While ARIMA models are effective for many time series, they often fall short when dealing with data exhibiting strong seasonal patterns – predictable cycles that repeat over a fixed period, such as monthly or quarterly variations.

This chapter introduces Seasonal ARIMA (SARIMA), an extension specifically designed to model and forecast time series data with seasonal components. We will cover how SARIMA incorporates seasonal terms alongside the non-seasonal components you learned about with ARIMA.

You will learn to:

• Understand the structure of a SARIMA model, denoted as $SARIMA(p, d, q)(P, D, Q)_m$, where $(P, D, Q)$ represent the seasonal autoregressive, differencing, and moving average orders, and $m$ is the seasonal period.
• Use Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots to identify potential seasonal orders.
• Select appropriate values for both non-seasonal $(p, d, q)$ and seasonal $(P, D, Q)_m$ parameters.
• Fit SARIMA models to data using Python's statsmodels library.
• Diagnose the fitted models by examining residuals.
• Generate forecasts that explicitly account for seasonal effects.

By the end of this chapter, you will be able to apply SARIMA models to effectively analyze and predict time series influenced by seasonality.