Parameters: 193, Trainable Parameters: 193, Non-Trainable Parameters: 0 |
More complex models can be created including:
- Multiple series to be modeled (levels)
- Multiple series to be used as predictors (series)
- Multiple steps to be predicted (steps)
- Multiple lags to be used as predictors (lags)
- Multiple recurrent layers (recurrent_units)
- Multiple dense layers (dense_units)
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# Model creation
# ==============================================================================
# Now, we have multiple series and multiple targets
series = ['pm2.5', 'co', 'no', 'no2', 'pm10', 'nox', 'o3', 'veloc.', 'direc.','so2']
levels = ['pm2.5', 'co', 'no', "o3"] # Features to predict. It can be all the series or less
lags = 32
steps = 5
data = air_quality[series].copy()
data_train = air_quality_train[series].copy()
data_val = air_quality_val[series].copy()
data_test = air_quality_test[series].copy()
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=[100, 50],
dense_units=[64, 32],
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
model.summary()
# Model creation
# ==============================================================================
# Now, we have multiple series and multiple targets
series = ['pm2.5', 'co', 'no', 'no2', 'pm10', 'nox', 'o3', 'veloc.', 'direc.','so2']
levels = ['pm2.5', 'co', 'no', "o3"] # Features to predict. It can be all the series or less
lags = 32
steps = 5
data = air_quality[series].copy()
data_train = air_quality_train[series].copy()
data_val = air_quality_val[series].copy()
data_test = air_quality_test[series].copy()
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=[100, 50],
dense_units=[64, 32],
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
model.summary()
keras version: 3.4.1 Using backend: torch torch version: 2.2.2+cpu
Model: "functional_5"
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓ ┃ Layer (type) ┃ Output Shape ┃ Param # ┃ ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩ │ input_layer_5 (InputLayer) │ (None, 32, 10) │ 0 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ lstm_7 (LSTM) │ (None, 32, 100) │ 44,400 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ lstm_8 (LSTM) │ (None, 50) │ 30,200 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_12 (Dense) │ (None, 64) │ 3,264 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_13 (Dense) │ (None, 32) │ 2,080 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ dense_14 (Dense) │ (None, 20) │ 660 │ ├─────────────────────────────────┼────────────────────────┼───────────────┤ │ reshape_5 (Reshape) │ (None, 5, 4) │ 0 │ └─────────────────────────────────┴────────────────────────┴───────────────┘
Total params: 80,604 (314.86 KB)
Trainable params: 80,604 (314.86 KB)
Non-trainable params: 0 (0.00 B)
Get training and test matrices¶
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# Model creation
# ==============================================================================
series = ['pm2.5', 'co', 'no', 'no2', 'pm10', 'nox', 'o3', 'veloc.', 'direc.','so2']
levels = ['pm2.5', 'co', 'no', "o3"] # Features to predict. It can be all the series or less
lags = 10
steps = 5
data = air_quality[series].copy()
data_train = air_quality_train[series].copy()
data_val = air_quality_val[series].copy()
data_test = air_quality_test[series].copy()
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=[100, 50],
dense_units=[64, 32],
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
forecaster = ForecasterRnn(
regressor=model,
levels=levels,
steps=steps,
lags=lags,
)
forecaster
# Model creation
# ==============================================================================
series = ['pm2.5', 'co', 'no', 'no2', 'pm10', 'nox', 'o3', 'veloc.', 'direc.','so2']
levels = ['pm2.5', 'co', 'no', "o3"] # Features to predict. It can be all the series or less
lags = 10
steps = 5
data = air_quality[series].copy()
data_train = air_quality_train[series].copy()
data_val = air_quality_val[series].copy()
data_test = air_quality_test[series].copy()
model = create_and_compile_model(
series=data_train,
levels=levels,
lags=lags,
steps=steps,
recurrent_layer="LSTM",
recurrent_units=[100, 50],
dense_units=[64, 32],
optimizer=Adam(learning_rate=0.01),
loss=MeanSquaredError()
)
forecaster = ForecasterRnn(
regressor=model,
levels=levels,
steps=steps,
lags=lags,
)
forecaster
keras version: 3.4.1 Using backend: torch torch version: 2.2.2+cpu
Out[46]:
=============
ForecasterRnn
