Facebook Prophet

Overview

Prophet is Facebook’s open-source time series forecasting library designed for business time series with strong seasonal effects, holidays, and missing data. It’s user-friendly and handles common time series challenges automatically.

Prophet Model

graph TB
    subgraph "Prophet Decomposition"
        Y[y(t)] --> T[Trend g(t)]
        Y --> S[Seasonality s(t)]
        Y --> H[Holiday Effects h(t)]
        Y --> E[Error ε(t)]
    end
    
    T --> F["y(t) = g(t) + s(t) + h(t) + ε(t)"]
    S --> F
    H --> F
    E --> F

Trend Models

1. Linear Trend

# Default: Linear trend with changepoints
from prophet import Prophet

model = Prophet(growth='linear')
model.fit(df)

2. Logistic Growth

# For data with saturation (carrying capacity)
df['cap'] = 10000  # Maximum value
df['floor'] = 0    # Minimum value

model = Prophet(growth='logistic')
model.fit(df)

graph LR
    subgraph "Growth Models"
        L[Linear: Unlimited growth]
        LG[Logistic: Saturates at capacity]
    end

Key Features

1. Seasonality

# Built-in seasonality
model = Prophet(
    yearly_seasonality=True,
    weekly_seasonality=True,
    daily_seasonality=False
)

# Custom seasonality
model.add_seasonality(
    name='monthly',
    period=30.5,
    fourier_order=5
)

2. Holidays

# Add holidays
holidays = pd.DataFrame({
    'holiday': 'black_friday',
    'ds': pd.to_datetime(['2023-11-24', '2024-11-29']),
    'lower_window': -1,
    'upper_window': 1,
})

model = Prophet(holidays=holidays)

3. Changepoints

# Automatic changepoint detection
model = Prophet(
    changepoint_prior_scale=0.05,  # Flexibility
    n_changepoints=25               # Number of changepoints
)

# Manual changepoints
model = Prophet(
    changepoints=['2023-03-15', '2023-06-01']
)

Usage Example

from prophet import Prophet
import pandas as pd

# Prepare data (must have 'ds' and 'y' columns)
df = pd.DataFrame({
    'ds': pd.date_range('2023-01-01', periods=365),
    'y': time_series_data
})

# Create and fit model
model = Prophet(
    yearly_seasonality=True,
    weekly_seasonality=True,
    changepoint_prior_scale=0.05
)

# Add regressors (external variables)
model.add_regressor('temperature')
model.add_regressor('is_holiday')

model.fit(df)

# Make future dataframe
future = model.make_future_dataframe(periods=30)
future['temperature'] = temperature_data
future['is_holiday'] = holiday_data

# Predict
forecast = model.predict(future)

# Plot
model.plot(forecast)
model.plot_components(forecast)

Prophet vs ARIMA

Interview Questions

1. What is Prophet and when would you use it?
2. How does Prophet handle seasonality?
3. What are changepoints in Prophet?
4. How do you add external variables to Prophet?
5. Compare Prophet with ARIMA for business forecasting.

Common Mistakes

• Not setting cap for logistic growth: Prophet needs explicit capacity
• Ignoring changepoint_prior_scale: Too high = overfit, too low = underfit
• Not validating with time split: Always use temporal validation
• Over-relying on defaults: Tune parameters for your specific data

Summary

Prophet is an excellent choice for business time series forecasting. It handles seasonality, holidays, and missing data automatically. Key features include trend models (linear/logistic), automatic changepoint detection, and easy addition of external regressors. It’s particularly useful when you need interpretable forecasts with component decomposition.

Cross-References

• ARIMA
• Time Series Overview
• Anomaly Detection
• Feature Engineering