Prophet for Time Series Forecasting: A Detailed Guide

1. Introduction to Prophet

Prophet is an open-source forecasting tool developed by Facebook (Meta). It is designed to handle time series forecasting efficiently, even when the data has missing values, outliers, and complex seasonal trends.

✅ Why Use Prophet?
✔ Handles daily, weekly, and yearly seasonality automatically.
✔ Works well with irregular time series data.
✔ Can handle holidays, special events, and custom seasonality.
✔ Interpretable results with clear trend and seasonality breakdown.
✔ Available in Python & R, making it widely accessible.

📌 Best Suited For:

• Business Forecasting
• Demand Forecasting
• Financial Forecasting
• Sales Predictions
• Stock Market Analysis
• Website Traffic Forecasting
• Weather Predictions

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2. Installing and Importing Prophet

Before using Prophet, install it using:

pip install prophet

Now, import necessary libraries:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from prophet import Prophet

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3. Understanding Prophet’s Model Components

Prophet follows an additive model structure: y(t)=g(t)+s(t)+h(t)+ϵty(t) = g(t) + s(t) + h(t) + \epsilon_t

Where:

• g(t) → Trend (long-term upward/downward movement).
• s(t) → Seasonality (recurring patterns like daily, weekly, or yearly effects).
• h(t) → Holidays or special events.
• ε_t → Residual errors (random noise).

Prophet automatically detects these components and builds a reliable forecasting model.

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4. Loading Time Series Data

Step 1: Load & Preprocess Data

Prophet requires a specific format with two columns:

• ds (Datetime column)
• y (Value to be forecasted)

# Load dataset
df = pd.read_csv("time_series_data.csv")

# Convert date column to datetime
df['ds'] = pd.to_datetime(df['Date'])  # Rename 'Date' to 'ds'

# Rename target variable to 'y'
df.rename(columns={'Sales': 'y'}, inplace=True)  # Change 'Sales' to your target variable

# Visualize data
plt.figure(figsize=(12,6))
plt.plot(df['ds'], df['y'], label="Original Data", color='blue')
plt.xlabel("Time")
plt.ylabel("Value")
plt.title("Time Series Data")
plt.legend()
plt.show()

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5. Building a Prophet Model

Step 1: Initialize Prophet Model

model = Prophet()

Step 2: Fit the Model

model.fit(df)

Step 3: Create Future Dates for Forecasting

future = model.make_future_dataframe(periods=365)  # Forecast for 1 year (365 days)
print(future.tail())  # Check future dates

Step 4: Generate Predictions

forecast = model.predict(future)

Step 5: Plot Forecast Results

model.plot(forecast)
plt.show()

✅ Prophet automatically detects trends, seasonality, and generates future predictions.

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6. Understanding the Forecast Output

The forecast dataframe contains:

• ds: Date of prediction
• yhat: Predicted value
• yhat_lower: Lower bound of confidence interval
• yhat_upper: Upper bound of confidence interval

📌 Check forecast results:

forecast[['ds', 'yhat', 'yhat_lower', 'yhat_upper']].tail(10)

📌 Plot Forecast Components (Trend & Seasonality):

model.plot_components(forecast)
plt.show()

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7. Handling Seasonality and Trends in Prophet

By default, Prophet captures daily, weekly, and yearly seasonality, but you can customize seasonality settings.

1️⃣ Customizing Seasonality

If your data has a special seasonal pattern, you can add it manually:

model = Prophet()
model.add_seasonality(name='quarterly', period=90, fourier_order=8)
model.fit(df)

2️⃣ Adding Holiday Effects

Holidays can impact time series data. Prophet allows defining holidays and adjusting forecasts.

# Define holiday dataframe
holidays = pd.DataFrame({
  'holiday': 'special_event',
  'ds': pd.to_datetime(['2023-12-25', '2024-01-01']),  # Example holiday dates
  'lower_window': 0,
  'upper_window': 1
})

# Add holidays to the model
model = Prophet(holidays=holidays)
model.fit(df)

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8. Handling Outliers in Prophet

Prophet is robust to outliers, but sometimes they may need adjustment.

Removing Outliers

df = df[df['y'] < df['y'].quantile(0.99)]  # Remove extreme outliers

Adding Change Points to Detect Trend Shifts

model = Prophet(changepoint_prior_scale=0.05)  # Adjust sensitivity
model.fit(df)

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9. Advanced Prophet Features

1️⃣ Adjusting Trend Flexibility

If the model underfits or overfits, adjust changepoint_prior_scale:

model = Prophet(changepoint_prior_scale=0.1)  # Increase flexibility

2️⃣ Forecasting at Different Frequencies

Forecast weekly or hourly instead of daily:

future = model.make_future_dataframe(periods=52, freq='W')  # Weekly Forecasting

future = model.make_future_dataframe(periods=24, freq='H')  # Hourly Forecasting

3️⃣ Using External Regressors

If additional variables impact the forecast (e.g., promotions, weather), Prophet allows adding extra regressors.

df['extra_feature'] = np.random.rand(len(df))  # Example feature
model.add_regressor('extra_feature')

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10. Evaluating Prophet’s Performance

After forecasting, compare predictions with actual values.

1️⃣ Calculate Mean Absolute Error (MAE) & RMSE

from sklearn.metrics import mean_absolute_error, mean_squared_error

actual = df['y']
predicted = forecast['yhat'][:len(df)]

mae = mean_absolute_error(actual, predicted)
rmse = np.sqrt(mean_squared_error(actual, predicted))

print(f"MAE: {mae}, RMSE: {rmse}")

✅ Lower MAE & RMSE = Better Model Performance.

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