=============
Regressor: <Functional name=functional_6, built=True>
Lags: [ 1 2 3 4 5 6 7 8 9 10]
Transformer for series: MinMaxScaler()
Window size: 10
Target series, levels: ['pm2.5', 'co', 'no', 'o3']
Multivariate series (names): None
Maximum steps predicted: [1 2 3 4 5]
Training range: None
Training index type: None
Training index frequency: None
Model parameters: {'name': 'functional_6', 'trainable': True, 'layers': [{'module': 'keras.layers', 'class_name': 'InputLayer', 'config': {'batch_shape': (None, 10, 10), 'dtype': 'float32', 'sparse': False, 'name': 'input_layer_6'}, 'registered_name': None, 'name': 'input_layer_6', 'inbound_nodes': []}, {'module': 'keras.layers', 'class_name': 'LSTM', 'config': {'name': 'lstm_9', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'return_sequences': True, 'return_state': False, 'go_backwards': False, 'stateful': False, 'unroll': False, 'zero_output_for_mask': False, 'units': 100, 'activation': 'relu', 'recurrent_activation': 'sigmoid', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'recurrent_initializer': {'module': 'keras.initializers', 'class_name': 'OrthogonalInitializer', 'config': {'gain': 1.0, 'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'unit_forget_bias': True, 'kernel_regularizer': None, 'recurrent_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'recurrent_constraint': None, 'bias_constraint': None, 'dropout': 0.0, 'recurrent_dropout': 0.0, 'seed': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 10, 10)}, 'name': 'lstm_9', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 10, 10), 'dtype': 'float32', 'keras_history': ['input_layer_6', 0, 0]}},), 'kwargs': {'training': False, 'mask': None}}]}, {'module': 'keras.layers', 'class_name': 'LSTM', 'config': {'name': 'lstm_10', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'return_sequences': False, 'return_state': False, 'go_backwards': False, 'stateful': False, 'unroll': False, 'zero_output_for_mask': False, 'units': 50, 'activation': 'relu', 'recurrent_activation': 'sigmoid', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'recurrent_initializer': {'module': 'keras.initializers', 'class_name': 'OrthogonalInitializer', 'config': {'gain': 1.0, 'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'unit_forget_bias': True, 'kernel_regularizer': None, 'recurrent_regularizer': None, 'bias_regularizer': None, 'activity_regularizer': None, 'kernel_constraint': None, 'recurrent_constraint': None, 'bias_constraint': None, 'dropout': 0.0, 'recurrent_dropout': 0.0, 'seed': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 10, 100)}, 'name': 'lstm_10', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 10, 100), 'dtype': 'float32', 'keras_history': ['lstm_9', 0, 0]}},), 'kwargs': {'training': False, 'mask': None}}]}, {'module': 'keras.layers', 'class_name': 'Dense', 'config': {'name': 'dense_15', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'units': 64, 'activation': 'relu', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'kernel_regularizer': None, 'bias_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 50)}, 'name': 'dense_15', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 50), 'dtype': 'float32', 'keras_history': ['lstm_10', 0, 0]}},), 'kwargs': {}}]}, {'module': 'keras.layers', 'class_name': 'Dense', 'config': {'name': 'dense_16', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'units': 32, 'activation': 'relu', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'kernel_regularizer': None, 'bias_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 64)}, 'name': 'dense_16', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 64), 'dtype': 'float32', 'keras_history': ['dense_15', 0, 0]}},), 'kwargs': {}}]}, {'module': 'keras.layers', 'class_name': 'Dense', 'config': {'name': 'dense_17', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'units': 20, 'activation': 'linear', 'use_bias': True, 'kernel_initializer': {'module': 'keras.initializers', 'class_name': 'GlorotUniform', 'config': {'seed': None}, 'registered_name': None}, 'bias_initializer': {'module': 'keras.initializers', 'class_name': 'Zeros', 'config': {}, 'registered_name': None}, 'kernel_regularizer': None, 'bias_regularizer': None, 'kernel_constraint': None, 'bias_constraint': None}, 'registered_name': None, 'build_config': {'input_shape': (None, 32)}, 'name': 'dense_17', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 32), 'dtype': 'float32', 'keras_history': ['dense_16', 0, 0]}},), 'kwargs': {}}]}, {'module': 'keras.layers', 'class_name': 'Reshape', 'config': {'name': 'reshape_6', 'trainable': True, 'dtype': {'module': 'keras', 'class_name': 'DTypePolicy', 'config': {'name': 'float32'}, 'registered_name': None}, 'target_shape': (5, 4)}, 'registered_name': None, 'build_config': {'input_shape': (None, 20)}, 'name': 'reshape_6', 'inbound_nodes': [{'args': ({'class_name': '__keras_tensor__', 'config': {'shape': (None, 20), 'dtype': 'float32', 'keras_history': ['dense_17', 0, 0]}},), 'kwargs': {}}]}], 'input_layers': [['input_layer_6', 0, 0]], 'output_layers': [['reshape_6', 0, 0]]}
