View source for Prophet (Facebooks time series forecasting procedure)

# Prophet: Facebook's Time Series Forecasting Procedure

== Introduction ==

Prophet is an open-source procedure for forecasting time series data based on an additive model where non-linear trends are fit with a piecewise linear or logistic growth curve. Developed by Facebook (now Meta) and released in 2017, it is designed to be usable by analysts who may not be deeply familiar with advanced time series modeling techniques.  Prophet is particularly well-suited for business time series with strong seasonality and trend changes. Unlike many statistical forecasting methods, Prophet is robust to missing data and shifts in the trend, and typically handles outliers well. This article provides a comprehensive introduction to Prophet, covering its core components, underlying principles, usage, strengths, and limitations. It's geared towards beginners with a basic understanding of time series data.

== Core Components of Prophet ==

Prophet decomposes a time series into several components:

* '''Trend:''' Represents the long-term direction of the data.  Prophet uses a piecewise linear or logistic growth model to capture this trend.  The model allows for changes in trend direction (called "changepoints") that are automatically detected. Understanding [[trend analysis]] is crucial for interpreting Prophet's output.
* '''Seasonality:''' Captures periodic fluctuations in the data. Prophet supports both annual, weekly, and daily seasonality, and can also model multiple seasonality periods simultaneously.  The seasonality is modeled using Fourier series, which are efficient for representing periodic patterns. [[Seasonal patterns]] are often a key driver of time series behavior.
* '''Holidays:''' Accounts for the impact of specific dates, such as holidays or promotional events. Users can provide a list of dates and Prophet will model their effect on the time series. Correctly identifying and incorporating [[market holidays]] is important for accurate forecasts.
* '''Regression:''' Allows for the inclusion of additional predictor variables (regressors) that are not time-dependent. These can be used to model the impact of external factors on the time series.  Using [[leading indicators]] as regressors can improve forecast accuracy.
* '''Error:''' Represents the unexplained variation in the data. Prophet assumes that the error term is normally distributed.  Analyzing the [[residual analysis]] can help assess the model's fit and identify potential issues.

== The Additive Model ==

Prophet's core model is an additive regression model:

'''y(t) = trend(t) + seasonality(t) + holidays(t) + regressors(t) + error(t)'''

Where:

*  '''y(t)''' is the time series value at time '''t'''.
*  '''trend(t)''' is the trend component at time '''t'''.
*  '''seasonality(t)''' is the seasonal component at time '''t'''.
*  '''holidays(t)''' is the holiday effect at time '''t'''.
*  '''regressors(t)''' is the effect of regressors at time '''t'''.
*  '''error(t)''' is the error term at time '''t'''.

This additive structure means that the components are combined by simply adding their values together. This is a key feature of Prophet, as it makes the model relatively easy to interpret and understand.  It differs from multiplicative models, which are useful when the magnitude of the seasonality changes with the level of the time series.  Understanding the difference between [[additive vs. multiplicative models]] is vital for selecting the appropriate approach.

== Trend Modeling in Detail ==

Prophet's trend modeling is a crucial element of its functionality. It offers two main trend options:

* '''Linear Trend:'''  A simple linear regression is used to capture a constant upward or downward trend. This is suitable for time series with a consistent trend over the entire period.
* '''Logistic Trend:''' This model is used when the trend has a saturation point – i.e., it grows quickly initially but then plateaus. This is common in situations like product adoption or market share.  The logistic growth curve is defined by three parameters:  the carrying capacity (maximum value), the growth rate, and the midpoint (time at which the growth rate is maximum).

Prophet automatically detects "changepoints" in the trend, which are points where the trend changes direction or slope. These changepoints are identified using a Bayesian approach, and the number of changepoints can be controlled by the user.  The ability to detect and model [[trend reversals]] is a significant advantage of Prophet.

