# Time Series Forecasting with Prophet and LSTM Hybrid Mode

In this post, we will explore the combination of two powerful time series forecasting techniques: Prophet and LSTM (Long Short-Term Memory) models. By leveraging the strengths of both approaches, we can create a hybrid model that provides accurate and reliable predictions for time series data.

# Introduction to Time Series Forecasting

Time series forecasting is the process of predicting future values based on historical data. It is widely used in various domains, including finance, sales, weather forecasting, and more. Traditional statistical methods, such as ARIMA (AutoRegressive Integrated Moving Average), have been commonly used for time series forecasting. However, with the advancements in deep learning, models like LSTM have gained popularity due to their ability to capture complex patterns and dependencies in the data.

# Prophet: A Powerful Forecasting Tool

Prophet is an open-source forecasting library developed by Facebook's Core Data Science team. It is designed to handle time series data with multiple seasonality patterns, outliers, and missing values. Prophet incorporates a decomposable time series model with three main components: trend, seasonality, and holidays. It provides a simple and intuitive interface for time series forecasting, making it accessible to both beginners and experts.

# LSTM: Capturing Temporal Dependencies

LSTM is a type of recurrent neural network (RNN) that is specifically designed to capture long-term dependencies in sequential data. Unlike traditional feedforward neural networks, LSTM models have a memory cell that can store information over long periods. This memory cell allows LSTM models to learn and predict sequences with complex temporal dependencies, making them well-suited for time series forecasting tasks.

# Combining Prophet and LSTM: The Hybrid Model

The hybrid model combines the strengths of Prophet and LSTM to improve the accuracy and robustness of time series forecasting. The workflow involves using Prophet to generate initial predictions and then using these predictions as input to train an LSTM model. The LSTM model learns from the residuals (the differences between the actual values and the Prophet predictions) and generates refined forecasts.

The hybrid model can be summarized in the following steps:

- Use Prophet to fit a time series and generate initial predictions.
- Calculate the residuals by subtracting the Prophet predictions from the actual values.
- Train an LSTM model using the residuals as input.
- Generate refined forecasts by combining the Prophet predictions and the LSTM predictions.

By combining the strengths of both models, the hybrid model can capture both the global trends and the local patterns in the time series data, resulting in more accurate and reliable forecasts.

# Implementation and Example

To implement the hybrid model, we can use popular libraries such as Prophet and TensorFlow/Keras for LSTM. We can start by fitting a Prophet model to the time series data and generating initial predictions. Then, we calculate the residuals and use them to train an LSTM model. Finally, we combine the Prophet predictions and the LSTM predictions to obtain the final forecasts.

Here is a code snippet demonstrating the implementation of the hybrid model:

`# Import necessary libraries`

from fbprophet import Prophet

from tensorflow.keras.models import Sequential

from tensorflow.keras.layers import LSTM, Dense

# Fit Prophet model and generate initial predictions

prophet_model = Prophet()

prophet_model.fit(train_data)

prophet_predictions = prophet_model.predict(future_data)

# Calculate residuals

residuals = actual_values - prophet_predictions['yhat']

# Train LSTM model using residuals

lstm_model = Sequential()

lstm_model.add(LSTM(units=64, input_shape=(n_steps, 1)))

lstm_model.add(Dense(units=1))

lstm_model.compile(optimizer='adam', loss='mse')

lstm_model.fit(residuals, epochs=10, batch_size=32)

# Generate LSTM predictions

lstm_predictions = lstm_model.predict(residuals)

# Combine Prophet and LSTM predictions

final_predictions = prophet_predictions['yhat'] + lstm_predictions

# Evaluate the performance of the hybrid model

evaluate_performance(actual_values, final_predictions)

In this example, we fit a Prophet model to the training data and generate initial predictions using the `predict()`

function. We then calculate the residuals by subtracting the Prophet predictions from the actual values. Next, we train an LSTM model using the residuals as input. Finally, we combine the Prophet predictions and the LSTM predictions to obtain the final forecasts.

# Conclusion

In this post, we explored the combination of Prophet and LSTM models to create a hybrid model for time series forecasting. By leveraging the strengths of both approaches, we can capture both the global trends and the local patterns in the data, resulting in more accurate and reliable predictions. The hybrid model provides a powerful tool for forecasting time series data in various domains.

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