Compile parameters: {'optimizer': {'module': 'keras.src.backend.torch.optimizers.torch_adam', 'class_name': 'Adam', 'config': {'name': 'adam', 'learning_rate': 0.009999999776482582, 'weight_decay': None, 'clipnorm': None, 'global_clipnorm': None, 'clipvalue': None, 'use_ema': False, 'ema_momentum': 0.99, 'ema_overwrite_frequency': None, 'loss_scale_factor': None, 'gradient_accumulation_steps': None, 'beta_1': 0.9, 'beta_2': 0.999, 'epsilon': 1e-07, 'amsgrad': False}, 'registered_name': 'Adam'}, 'loss': {'module': 'keras.losses', 'class_name': 'MeanSquaredError', 'config': {'name': 'mean_squared_error', 'reduction': 'sum_over_batch_size'}, 'registered_name': None}, 'loss_weights': None, 'metrics': None, 'weighted_metrics': None, 'run_eagerly': False, 'steps_per_execution': 1, 'jit_compile': False}
fit_kwargs: {}
Creation date: 2024-07-30 13:24:02
Last fit date: None
Skforecast version: 0.13.0
Python version: 3.11.5
Forecaster id: None
In [47]:
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forecaster.create_train_X_y(data_train)[2]["X_train"][2]
forecaster.create_train_X_y(data_train)[2]["X_train"][2]
Out[47]:
['pm2.5', 'co', 'no', 'no2', 'pm10', 'nox', 'o3', 'veloc.', 'direc.', 'so2']
The RNN Forecaster can also be used to generate the X_train and y_train matrices that will be used to train the model. The create_train_X_y method allows the user to obtain the training and test matrices that will be used to train the model. The method return 3 elements: X_train, y_train, and dimension_information. The X_train matrix has dimensions (n_samples, n_lags, n_series), while the y_train matrix has dimensions (n_samples, n_steps, n_levels).
In [48]:
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X_train, y_train, dimension_info = forecaster.create_train_X_y(data_train)
X_train, y_train, dimension_info = forecaster.create_train_X_y(data_train)
In [49]:
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X_train.shape, y_train.shape
X_train.shape, y_train.shape
Out[49]:
((19690, 10, 10), (19690, 5, 4))
The dimension_information dictionary contains the information of each dimension value for both X_train and y_train.
In [50]:
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dimension_info["X_train"][0][:10]
dimension_info["X_train"][0][:10]
Out[50]:
[Timestamp('2019-01-01 10:00:00'),
Timestamp('2019-01-01 11:00:00'),
Timestamp('2019-01-01 12:00:00'),
Timestamp('2019-01-01 13:00:00'),
Timestamp('2019-01-01 14:00:00'),
Timestamp('2019-01-01 15:00:00'),
Timestamp('2019-01-01 16:00:00'),
Timestamp('2019-01-01 17:00:00'),
Timestamp('2019-01-01 18:00:00'),
Timestamp('2019-01-01 19:00:00')]
In [51]:
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dimension_info["X_train"][1]
dimension_info["X_train"][1]
Out[51]:
['lag_1', 'lag_2', 'lag_3', 'lag_4', 'lag_5', 'lag_6', 'lag_7', 'lag_8', 'lag_9', 'lag_10']
In [52]:
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dimension_info["X_train"][2]
dimension_info["X_train"][2]
Out[52]:
['pm2.5', 'co', 'no', 'no2', 'pm10', 'nox', 'o3', 'veloc.', 'direc.', 'so2']
In [53]:
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dimension_info["y_train"][0][:10]
dimension_info["y_train"][0][:10]
Out[53]:
[Timestamp('2019-01-01 10:00:00'),
Timestamp('2019-01-01 11:00:00'),
Timestamp('2019-01-01 12:00:00'),
Timestamp('2019-01-01 13:00:00'),
Timestamp('2019-01-01 14:00:00'),
Timestamp('2019-01-01 15:00:00'),
Timestamp('2019-01-01 16:00:00'),
Timestamp('2019-01-01 17:00:00'),
Timestamp('2019-01-01 18:00:00'),
Timestamp('2019-01-01 19:00:00')]
In [54]:
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dimension_info["y_train"][1]
dimension_info["y_train"][1]
Out[54]:
['step_1', 'step_2', 'step_3', 'step_4', 'step_5']
In [55]:
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dimension_info["y_train"][2]
dimension_info["y_train"][2]
Out[55]:
['pm2.5', 'co', 'no', 'o3']