== Seasonality Modeling in Detail ==

Prophet models seasonality using Fourier series. A Fourier series represents a periodic function as a sum of sine and cosine waves with different frequencies.  The number of terms in the Fourier series (the "order") determines the complexity of the seasonality pattern that can be captured.  Higher order Fourier series can represent more complex seasonal patterns but can also lead to overfitting.

Prophet supports multiple seasonality periods, allowing you to model both annual and weekly seasonality simultaneously, for example.  It automatically estimates the optimal order of the Fourier series for each seasonality period.  Understanding [[Fourier analysis]] can provide deeper insights into Prophet's seasonality modeling.

== Holiday Effects ==

Prophet allows you to specify a list of dates that represent holidays or special events. For each holiday, you can specify a prior scale, which determines the strength of the holiday effect.  Prophet estimates the effect of each holiday on the time series data. This is particularly useful for time series that are affected by specific events, such as retail sales during the holiday season.  Identifying relevant [[economic calendar events]] is vital for accurate forecasting.

== Regression Modeling ==

Prophet allows you to include additional predictor variables (regressors) in the model. These regressors can be any variables that are correlated with the time series data. They can be used to model the impact of external factors, such as marketing spend, price changes, or economic indicators. The regressors are included in the model as linear terms.  The use of [[fundamental analysis]] can help identify relevant regressors.

== Using Prophet: A Step-by-Step Guide ==

1. '''Installation:''' Prophet is a Python package and can be installed using pip: `pip install prophet`. You'll also need pandas for data manipulation.
2. '''Data Preparation:''' Prophet requires the input data to be in a specific format: a DataFrame with two columns: 'ds' (datetime) and 'y' (the time series value).
3. '''Model Initialization:''' Create a Prophet object: `m = Prophet()`.  You can customize the model by specifying parameters such as the growth rate, seasonality mode, and holiday list.
4. '''Model Fitting:''' Fit the model to the data: `m.fit(df)`.
5. '''Making Predictions:''' Create a future DataFrame with the dates for which you want to make predictions: `future = m.make_future_dataframe(periods=365)`.
6. '''Generating Forecasts:''' Generate the forecasts: `forecast = m.predict(future)`.
7. '''Visualizing Results:''' Prophet provides functions for visualizing the forecasts, including the trend, seasonality, and holiday components. `m.plot(forecast)` and `m.plot_components(forecast)`.

== Strengths of Prophet ==

* '''Ease of Use:'''  Prophet is designed to be easy to use, even for users without extensive time series modeling experience.
* '''Robustness to Missing Data and Outliers:'''  Prophet handles missing data and outliers relatively well.
* '''Automatic Changepoint Detection:'''  Prophet automatically detects changes in the trend, which can be useful for forecasting time series with non-stationary trends.
* '''Interpretability:'''  The additive model structure makes Prophet's forecasts relatively easy to interpret and understand.
* '''Handles Seasonality Effectively:'''  Prophet's Fourier series-based seasonality modeling is effective for capturing complex seasonal patterns.
* '''Holiday Effect Modeling:'''  The ability to model holiday effects is a significant advantage for business time series.
* '''Open Source:'''  Prophet is open-source, which means that it is free to use and modify.

== Limitations of Prophet ==

* '''Assumes Additive Model:'''  The additive model structure may not be appropriate for all time series. Multiplicative models might be better suited for data where the magnitude of the seasonality changes with the level of the time series.
* '''Limited Support for Complex Dependencies:'''  Prophet does not explicitly model complex dependencies between time series.  For multivariate time series forecasting, other methods like [[VAR models]] or [[state space models]] may be more appropriate.
* '''Parameter Tuning:'''  While Prophet has default parameters that often work well, careful parameter tuning can improve forecast accuracy.
* '''Not Ideal for Short Time Series:'''  Prophet requires a sufficient amount of historical data to accurately estimate the trend and seasonality components.  For very short time series, other methods may be more appropriate.
* '''Sensitivity to Initial Values:''' The optimization process can be sensitive to initial values, potentially leading to suboptimal results.
* '''Difficulty Modeling Complex Regressions:''' While regressors can be added, modeling highly complex relationships between regressors and the time series may require more sophisticated techniques. Understanding [[regression analysis]] is crucial for effective use of regressors.

