SARIMA and SARIMAX Models

Introduction to Seasonal ARIMA

• Seasonal ARIMA (SARIMA) is an extension of the ARIMA model that introduces a seasonal component.
• ARIMA Basics:
  • p: Order of the autoregressive part.
  • q: Order of the moving average part.
  • d: Differencing needed to make the time series stationary.

Key Concepts in SARIMA

• Seasonal Components:
  • Introduces additional terms for autoregression, moving average, and differencing that correspond to the seasonal factor.
  • Define seasonality in terms of a specific period (e.g., 1 year, 12 months).
    • Example: 1 year seasonality = 12 months (lags of 12).
    • For two seasonal lags: 24 months or 2 years.

Implementation in Python

• Libraries: statsmodels.tsa
  • SARIMA can be implemented using statsmodels in Python.
  • Function: SARIMAX for time series data.
    • Order Parameter: Defines non-seasonal components (p, d, q).
    • Seasonal Order: Defined by capital letters (P, D, Q, m) where m represents the number of periods in each season.
    • Exogenous Component: Parallel time series data not directly related to the original time series; accounts for external effects.
      • Example: exog = some_external_data.

SARIMA vs SARIMAX

• SARIMA: Seasonal ARIMA without exogenous variables.
• SARIMAX: Seasonal ARIMA including exogenous variables.
  • If no exogenous data is provided, SARIMAX defaults to SARIMA.

Summary

• Use SARIMA for modeling seasonal patterns in time series data.
• Use SARIMAX when there are external factors affecting the time series.
• Both models can be used within the statsmodels.tsa framework in Python.