== Prophet vs. Other Time Series Forecasting Methods ==

Compared to other time series forecasting methods, Prophet offers a unique set of strengths and weaknesses.

* '''ARIMA:'''  ARIMA models require more expertise in time series modeling and are often more difficult to tune. Prophet is generally easier to use and more robust to missing data.  Understanding [[ARIMA modeling]] provides a good comparative perspective.
* '''Exponential Smoothing:'''  Exponential smoothing methods are simpler than Prophet but may not be as effective for time series with complex seasonality or trend changes.
* '''State Space Models:'''  State space models are more flexible than Prophet but are also more complex and require more expertise.
* '''Machine Learning Models (e.g., Random Forest, Gradient Boosting):''' Machine learning models can capture complex relationships but often require more data and are less interpretable than Prophet. Understanding [[machine learning for time series]] is important for evaluating alternatives.
* '''Neural Networks (e.g., LSTM):'''  Neural networks, particularly LSTMs, are powerful but require significant data and computational resources. They are often used for very complex time series forecasting tasks where interpretability is less important.  Learning about [[deep learning for time series]] can offer alternative approaches.

== Advanced Techniques and Considerations ==

* '''Cross-Validation:''' Use time series cross-validation to evaluate the model's performance and tune its parameters.
* '''Hyperparameter Optimization:''' Experiment with different parameter settings to find the optimal configuration for your data.
* '''Ensemble Methods:''' Combine Prophet with other forecasting methods to improve forecast accuracy.
* '''Feature Engineering:''' Create new regressors based on domain knowledge or data analysis.
* '''Data Scaling:''' Consider scaling the data before fitting the model, especially if you are using regressors with different scales.
* '''Monitoring Forecast Accuracy:''' Regularly monitor the model's performance and retrain it as needed.  Tracking [[forecast error metrics]] is essential for performance evaluation.

== Resources ==

* '''Prophet Documentation:''' [https://prophet.fb.com/docs/](https://prophet.fb.com/docs/)
* '''Prophet GitHub Repository:''' [https://github.com/facebook/prophet](https://github.com/facebook/prophet)
* '''Prophet Tutorial:''' [https://prophet.fb.com/docs/quick_start.html](https://prophet.fb.com/docs/quick_start.html)
* '''Time Series Analysis:''' [[Time Series Analysis]]
* '''Statistical Modeling:''' [[Statistical Modeling]]
* '''Data Preprocessing:''' [[Data Preprocessing]]
* '''Model Evaluation:''' [[Model Evaluation]]
* '''Forecasting Techniques:''' [[Forecasting Techniques]]
* '''Regression Analysis:''' [[Regression Analysis]]
* '''Trend Analysis:''' [[Trend Analysis]]
* '''Seasonal Patterns:''' [[Seasonal Patterns]]
* '''Market Holidays:''' [[Market Holidays]]
* '''Leading Indicators:''' [[Leading Indicators]]
* '''Residual Analysis:''' [[Residual Analysis]]
* '''Additive vs. Multiplicative Models:''' [[Additive vs. Multiplicative Models]]
* '''Fourier Analysis:''' [[Fourier Analysis]]
* '''Economic Calendar Events:''' [[Economic Calendar Events]]
* '''Fundamental Analysis:''' [[Fundamental Analysis]]
* '''VAR Models:''' [[VAR Models]]
* '''State Space Models:''' [[State Space Models]]
* '''ARIMA Modeling:''' [[ARIMA Modeling]]
* '''Machine Learning for Time Series:''' [[Machine Learning for Time Series]]
* '''Deep Learning for Time Series:''' [[Deep Learning for Time Series]]
* '''Forecast Error Metrics:''' [[Forecast Error Metrics]]

[[Category:Time Series Forecasting]]

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